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Delgado Moya EM, Ordoñez JA, Alves Rubio F, Niskier Sanchez M, de Oliveira RB, Volmir Anderle R, Rasella D. A Mathematical Model for the Impact of 3HP and Social Programme Implementation on the Incidence and Mortality of Tuberculosis: Study in Brazil. Bull Math Biol 2024; 86:61. [PMID: 38662288 DOI: 10.1007/s11538-024-01285-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Accepted: 03/19/2024] [Indexed: 04/26/2024]
Abstract
In this paper, we presented a mathematical model for tuberculosis with treatment for latent tuberculosis cases and incorporated social implementations based on the impact they will have on tuberculosis incidence, cure, and recovery. We incorporated two variables containing the accumulated deaths and active cases into the model in order to study the incidence and mortality rate per year with the data reported by the model. Our objective is to study the impact of social program implementations and therapies on latent tuberculosis in particular the use of once-weekly isoniazid-rifapentine for 12 weeks (3HP). The computational experimentation was performed with data from Brazil and for model calibration, we used the Markov Chain Monte Carlo method (MCMC) with a Bayesian approach. We studied the effect of increasing the coverage of social programs, the Bolsa Familia Programme (BFP) and the Family Health Strategy (FHS) and the implementation of the 3HP as a substitution therapy for two rates of diagnosis and treatment of latent at 1% and 5%. Based of the data obtained by the model in the period 2023-2035, the FHS reported better results than BFP in the case of social implementations and 3HP with a higher rate of diagnosis and treatment of latent in the reduction of incidence and mortality rate and in cases and deaths avoided. With the objective of linking the social and biomedical implementations, we constructed two different scenarios with the rate of diagnosis and treatment. We verified with results reported by the model that with the social implementations studied and the 3HP with the highest rate of diagnosis and treatment of latent, the best results were obtained in comparison with the other independent and joint implementations. A reduction of the incidence by 36.54% with respect to the model with the current strategies and coverage was achieved, and a greater number of cases and deaths from tuberculosis was avoided.
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Affiliation(s)
- Erick Manuel Delgado Moya
- Institute of Collective Health (ISC), Federal University of Bahia (UFBA), Rua Basilio da Gama, Salvador, Bahia, 40.110-040, Brazil.
| | - Jose Alejandro Ordoñez
- Institute of Collective Health (ISC), Federal University of Bahia (UFBA), Rua Basilio da Gama, Salvador, Bahia, 40.110-040, Brazil
| | - Felipe Alves Rubio
- Institute of Collective Health (ISC), Federal University of Bahia (UFBA), Rua Basilio da Gama, Salvador, Bahia, 40.110-040, Brazil
| | - Mauro Niskier Sanchez
- Institute of Collective Health (ISC), Federal University of Bahia (UFBA), Rua Basilio da Gama, Salvador, Bahia, 40.110-040, Brazil
- Department of Public Health, University of Brasilia, Campus Universitarios Darcy Ribeiro, Brasilia, Brasilia-DF, 70.910900, Brazil
| | - Robson Bruniera de Oliveira
- Institute of Collective Health (ISC), Federal University of Bahia (UFBA), Rua Basilio da Gama, Salvador, Bahia, 40.110-040, Brazil
| | - Rodrigo Volmir Anderle
- Institute of Collective Health (ISC), Federal University of Bahia (UFBA), Rua Basilio da Gama, Salvador, Bahia, 40.110-040, Brazil
| | - Davide Rasella
- Institute of Collective Health (ISC), Federal University of Bahia (UFBA), Rua Basilio da Gama, Salvador, Bahia, 40.110-040, Brazil
- Institute of Global Health (ISGlobal), Barcelona, Spain
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2
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Champagne C, Gerhards M, Lana JT, Le Menach A, Pothin E. Quantifying the impact of interventions against Plasmodium vivax: A model for country-specific use. Epidemics 2024; 46:100747. [PMID: 38330786 PMCID: PMC10944169 DOI: 10.1016/j.epidem.2024.100747] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2023] [Revised: 11/03/2023] [Accepted: 01/23/2024] [Indexed: 02/10/2024] Open
Abstract
In order to evaluate the impact of various intervention strategies on Plasmodium vivax dynamics in low endemicity settings without significant seasonal pattern, we introduce a simple mathematical model that can be easily adapted to reported case numbers similar to that collected by surveillance systems in various countries. The model includes case management, vector control, mass drug administration and reactive case detection interventions and is implemented in both deterministic and stochastic frameworks. It is available as an R package to enable users to calibrate and simulate it with their own data. Although we only illustrate its use on fictitious data, by simulating and comparing the impact of various intervention combinations on malaria risk and burden, this model could be a useful tool for strategic planning, implementation and resource mobilization.
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Affiliation(s)
- C Champagne
- Swiss Tropical and Public Health Institute, Basel, Switzerland; University of Basel, Basel, Switzerland.
| | - M Gerhards
- Swiss Tropical and Public Health Institute, Basel, Switzerland; University of Basel, Basel, Switzerland
| | - J T Lana
- Clinton Health Access Initiative, Boston, USA
| | - A Le Menach
- Clinton Health Access Initiative, Boston, USA
| | - E Pothin
- Swiss Tropical and Public Health Institute, Basel, Switzerland; University of Basel, Basel, Switzerland; Clinton Health Access Initiative, Boston, USA
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Simpson MJ, Maclaren OJ. Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models. PLoS Comput Biol 2023; 19:e1011515. [PMID: 37773942 PMCID: PMC10566698 DOI: 10.1371/journal.pcbi.1011515] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2023] [Revised: 10/11/2023] [Accepted: 09/14/2023] [Indexed: 10/01/2023] Open
Abstract
Interpreting data using mechanistic mathematical models provides a foundation for discovery and decision-making in all areas of science and engineering. Developing mechanistic insight by combining mathematical models and experimental data is especially critical in mathematical biology as new data and new types of data are collected and reported. Key steps in using mechanistic mathematical models to interpret data include: (i) identifiability analysis; (ii) parameter estimation; and (iii) model prediction. Here we present a systematic, computationally-efficient workflow we call Profile-Wise Analysis (PWA) that addresses all three steps in a unified way. Recently-developed methods for constructing 'profile-wise' prediction intervals enable this workflow and provide the central linkage between different workflow components. These methods propagate profile-likelihood-based confidence sets for model parameters to predictions in a way that isolates how different parameter combinations affect model predictions. We show how to extend these profile-wise prediction intervals to two-dimensional interest parameters. We then demonstrate how to combine profile-wise prediction confidence sets to give an overall prediction confidence set that approximates the full likelihood-based prediction confidence set well. Our three case studies illustrate practical aspects of the workflow, focusing on ordinary differential equation (ODE) mechanistic models with both Gaussian and non-Gaussian noise models. While the case studies focus on ODE-based models, the workflow applies to other classes of mathematical models, including partial differential equations and simulation-based stochastic models. Open-source software on GitHub can be used to replicate the case studies.
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Affiliation(s)
- Matthew J. Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
| | - Oliver J. Maclaren
- Department of Engineering Science, University of Auckland, Auckland, New Zealand
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4
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Zelenkov Y, Reshettsov I. Analysis of the COVID-19 pandemic using a compartmental model with time-varying parameters fitted by a genetic algorithm. EXPERT SYSTEMS WITH APPLICATIONS 2023; 224:120034. [PMID: 37033691 PMCID: PMC10072952 DOI: 10.1016/j.eswa.2023.120034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Revised: 03/13/2023] [Accepted: 04/01/2023] [Indexed: 05/21/2023]
Abstract
Analyzing the COVID-19 pandemic is a critical factor in developing effective policies to deal with similar challenges in the future. However, many parameters (e.g., the actual number of infected people, the effectiveness of vaccination) are still subject to considerable debate because they are unobservable. To model a pandemic and estimate unobserved parameters, researchers use compartmental models. Most often, in such models, the transition rates are considered as constants, which allows simulating only one epidemiological wave. However, multiple waves have been reported for COVID-19 caused by different strains of the virus. This paper presents an approach based on the reconstruction of real distributions of transition rates using genetic algorithms, which makes it possible to create a model that describes several pandemic peaks. The model is fitted on registered COVID-19 cases in four countries with different pandemic control strategies (Germany, Sweden, UK, and US). Mean absolute percentage error (MAPE) was chosen as the objective function, the MAPE values of 2.168%, 2.096%, 1.208% and 1.703% were achieved for the listed countries, respectively. Simulation results are consistent with the empirical statistics of medical studies, which confirms the quality of the model. In addition to observables such as registered infected, the output of the model contains variables that cannot be measured directly. Among them are the proportion of the population protected by vaccines, the size of the exposed compartment, and the number of unregistered cases of COVID-19. According to the results, at the peak of the pandemic, between 14% (Sweden) and 25% (the UK) of the population were infected. At the same time, the number of unregistered cases exceeds the number of registered cases by 17 and 3.4 times, respectively. The average duration of the vaccine induced immune period is shorter than claimed by vaccine manufacturers, and the effectiveness of vaccination has declined sharply since the appearance of the Delta and Omicron strains. However, on average, vaccination reduces the risk of infection by about 65-70%.
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Affiliation(s)
- Yuri Zelenkov
- HSE Graduate School of Business, HSE University, 109028, 11 Pokrovsky blv., Moscow, Russian Federation
| | - Ivan Reshettsov
- HSE Graduate School of Business, HSE University, 109028, 11 Pokrovsky blv., Moscow, Russian Federation
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5
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Andrade J, Duggan J. Anchoring the mean generation time in the SEIR to mitigate biases in ℜ 0 estimates due to uncertainty in the distribution of the epidemiological delays. ROYAL SOCIETY OPEN SCIENCE 2023; 10:230515. [PMID: 37538746 PMCID: PMC10394422 DOI: 10.1098/rsos.230515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/19/2023] [Accepted: 07/13/2023] [Indexed: 08/05/2023]
Abstract
The basic reproduction number, ℜ 0 , is of paramount importance in the study of infectious disease dynamics. Primarily, ℜ 0 serves as an indicator of the transmission potential of an emerging infectious disease and the effort required to control the invading pathogen. However, its estimates from compartmental models are strongly conditioned by assumptions in the model structure, such as the distributions of the latent and infectious periods (epidemiological delays). To further complicate matters, models with dissimilar delay structures produce equivalent incidence dynamics. Following a simulation study, we reveal that the nature of such equivalency stems from a linear relationship between ℜ 0 and the mean generation time, along with adjustments to other parameters in the model. Leveraging this knowledge, we propose and successfully test an alternative parametrization of the SEIR model that produces accurate ℜ 0 estimates regardless of the distribution of the epidemiological delays, at the expense of biases in other quantities deemed of lesser importance. We further explore this approach's robustness by testing various transmissibility levels, generation times and data fidelity (overdispersion). Finally, we apply the proposed approach to data from the 1918 influenza pandemic. We anticipate that this work will mitigate biases in estimating ℜ 0 .
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Affiliation(s)
- Jair Andrade
- Data Science Institute and School of Computer Science, University of Galway, Galway, Republic of Ireland
| | - Jim Duggan
- Insight Centre for Data Analytics and School of Computer Science, University of Galway, Galway, Republic of Ireland
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6
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Brand SPC, Cavallaro M, Cumming F, Turner C, Florence I, Blomquist P, Hilton J, Guzman-Rincon LM, House T, Nokes DJ, Keeling MJ. The role of vaccination and public awareness in forecasts of Mpox incidence in the United Kingdom. Nat Commun 2023; 14:4100. [PMID: 37433797 PMCID: PMC10336136 DOI: 10.1038/s41467-023-38816-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Accepted: 05/15/2023] [Indexed: 07/13/2023] Open
Abstract
Beginning in May 2022, Mpox virus spread rapidly in high-income countries through close human-to-human contact primarily amongst communities of gay, bisexual and men who have sex with men (GBMSM). Behavioural change arising from increased knowledge and health warnings may have reduced the rate of transmission and modified Vaccinia-based vaccination is likely to be an effective longer-term intervention. We investigate the UK epidemic presenting 26-week projections using a stochastic discrete-population transmission model which includes GBMSM status, rate of formation of new sexual partnerships, and clique partitioning of the population. The Mpox cases peaked in mid-July; our analysis is that the decline was due to decreased transmission rate per infected individual and infection-induced immunity among GBMSM, especially those with the highest rate of new partners. Vaccination did not cause Mpox incidence to turn over, however, we predict that a rebound in cases due to behaviour reversion was prevented by high-risk group-targeted vaccination.
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Affiliation(s)
- Samuel P C Brand
- The Zeeman Institute for Systems Biology Infectious Disease Epidemiology Research (SBIDER), Coventry, UK.
- School of Life Sciences, University of Warwick, Coventry, UK.
| | - Massimo Cavallaro
- The Zeeman Institute for Systems Biology Infectious Disease Epidemiology Research (SBIDER), Coventry, UK
- School of Life Sciences, University of Warwick, Coventry, UK
- Mathematics Institute, University of Warwick, Coventry, UK
| | | | | | | | | | - Joe Hilton
- The Zeeman Institute for Systems Biology Infectious Disease Epidemiology Research (SBIDER), Coventry, UK
- School of Life Sciences, University of Warwick, Coventry, UK
| | - Laura M Guzman-Rincon
- The Zeeman Institute for Systems Biology Infectious Disease Epidemiology Research (SBIDER), Coventry, UK
- School of Life Sciences, University of Warwick, Coventry, UK
| | - Thomas House
- Department of Mathematics, University of Manchester, Manchester, UK
| | - D James Nokes
- The Zeeman Institute for Systems Biology Infectious Disease Epidemiology Research (SBIDER), Coventry, UK
- School of Life Sciences, University of Warwick, Coventry, UK
| | - Matt J Keeling
- The Zeeman Institute for Systems Biology Infectious Disease Epidemiology Research (SBIDER), Coventry, UK
- School of Life Sciences, University of Warwick, Coventry, UK
- Mathematics Institute, University of Warwick, Coventry, UK
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7
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Akuno AO, Ramírez-Ramírez LL, Espinoza JF. Inference on a Multi-Patch Epidemic Model with Partial Mobility, Residency, and Demography: Case of the 2020 COVID-19 Outbreak in Hermosillo, Mexico. ENTROPY (BASEL, SWITZERLAND) 2023; 25:968. [PMID: 37509915 PMCID: PMC10378648 DOI: 10.3390/e25070968] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Revised: 06/02/2023] [Accepted: 06/14/2023] [Indexed: 07/30/2023]
Abstract
Most studies modeling population mobility and the spread of infectious diseases, particularly those using meta-population multi-patch models, tend to focus on the theoretical properties and numerical simulation of such models. As such, there is relatively scant literature focused on numerical fit, inference, and uncertainty quantification of epidemic models with population mobility. In this research, we use three estimation techniques to solve an inverse problem and quantify its uncertainty for a human-mobility-based multi-patch epidemic model using mobile phone sensing data and confirmed COVID-19-positive cases in Hermosillo, Mexico. First, we utilize a Brownian bridge model using mobile phone GPS data to estimate the residence and mobility parameters of the epidemic model. In the second step, we estimate the optimal model epidemiological parameters by deterministically inverting the model using a Darwinian-inspired evolutionary algorithm (EA)-that is, a genetic algorithm (GA). The third part of the analysis involves performing inference and uncertainty quantification in the epidemic model using two Bayesian Monte Carlo sampling methods: t-walk and Hamiltonian Monte Carlo (HMC). The results demonstrate that the estimated model parameters and incidence adequately fit the observed daily COVID-19 incidence in Hermosillo. Moreover, the estimated parameters from the HMC method yield large credible intervals, improving their coverage for the observed and predicted daily incidences. Furthermore, we observe that the use of a multi-patch model with mobility yields improved predictions when compared to a single-patch model.
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Affiliation(s)
- Albert Orwa Akuno
- Departamento de Probabilidad y Estadística, Centro de Investigación en Matemáticas A.C., Jalisco s/n, Colonia Valenciana, Guanajuato C.P. 36023, Gto, Mexico
| | - L Leticia Ramírez-Ramírez
- Departamento de Probabilidad y Estadística, Centro de Investigación en Matemáticas A.C., Jalisco s/n, Colonia Valenciana, Guanajuato C.P. 36023, Gto, Mexico
| | - Jesús F Espinoza
- Departamento de Matemáticas, Universidad de Sonora, Rosales y Boulevard Luis Encinas, Hermosillo C.P. 83000, Sonora, Mexico
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Friston K. Really radical? Behav Brain Sci 2023; 46:e93. [PMID: 37154143 DOI: 10.1017/s0140525x2200276x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
I enjoyed reading this compelling account of Conviction Narrative Theory (CNT). As a theoretical neurobiologist, I recognised - and applauded - the tenets of CNT. My commentary asks whether its claims could be installed into a Bayesian mechanics of decision-making, in a way that would enable theoreticians to model, reproduce and predict decision-making.
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Affiliation(s)
- Karl Friston
- The Wellcome Centre for Human Neuroimaging, UCL Queen Square Institute of Neurology, London WC1N 3AR, UK. ://www.fil.ion.ucl.ac.uk/~karl/
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Wu D, Petousis-Harris H, Paynter J, Suresh V, Maclaren OJ. Likelihood-based estimation and prediction for a measles outbreak in Samoa. Infect Dis Model 2023; 8:212-227. [PMID: 36824221 PMCID: PMC9941367 DOI: 10.1016/j.idm.2023.01.007] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Revised: 01/19/2023] [Accepted: 01/29/2023] [Indexed: 02/05/2023] Open
Abstract
Prediction of the progression of an infectious disease outbreak is important for planning and coordinating a response. Differential equations are often used to model an epidemic outbreak's behaviour but are challenging to parameterise. Furthermore, these models can suffer from misspecification, which biases predictions and parameter estimates. Stochastic models can help with misspecification but are even more expensive to simulate and perform inference with. Here, we develop an explicitly likelihood-based variation of the generalised profiling method as a tool for prediction and inference under model misspecification. Our approach allows us to carry out identifiability analysis and uncertainty quantification using profile likelihood-based methods without the need for marginalisation. We provide justification for this approach by introducing a new interpretation of the model approximation component as a stochastic constraint. This preserves the rationale for using profiling rather than integration to remove nuisance parameters while also providing a link back to stochastic models. We applied an initial version of this method during an outbreak of measles in Samoa in 2019-2020 and found that it achieved relatively fast, accurate predictions. Here we present the most recent version of our method and its application to this measles outbreak, along with additional validation.
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Affiliation(s)
- David Wu
- Department of Engineering Science, University of Auckland, Grafton, Auckland, 1010, New Zealand
| | - Helen Petousis-Harris
- Department of General Practice and Primary Health Care, University of Auckland, Grafton, Auckland, 1023, New Zealand
| | - Janine Paynter
- Department of General Practice and Primary Health Care, University of Auckland, Grafton, Auckland, 1023, New Zealand
| | - Vinod Suresh
- Department of Engineering Science, University of Auckland, Grafton, Auckland, 1010, New Zealand
- Auckland Bioengineering Institute, University of Auckland, Grafton, Auckland, 1010, New Zealand
| | - Oliver J. Maclaren
- Department of Engineering Science, University of Auckland, Grafton, Auckland, 1010, New Zealand
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Li K, McCaw JM, Cao P. Enhanced viral infectivity and reduced interferon production are associated with high pathogenicity for influenza viruses. PLoS Comput Biol 2023; 19:e1010886. [PMID: 36758109 PMCID: PMC9946260 DOI: 10.1371/journal.pcbi.1010886] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2022] [Revised: 02/22/2023] [Accepted: 01/20/2023] [Indexed: 02/11/2023] Open
Abstract
Epidemiological and clinical evidence indicates that humans infected with the 1918 pandemic H1N1 influenza virus and highly pathogenic avian H5N1 influenza viruses often displayed severe lung pathology. High viral load and extensive infiltration of macrophages are the hallmarks of highly pathogenic (HP) influenza viral infections. However, it remains unclear what biological mechanisms primarily determine the observed difference in the kinetics of viral load and macrophages between HP and low pathogenic (LP) viral infections, and how the mechanistic differences are associated with viral pathogenicity. In this study, we develop a mathematical model of viral dynamics that includes the dynamics of different macrophage populations and interferon. We fit the model to in vivo kinetic data of viral load and macrophage level from BALB/c mice infected with an HP or LP strain of H1N1/H5N1 virus to estimate model parameters using Bayesian inference. Our primary finding is that HP viruses have a higher viral infection rate, a lower interferon production rate and a lower macrophage recruitment rate compared to LP viruses, which are strongly associated with more severe tissue damage (quantified by a higher percentage of epithelial cell loss). We also quantify the relative contribution of macrophages to viral clearance and find that macrophages do not play a dominant role in the direct clearance of free viruses although their role in mediating immune responses such as interferon production is crucial. Our work provides new insight into the mechanisms that convey the observed difference in viral and macrophage kinetics between HP and LP infections and establishes an improved model-fitting framework to enhance the analysis of new data on viral pathogenicity.
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Affiliation(s)
- Ke Li
- School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, Australia
- * E-mail:
| | - James M. McCaw
- School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, Australia
- Peter Doherty Institute for Infection and Immunity, The Royal Melbourne Hospital and The University of Melbourne, Parkville, VIC, Australia
- Melbourne School of Population and Global Health, The University of Melbourne, Parkville, VIC, Australia
| | - Pengxing Cao
- School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, Australia
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Little S, Woodward A, Browning G, Billman-Jacobe H. Water use patterns within each day: Variation between batches of growing pigs in commercial production systems. JOURNAL OF SWINE HEALTH AND PRODUCTION 2023. [DOI: 10.54846/jshap/1297] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Objective: To measure, describe, and compare the water use patterns within each day for multiple cohorts of weaner, grower, and finisher pigs in farm buildings. Materials and methods: Prospective, observational cohort studies of the water use patterns within each day were conducted in 5 pig buildings using either a turbine or ultrasonic water flow meter attached to the main water pipe entering each building. Water use data were collected from multiple batches of pigs (second-stage weaners over eleven 48-day periods and grower-finishers over 4 periods of 21-43 days). Semi-parametric models of pig water use patterns within each day were estimated using the brms software package in R. To estimate the interacting effects of time and pig body weight on water use by pigs, we used tensor product smooths for time and pig body weight. Results: The water use pattern within each day varied between the cohorts, and the pattern of many cohorts changed as the pigs gained weight. Some patterns were unimodal and others were bimodal, with the main peak in water use occurring early afternoon to late afternoon. Implications: Water use patterns of pigs within each day varied between and within cohorts. The water use pattern of one cohort cannot be used reliably to predict that of other cohorts, even if they are reared in the same building. Water use pattern data may be valuable for optimizing in-water antimicrobial dosing regimens.
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12
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Lin CP, Dorigatti I, Tsui KL, Xie M, Ling MH, Yuan HY. Impact of early phase COVID-19 precautionary behaviors on seasonal influenza in Hong Kong: A time-series modeling approach. Front Public Health 2022; 10:992697. [PMID: 36504934 PMCID: PMC9728392 DOI: 10.3389/fpubh.2022.992697] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2022] [Accepted: 09/28/2022] [Indexed: 11/15/2022] Open
Abstract
Background Before major non-pharmaceutical interventions were implemented, seasonal incidence of influenza in Hong Kong showed a rapid and unexpected reduction immediately following the early spread of COVID-19 in mainland China in January 2020. This decline was presumably associated with precautionary behavioral changes (e.g., wearing face masks and avoiding crowded places). Knowing their effectiveness on the transmissibility of seasonal influenza can inform future influenza prevention strategies. Methods We estimated the effective reproduction number (R t ) of seasonal influenza in 2019/20 winter using a time-series susceptible-infectious-recovered (TS-SIR) model with a Bayesian inference by integrated nested Laplace approximation (INLA). After taking account of changes in underreporting and herd immunity, the individual effects of the behavioral changes were quantified. Findings The model-estimated mean R t reduced from 1.29 (95%CI, 1.27-1.32) to 0.73 (95%CI, 0.73-0.74) after the COVID-19 community spread began. Wearing face masks protected 17.4% of people (95%CI, 16.3-18.3%) from infections, having about half of the effect as avoiding crowded places (44.1%, 95%CI, 43.5-44.7%). Within the current model, if more than 85% of people had adopted both behaviors, the initial R t could have been less than 1. Conclusion Our model results indicate that wearing face masks and avoiding crowded places could have potentially significant suppressive impacts on influenza.
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Affiliation(s)
- Chun-Pang Lin
- School of Data Science, City University of Hong Kong, Kowloon, Hong Kong SAR, China,Department of Statistics, School of Arts and Sciences, Rutgers University, New Brunswick, NJ, United States
| | - Ilaria Dorigatti
- MRC Centre for Global Infectious Disease Analysis, School of Public Health, Imperial College London, London, United Kingdom
| | - Kwok-Leung Tsui
- Grado Department of Industrial and Systems Engineering, College of Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, United States
| | - Min Xie
- School of Data Science, City University of Hong Kong, Kowloon, Hong Kong SAR, China
| | - Man-Ho Ling
- Department of Mathematics and Information Technology, Faculty of Liberal Arts and Social Sciences, The Education University of Hong Kong, Tai Po, Hong Kong SAR, China
| | - Hsiang-Yu Yuan
- Department of Biomedical Sciences, Jockey Club College of Veterinary Medicine and Life Sciences, City University of Hong Kong, Kowloon, Hong Kong SAR, China,*Correspondence: Hsiang-Yu Yuan
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13
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Little SB, Browning GF, Woodward AP, Billman-Jacobe H. Water consumption and wastage behaviour in pigs: implications for antimicrobial administration and stewardship. Animal 2022; 16:100586. [PMID: 35841824 DOI: 10.1016/j.animal.2022.100586] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2021] [Revised: 06/09/2022] [Accepted: 06/10/2022] [Indexed: 11/16/2022] Open
Abstract
Daily water use and wastage patterns of pigs have major effects on the efficacy of in-water antimicrobial dosing events when conducted for metaphylaxis or to treat clinical disease. However, daily water use and wastage patterns of pigs are not routinely quantified on farms and are not well understood. We conducted a prospective, observational 27-day study of the daily water use and wastage patterns of a pen group of 15 finisher pigs reared in a farm building. We found that the group of pigs wasted a median of 36.5% of the water used per day. We developed models of the patterns of water used and wasted by pigs over each 24-h period using a Bayesian statistical method with the brm() function in the brms package. Both patterns were uni-modal, peaking at 1400-1700, and closely aligned. Wastage was slightly greater during hours of higher water use. We have shown that it is feasible to quantify the water use and wastage patterns of pigs in farm buildings using a system that records and aggregates data, and analyses them using hierarchical generalised additive models. This system could support more efficacious in-water antimicrobial dosing on farms, and better antimicrobial stewardship, by helping to reduce the quantities of antimicrobials used and disseminated into the environment.
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Affiliation(s)
- S B Little
- Asia Pacific Centre for Animal Health, Melbourne Veterinary School, Faculty of Veterinary and Agricultural Sciences, and National Centre for Antimicrobial Stewardship, University of Melbourne, Parkville, Victoria 3010, Australia.
| | - G F Browning
- Asia Pacific Centre for Animal Health, Melbourne Veterinary School, Faculty of Veterinary and Agricultural Sciences, and National Centre for Antimicrobial Stewardship, University of Melbourne, Parkville, Victoria 3010, Australia
| | - A P Woodward
- Faculty of Health, University of Canberra, Bruce, ACT 2617, Australia
| | - H Billman-Jacobe
- Asia Pacific Centre for Animal Health, Melbourne Veterinary School, Faculty of Veterinary and Agricultural Sciences, and National Centre for Antimicrobial Stewardship, University of Melbourne, Parkville, Victoria 3010, Australia
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14
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Wood F, Warrington A, Naderiparizi S, Weilbach C, Masrani V, Harvey W, Ścibior A, Beronov B, Grefenstette J, Campbell D, Nasseri SA. Planning as Inference in Epidemiological Dynamics Models. Front Artif Intell 2022; 4:550603. [PMID: 35434605 PMCID: PMC9009395 DOI: 10.3389/frai.2021.550603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Accepted: 10/25/2021] [Indexed: 01/10/2023] Open
Abstract
In this work we demonstrate how to automate parts of the infectious disease-control policy-making process via performing inference in existing epidemiological models. The kind of inference tasks undertaken include computing the posterior distribution over controllable, via direct policy-making choices, simulation model parameters that give rise to acceptable disease progression outcomes. Among other things, we illustrate the use of a probabilistic programming language that automates inference in existing simulators. Neither the full capabilities of this tool for automating inference nor its utility for planning is widely disseminated at the current time. Timely gains in understanding about how such simulation-based models and inference automation tools applied in support of policy-making could lead to less economically damaging policy prescriptions, particularly during the current COVID-19 pandemic.
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Affiliation(s)
- Frank Wood
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
- Associate Academic Member and Canada CIFAR AI Chair, Mila Institute, Montreal, QC, Canada
| | - Andrew Warrington
- Department of Engineering Science, University of Oxford, Oxford, United Kingdom
| | - Saeid Naderiparizi
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
| | - Christian Weilbach
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
| | - Vaden Masrani
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
| | - William Harvey
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
| | - Adam Ścibior
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
| | - Boyan Beronov
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
| | | | | | - S. Ali Nasseri
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
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15
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Prieto K, Chávez–Hernández MV, Romero–Leiton JP. On mobility trends analysis of COVID-19 dissemination in Mexico City. PLoS One 2022; 17:e0263367. [PMID: 35143548 PMCID: PMC8830699 DOI: 10.1371/journal.pone.0263367] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Accepted: 01/18/2022] [Indexed: 01/04/2023] Open
Abstract
This work presents a tool for forecasting the spread of the new coronavirus in Mexico City, which is based on a mathematical model with a metapopulation structure that uses Bayesian statistics and is inspired by a data-driven approach. The daily mobility of people in Mexico City is mathematically represented by an origin-destination matrix using the open mobility data from Google and the Transportation Mexican Survey. This matrix is incorporated in a compartmental model. We calibrate the model against borough-level incidence data collected between 27 February 2020 and 27 October 2020, while using Bayesian inference to estimate critical epidemiological characteristics associated with the coronavirus spread. Given that working with metapopulation models leads to rather high computational time consumption, and parameter estimation of these models may lead to high memory RAM consumption, we do a clustering analysis that is based on mobility trends to work on these clusters of borough separately instead of taken all of the boroughs together at once. This clustering analysis can be implemented in smaller or larger scales in different parts of the world. In addition, this clustering analysis is divided into the phases that the government of Mexico City has set up to restrict individual movement in the city. We also calculate the reproductive number in Mexico City using the next generation operator method and the inferred model parameters obtaining that this threshold is in the interval (1.2713, 1.3054). Our analysis of mobility trends can be helpful when making public health decisions.
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Affiliation(s)
- Kernel Prieto
- Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico, México
- * E-mail:
| | - M. Victoria Chávez–Hernández
- Facultad de Ingeniería Mecánica y Eléctrica, Universidad Autónoma de Nuevo León, San Nicolás de los Garza, Mexico, México
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16
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Abstract
Bayesian estimation of multidimensional item response theory (IRT) models in large data sets may come with impractical computational burdens when general-purpose Markov chain Monte Carlo (MCMC) samplers are employed. Variational Bayes (VB)—a method for approximating the posterior distribution—poses a potential remedy. Stan’s general-purpose VB algorithms have drastically improved the accessibility of VB methods for a wide psychometric audience. Using marginal maximum likelihood (MML) and MCMC as benchmarks, the present simulation study investigates the utility of Stan’s built-in VB function for estimating multidimensional IRT models with between-item dimensionality. VB yielded a marked speed-up in comparison to MCMC, but did not generally outperform MML in terms of run time. VB estimates were trustworthy only for item difficulties, while bias in item discriminations depended on the model’s dimensionality. Under realistic conditions of non-zero correlations between dimensions, VB correlation estimates were subject to severe bias. The practical relevance of performance differences is illustrated with data from PISA 2018. We conclude that in its current form, Stan’s built-in VB algorithm does not pose a viable alternative for estimating multidimensional IRT models.
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17
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Prieto K. Current forecast of COVID-19 in Mexico: A Bayesian and machine learning approaches. PLoS One 2022; 17:e0259958. [PMID: 35061688 PMCID: PMC8782335 DOI: 10.1371/journal.pone.0259958] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2021] [Accepted: 10/29/2021] [Indexed: 12/24/2022] Open
Abstract
The COVID-19 pandemic has been widely spread and affected millions of people and caused hundreds of deaths worldwide, especially in patients with comorbilities and COVID-19. This manuscript aims to present models to predict, firstly, the number of coronavirus cases and secondly, the hospital care demand and mortality based on COVID-19 patients who have been diagnosed with other diseases. For the first part, I present a projection of the spread of coronavirus in Mexico, which is based on a contact tracing model using Bayesian inference. I investigate the health profile of individuals diagnosed with coronavirus to predict their type of patient care (inpatient or outpatient) and survival. Specifically, I analyze the comorbidity associated with coronavirus using Machine Learning. I have implemented two classifiers: I use the first classifier to predict the type of care procedure that a person diagnosed with coronavirus presenting chronic diseases will obtain (i.e. outpatient or hospitalised), in this way I estimate the hospital care demand; I use the second classifier to predict the survival or mortality of the patient (i.e. survived or deceased). I present two techniques to deal with these kinds of unbalanced datasets related to outpatient/hospitalised and survived/deceased cases (which occur in general for these types of coronavirus datasets) to obtain a better performance for the classification.
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Affiliation(s)
- Kernel Prieto
- Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico City, México
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18
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Gleeson JP, Brendan Murphy T, O’Brien JD, Friel N, Bargary N, O'Sullivan DJP. Calibrating COVID-19 susceptible-exposed-infected-removed models with time-varying effectivecontact rates. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210120. [PMID: 34802273 PMCID: PMC8607149 DOI: 10.1098/rsta.2021.0120] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
We describe the population-based susceptible-exposed-infected-removed (SEIR) model developed by the Irish Epidemiological Modelling Advisory Group (IEMAG), which advises the Irish government on COVID-19 responses. The model assumes a time-varying effective contact rate (equivalently, a time-varying reproduction number) to model the effect of non-pharmaceutical interventions. A crucial technical challenge in applying such models is their accurate calibration to observed data, e.g. to the daily number of confirmed new cases, as the history of the disease strongly affects predictions of future scenarios. We demonstrate an approach based on inversion of the SEIR equations in conjunction with statistical modelling and spline-fitting of the data to produce a robust methodology for calibration of a wide class of models of this type. This article is part of the theme issue 'Data science approaches to infectious disease surveillance'.
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Affiliation(s)
- James P. Gleeson
- MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick, V94 T9PX, Ireland
- Insight Centre for Data Analytics, Ireland
- Confirm Centre for Smart Manufacturing, Ireland
- Irish Epidemiological Modelling Advisory Group (IEMAG), Ireland
| | - Thomas Brendan Murphy
- School of Mathematics and Statistics, University College Dublin, Dublin, D04 V1W8, Ireland
- Insight Centre for Data Analytics, Ireland
- Irish Epidemiological Modelling Advisory Group (IEMAG), Ireland
| | - Joseph D. O’Brien
- MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick, V94 T9PX, Ireland
| | - Nial Friel
- School of Mathematics and Statistics, University College Dublin, Dublin, D04 V1W8, Ireland
- Insight Centre for Data Analytics, Ireland
| | - Norma Bargary
- MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick, V94 T9PX, Ireland
- Insight Centre for Data Analytics, Ireland
- Confirm Centre for Smart Manufacturing, Ireland
| | - David J. P. O'Sullivan
- MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick, V94 T9PX, Ireland
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19
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Best N, Perevozskaya I, Lunn D, Archer G, Euesden J, Fillmore C, Sherina V, Thompson D, Zwierzyna M. Predicting the COVID-19 Pandemic Impact on Clinical Trial Recruitment. Stat Biopharm Res 2021. [DOI: 10.1080/19466315.2021.2000487] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Nicky Best
- Advanced Biostatistics and Data Analytics, GlaxoSmithKline, Brentford, UK
| | - Inna Perevozskaya
- Advanced Biostatistics and Data Analytics, GlaxoSmithKline, Collegeville, PA
| | - Dave Lunn
- Advanced Biostatistics and Data Analytics, GlaxoSmithKline, Brentford, UK
| | - Graeme Archer
- Non-clinical and Translational Statistics, GlaxoSmithKline, Stevenage, UK
| | - Jack Euesden
- Research Statistics, GlaxoSmithKline, Stevenage, UK
| | | | | | - Doug Thompson
- Statistical Data Sciences, GlaxoSmithKline, Brentford, UK
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20
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Chagas ETC, Barros PH, Cardoso-Pereira I, Ponte IV, Ximenes P, Figueiredo F, Murai F, Couto da Silva AP, Almeida JM, Loureiro AAF, Ramos HS. Effects of population mobility on the COVID-19 spread in Brazil. PLoS One 2021; 16:e0260610. [PMID: 34874978 PMCID: PMC8651143 DOI: 10.1371/journal.pone.0260610] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2021] [Accepted: 11/13/2021] [Indexed: 01/12/2023] Open
Abstract
This article proposes a study of the SARS-CoV-2 virus spread and the efficacy of public policies in Brazil. Using both aggregated (from large Internet companies) and fine-grained (from Departments of Motor Vehicles) mobility data sources, our work sheds light on the effect of mobility on the pandemic situation in the Brazilian territory. Our main contribution is to show how mobility data, particularly fine-grained ones, can offer valuable insights into virus propagation. For this, we propose a modification in the SENUR model to add mobility information, evaluating different data availability scenarios (different information granularities), and finally, we carry out simulations to evaluate possible public policies. In particular, we conduct a case study that shows, through simulations of hypothetical scenarios, that the contagion curve in several Brazilian cities could have been milder if the government had imposed mobility restrictions soon after reporting the first case. Our results also show that if the government had not taken any action and the only safety measure taken was the population's voluntary isolation (out of fear), the time until the contagion peak for the first wave would have been postponed, but its value would more than double.
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Affiliation(s)
- Eduarda T. C. Chagas
- Department of Computer Science, Federal University of Minas Gerais, Belo Horizonte, Minas Gerais, Brazil
| | - Pedro H. Barros
- Department of Computer Science, Federal University of Minas Gerais, Belo Horizonte, Minas Gerais, Brazil
| | - Isadora Cardoso-Pereira
- Department of Computer Science, Federal University of Minas Gerais, Belo Horizonte, Minas Gerais, Brazil
| | - Igor V. Ponte
- Department of Motor Vehicles, Government of the State of Ceará, Fortaleza, Ceará, Brazil
| | - Pablo Ximenes
- Department of Motor Vehicles, Government of the State of Ceará, Fortaleza, Ceará, Brazil
- School of Cybersecurity and Privacy, College of Computing, Georgia Institute of Technology, Atlanta, Georgia, United States of America
| | - Flávio Figueiredo
- Department of Computer Science, Federal University of Minas Gerais, Belo Horizonte, Minas Gerais, Brazil
| | - Fabricio Murai
- Department of Computer Science, Federal University of Minas Gerais, Belo Horizonte, Minas Gerais, Brazil
| | - Ana Paula Couto da Silva
- Department of Computer Science, Federal University of Minas Gerais, Belo Horizonte, Minas Gerais, Brazil
| | - Jussara M. Almeida
- Department of Computer Science, Federal University of Minas Gerais, Belo Horizonte, Minas Gerais, Brazil
| | - Antonio A. F. Loureiro
- Department of Computer Science, Federal University of Minas Gerais, Belo Horizonte, Minas Gerais, Brazil
| | - Heitor S. Ramos
- Department of Computer Science, Federal University of Minas Gerais, Belo Horizonte, Minas Gerais, Brazil
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21
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Grinsztajn L, Semenova E, Margossian CC, Riou J. Bayesian workflow for disease transmission modeling in Stan. Stat Med 2021; 40:6209-6234. [PMID: 34494686 PMCID: PMC8661657 DOI: 10.1002/sim.9164] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2021] [Revised: 07/06/2021] [Accepted: 07/29/2021] [Indexed: 12/18/2022]
Abstract
This tutorial shows how to build, fit, and criticize disease transmission models in Stan, and should be useful to researchers interested in modeling the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic and other infectious diseases in a Bayesian framework. Bayesian modeling provides a principled way to quantify uncertainty and incorporate both data and prior knowledge into the model estimates. Stan is an expressive probabilistic programming language that abstracts the inference and allows users to focus on the modeling. As a result, Stan code is readable and easily extensible, which makes the modeler's work more transparent. Furthermore, Stan's main inference engine, Hamiltonian Monte Carlo sampling, is amiable to diagnostics, which means the user can verify whether the obtained inference is reliable. In this tutorial, we demonstrate how to formulate, fit, and diagnose a compartmental transmission model in Stan, first with a simple susceptible-infected-recovered model, then with a more elaborate transmission model used during the SARS-CoV-2 pandemic. We also cover advanced topics which can further help practitioners fit sophisticated models; notably, how to use simulations to probe the model and priors, and computational techniques to scale-up models based on ordinary differential equations.
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Affiliation(s)
| | - Elizaveta Semenova
- Data Sciences and Quantitative BiologyDiscovery Sciences, R&D, AstraZenecaCambridgeUK
| | | | - Julien Riou
- Institute of Social and Preventive MedicineUniversity of BernBernSwitzerland
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22
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Brand SPC, Ojal J, Aziza R, Were V, Okiro EA, Kombe IK, Mburu C, Ogero M, Agweyu A, Warimwe GM, Nyagwange J, Karanja H, Gitonga JN, Mugo D, Uyoga S, Adetifa IMO, Scott JAG, Otieno E, Murunga N, Otiende M, Ochola-Oyier LI, Agoti CN, Githinji G, Kasera K, Amoth P, Mwangangi M, Aman R, Ng’ang’a W, Tsofa B, Bejon P, Keeling MJ, Nokes DJ, Barasa E. COVID-19 transmission dynamics underlying epidemic waves in Kenya. Science 2021; 374:989-994. [PMID: 34618602 PMCID: PMC7612211 DOI: 10.1126/science.abk0414] [Citation(s) in RCA: 41] [Impact Index Per Article: 13.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 10/04/2021] [Indexed: 01/16/2023]
Abstract
Policy decisions on COVID-19 interventions should be informed by a local, regional and national understanding of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission. Epidemic waves may result when restrictions are lifted or poorly adhered to, variants with new phenotypic properties successfully invade, or infection spreads to susceptible subpopulations. Three COVID-19 epidemic waves have been observed in Kenya. Using a mechanistic mathematical model, we explain the first two distinct waves by differences in contact rates in high and low social-economic groups, and the third wave by the introduction of higher-transmissibility variants. Reopening schools led to a minor increase in transmission between the second and third waves. Socioeconomic and urban–rural population structure are critical determinants of viral transmission in Kenya.
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Affiliation(s)
- Samuel P. C. Brand
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
- The Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research (SBIDER), University of Warwick, Warwick, UK
- School of Life Sciences, University of Warwick, Warwick, UK
| | - John Ojal
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
- London School of Hygiene and Tropical Medicine (LSHTM), London, UK
| | - Rabia Aziza
- The Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research (SBIDER), University of Warwick, Warwick, UK
- School of Life Sciences, University of Warwick, Warwick, UK
| | - Vincent Were
- Health Economics Research Unit, KEMRI–Wellcome Trust Research Programme, Nairobi, Kenya
| | - Emelda A. Okiro
- Population Health Unit, Kenya Medical Research Institute–Wellcome Trust Research Programme, Nairobi, Kenya
- Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, Oxford, UK
| | - Ivy K Kombe
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | - Caroline Mburu
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | - Morris Ogero
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | - Ambrose Agweyu
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
- Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, Oxford, UK
| | - George M. Warimwe
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
- Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, Oxford, UK
| | - James Nyagwange
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | - Henry Karanja
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | - John N. Gitonga
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | - Daisy Mugo
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | - Sophie Uyoga
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | - Ifedayo M. O. Adetifa
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
- Department of Infectious Diseases Epidemiology, London School of Hygiene and Tropical Medicine, London, UK
| | - J. Anthony G. Scott
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
- Department of Infectious Diseases Epidemiology, London School of Hygiene and Tropical Medicine, London, UK
| | - Edward Otieno
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | - Nickson Murunga
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | - Mark Otiende
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | - Lynette I. Ochola-Oyier
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | - Charles N. Agoti
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | - George Githinji
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | | | - Patrick Amoth
- Ministry of Health, Government of Kenya, Nairobi, Kenya
| | | | - Rashid Aman
- Ministry of Health, Government of Kenya, Nairobi, Kenya
| | - Wangari Ng’ang’a
- Presidential Policy and Strategy Unit, The Presidency, Government of Kenya
| | - Benjamin Tsofa
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
| | - Philip Bejon
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
- Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, Oxford, UK
| | - Matt. J. Keeling
- The Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research (SBIDER), University of Warwick, Warwick, UK
- School of Life Sciences, University of Warwick, Warwick, UK
- Mathematics Institute, University of Warwick, Warwick, UK
| | - D. James Nokes
- Kenya Medical Research Institute (KEMRI)–Wellcome Trust Research Programme (KWTRP), Kilifi, Kenya
- The Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research (SBIDER), University of Warwick, Warwick, UK
- School of Life Sciences, University of Warwick, Warwick, UK
| | - Edwine Barasa
- Health Economics Research Unit, KEMRI–Wellcome Trust Research Programme, Nairobi, Kenya
- Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, Oxford, UK
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23
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Dasgupta S, Moore MR, Dimitrov DT, Hughes JP. Bayesian validation framework for dynamic epidemic models. Epidemics 2021; 37:100514. [PMID: 34763161 PMCID: PMC8720263 DOI: 10.1016/j.epidem.2021.100514] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2020] [Revised: 08/23/2021] [Accepted: 10/21/2021] [Indexed: 11/29/2022] Open
Abstract
Complex models of infectious diseases are used to understand the transmission dynamics of the disease, project the course of an epidemic, predict the effect of interventions and/or provide information for power calculations of community level intervention studies. However, there have been relatively few opportunities to rigorously evaluate the predictions of such models till now. Indeed, while there is a large literature on calibration (fitting model parameters) and validation (comparing model outputs to data) of complex models based on empirical data, the lack of uniformity in accepted criteria for such procedures for models of infectious diseases has led to simple procedures being prevalent for such steps. However, recently, several community level randomized trials of combination HIV intervention have been planned and/or initiated, and in each case, significant epidemic modeling efforts were conducted during trial planning which were integral to the design of these trials. The existence of these models and the (anticipated) availability of results from the related trials, provide a unique opportunity to evaluate the models and their usefulness in trial design. In this project, we outline a framework for evaluating the predictions of complex epidemiological models and describe experiments that can be used to test their predictions.
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Affiliation(s)
- Sayan Dasgupta
- Fred Hutchinson Cancer Research Center, Seattle WA 98122, USA.
| | - Mia R Moore
- Fred Hutchinson Cancer Research Center, Seattle WA 98122, USA
| | | | - James P Hughes
- Fred Hutchinson Cancer Research Center, Seattle WA 98122, USA
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24
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Li YI, Turk G, Rohrbach PB, Pietzonka P, Kappler J, Singh R, Dolezal J, Ekeh T, Kikuchi L, Peterson JD, Bolitho A, Kobayashi H, Cates ME, Adhikari R, Jack RL. Efficient Bayesian inference of fully stochastic epidemiological models with applications to COVID-19. ROYAL SOCIETY OPEN SCIENCE 2021; 8:211065. [PMID: 34430050 PMCID: PMC8355677 DOI: 10.1098/rsos.211065] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/21/2021] [Accepted: 07/23/2021] [Indexed: 06/13/2023]
Abstract
Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age-structured data for the number of deaths. This includes maximum a posteriori estimates, Markov chain Monte Carlo sampling of the posterior, computation of the model evidence, and the determination of parameter sensitivities via the Fisher information matrix. Our methodology is implemented in PyRoss, an open-source platform for analysis of epidemiological compartment models.
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Affiliation(s)
- Yuting I. Li
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Günther Turk
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Paul B. Rohrbach
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Patrick Pietzonka
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Julian Kappler
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Rajesh Singh
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Jakub Dolezal
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Timothy Ekeh
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Lukas Kikuchi
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Joseph D. Peterson
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Austen Bolitho
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Hideki Kobayashi
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
| | - Michael E. Cates
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - R. Adhikari
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Robert L. Jack
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
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Acuña-Zegarra MA, Díaz-Infante S, Baca-Carrasco D, Olmos-Liceaga D. COVID-19 optimal vaccination policies: A modeling study on efficacy, natural and vaccine-induced immunity responses. Math Biosci 2021; 337:108614. [PMID: 33961878 PMCID: PMC8095066 DOI: 10.1016/j.mbs.2021.108614] [Citation(s) in RCA: 40] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2020] [Revised: 02/28/2021] [Accepted: 04/04/2021] [Indexed: 12/23/2022]
Abstract
About a year into the pandemic, COVID-19 accumulates more than two million deaths worldwide. Despite non-pharmaceutical interventions such as social distance, mask-wearing, and restrictive lockdown, the daily confirmed cases remain growing. Vaccine developments from Pfizer, Moderna, and Gamaleya Institute reach more than 90% efficacy and sustain the vaccination campaigns in multiple countries. However, natural and vaccine-induced immunity responses remain poorly understood. There are great expectations, but the new SARS-CoV-2 variants demand to inquire if the vaccines will be highly protective or induce permanent immunity. Further, in the first quarter of 2021, vaccine supply is scarce. Consequently, some countries that are applying the Pfizer vaccine will delay its second required dose. Likewise, logistic supply, economic and political implications impose a set of grand challenges to develop vaccination policies. Therefore, health decision-makers require tools to evaluate hypothetical scenarios and evaluate admissible responses. Following some of the WHO-SAGE recommendations, we formulate an optimal control problem with mixed constraints to describe vaccination schedules. Our solution identifies vaccination policies that minimize the burden of COVID-19 quantified by the number of disability-adjusted years of life lost. These optimal policies ensure the vaccination coverage of a prescribed population fraction in a given time horizon and preserve hospitalization occupancy below a risk level. We explore "via simulation" plausible scenarios regarding efficacy, coverage, vaccine-induced, and natural immunity. Our simulations suggest that response regarding vaccine-induced immunity and reinfection periods would play a dominant role in mitigating COVID-19.
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Affiliation(s)
- Manuel Adrian Acuña-Zegarra
- Departamento de Matemáticas, Universidad de Sonora, Blvd. Luis Encinas y Rosales S/N, Hermosillo, Col. Centro, Sonora, C.P. 83000, Mexico.
| | - Saúl Díaz-Infante
- CONACYT-Universidad de Sonora, Departamento de Matemáticas, Blvd. Luis Encinas y Rosales S/N, Hermosillo, Col. Centro, Sonora, C.P. 83000, Mexico.
| | - David Baca-Carrasco
- Departamento de Matemáticas, Instituto Tecnológico de Sonora, 5 de Febrero 818 Sur, Col. Centro, Ciudad Obregón, Sonora, C.P. 85000, Mexico.
| | - Daniel Olmos-Liceaga
- Departamento de Matemáticas, Universidad de Sonora, Blvd. Luis Encinas y Rosales S/N, Hermosillo, Col. Centro, Sonora, C.P. 83000, Mexico.
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26
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Huo X, Chen J, Ruan S. Estimating asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan: a mathematical modeling study. BMC Infect Dis 2021; 21:476. [PMID: 34034662 PMCID: PMC8148404 DOI: 10.1186/s12879-021-06078-8] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2020] [Accepted: 04/15/2021] [Indexed: 12/20/2022] Open
Abstract
BACKGROUND The COVID-19 outbreak in Wuhan started in December 2019 and was under control by the end of March 2020 with a total of 50,006 confirmed cases by the implementation of a series of nonpharmaceutical interventions (NPIs) including unprecedented lockdown of the city. This study analyzes the complete outbreak data from Wuhan, assesses the impact of these public health interventions, and estimates the asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan. METHODS By taking different stages of the outbreak into account, we developed a time-dependent compartmental model to describe the dynamics of disease transmission and case detection and reporting. Model coefficients were parameterized by using the reported cases and following key events and escalated control strategies. Then the model was used to calibrate the complete outbreak data by using the Monte Carlo Markov Chain (MCMC) method. Finally we used the model to estimate asymptomatic and undetected cases and approximate the overall antibody prevalence level. RESULTS We found that the transmission rate between Jan 24 and Feb 1, 2020, was twice as large as that before the lockdown on Jan 23 and 67.6% (95% CI [0.584,0.759]) of detectable infections occurred during this period. Based on the reported estimates that around 20% of infections were asymptomatic and their transmission ability was about 70% of symptomatic ones, we estimated that there were about 14,448 asymptomatic and undetected cases (95% CI [12,364,23,254]), which yields an estimate of a total of 64,454 infected cases (95% CI [62,370,73,260]), and the overall antibody prevalence level in the population of Wuhan was 0.745% (95% CI [0.693%,0.814%]) by March 31, 2020. CONCLUSIONS We conclude that the control of the COVID-19 outbreak in Wuhan was achieved via the enforcement of a combination of multiple NPIs: the lockdown on Jan 23, the stay-at-home order on Feb 2, the massive isolation of all symptomatic individuals via newly constructed special shelter hospitals on Feb 6, and the large scale screening process on Feb 18. Our results indicate that the population in Wuhan is far away from establishing herd immunity and provide insights for other affected countries and regions in designing control strategies and planing vaccination programs.
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Affiliation(s)
- Xi Huo
- Department of Mathematics, University of Miami, 1365 Memorial Drive, Coral Gables, FL, 33146, USA
| | - Jing Chen
- Department of Mathematics, Nova Southeastern University, 3301 College Ave, Fort Lauderdale, FL, 33314, USA
| | - Shigui Ruan
- Department of Mathematics, University of Miami, 1365 Memorial Drive, Coral Gables, FL, 33146, USA.
- Sylvester Comprehensive Cancer Center, University of Miami Miller School of Medicine, 1475 NW 12th Ave, Miami, FL, 33316, USA.
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IBARGÜEN-MONDRAGÓN EDUARDO, PRIETO KERNEL, HIDALGO-BONILLA SANDRAPATRICIA. A MODEL ON BACTERIAL RESISTANCE CONSIDERING A GENERALIZED LAW OF MASS ACTION FOR PLASMID REPLICATION. J BIOL SYST 2021. [DOI: 10.1142/s0218339021400118] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Bacterial plasmids play a fundamental role in antibiotic resistance. However, a lack of knowledge about their biology is an obstacle in fully understanding the mechanisms and properties of plasmid-mediated resistance. This has motivated investigations of real systems in vitro to analyze the transfer and replication of plasmids. In this work, we address this issue with mathematical modeling. We formulate and perform a qualitative analysis of a nonlinear system of ordinary differential equations describing the competition dynamics between plasmids and sensitive and resistant bacteria. In addition, we estimated parameter values from empirical data. Our model predicts scenarios consistent with biological phenomena. The elimination or spread of infection depends on factors associated with bacterial reproduction and the transfer and replication of plasmids. From the estimated parameters, three bacterial growth experiments were analyzed in vitro. We determined the experiment with the highest bacterial growth rate and the highest rate of plasmid transfer. Moreover, numerical simulations were performed to predict bacterial growth.
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Affiliation(s)
| | - KERNEL PRIETO
- Instituto de Matemáticas, Universidad Nacional Autónoma de México, Cuernavaca, México
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28
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Li K, Cao P, McCaw JM. Modelling the Effect of MUC1 on Influenza Virus Infection Kinetics and Macrophage Dynamics. Viruses 2021; 13:v13050850. [PMID: 34066999 PMCID: PMC8150684 DOI: 10.3390/v13050850] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Revised: 04/20/2021] [Accepted: 05/04/2021] [Indexed: 12/11/2022] Open
Abstract
MUC1 belongs to the family of cell surface (cs-) mucins. Experimental evidence indicates that its presence reduces in vivo influenza viral infection severity. However, the mechanisms by which MUC1 influences viral dynamics and the host immune response are not yet well understood, limiting our ability to predict the efficacy of potential treatments that target MUC1. To address this limitation, we use available in vivo kinetic data for both virus and macrophage populations in wildtype and MUC1 knockout mice. We apply two mathematical models of within-host influenza dynamics to this data. The models differ in how they categorise the mechanisms of viral control. Both models provide evidence that MUC1 reduces the susceptibility of epithelial cells to influenza virus and regulates macrophage recruitment. Furthermore, we predict and compare some key infection-related quantities between the two mice groups. We find that MUC1 significantly reduces the basic reproduction number of viral replication as well as the number of cumulative macrophages but has little impact on the cumulative viral load. Our analyses suggest that the viral replication rate in the early stages of infection influences the kinetics of the host immune response, with consequences for infection outcomes, such as severity. We also show that MUC1 plays a strong anti-inflammatory role in the regulation of the host immune response. This study improves our understanding of the dynamic role of MUC1 against influenza infection and may support the development of novel antiviral treatments and immunomodulators that target MUC1.
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Affiliation(s)
- Ke Li
- School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia; (P.C.); (J.M.M.)
- Correspondence:
| | - Pengxing Cao
- School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia; (P.C.); (J.M.M.)
| | - James M. McCaw
- School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia; (P.C.); (J.M.M.)
- Peter Doherty Institute for Infection and Immunity, The Royal Melbourne Hospital and The University of Melbourne, Parkville, VIC 3010, Australia
- Melbourne School of Population and Global Health, The University of Melbourne, Parkville, VIC 3010, Australia
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Raimúndez E, Dudkin E, Vanhoefer J, Alamoudi E, Merkt S, Fuhrmann L, Bai F, Hasenauer J. COVID-19 outbreak in Wuhan demonstrates the limitations of publicly available case numbers for epidemiological modeling. Epidemics 2021; 34:100439. [PMID: 33556763 PMCID: PMC7845523 DOI: 10.1016/j.epidem.2021.100439] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Revised: 01/19/2021] [Accepted: 01/21/2021] [Indexed: 01/12/2023] Open
Abstract
Epidemiological models are widely used to analyze the spread of diseases such as the global COVID-19 pandemic caused by SARS-CoV-2. However, all models are based on simplifying assumptions and often on sparse data. This limits the reliability of parameter estimates and predictions. In this manuscript, we demonstrate the relevance of these limitations and the pitfalls associated with the use of overly simplistic models. We considered the data for the early phase of the COVID-19 outbreak in Wuhan, China, as an example, and perform parameter estimation, uncertainty analysis and model selection for a range of established epidemiological models. Amongst others, we employ Markov chain Monte Carlo sampling, parameter and prediction profile calculation algorithms. Our results show that parameter estimates and predictions obtained for several established models on the basis of reported case numbers can be subject to substantial uncertainty. More importantly, estimates were often unrealistic and the confidence/credibility intervals did not cover plausible values of critical parameters obtained using different approaches. These findings suggest, amongst others, that standard compartmental models can be overly simplistic and that the reported case numbers provide often insufficient information for obtaining reliable and realistic parameter values, and for forecasting the evolution of epidemics.
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Affiliation(s)
- Elba Raimúndez
- Faculty of Mathematics and Natural Sciences, University of Bonn, Bonn, Germany; Technische Universität München, Center for Mathematics, Garching, Germany
| | - Erika Dudkin
- Faculty of Mathematics and Natural Sciences, University of Bonn, Bonn, Germany
| | - Jakob Vanhoefer
- Faculty of Mathematics and Natural Sciences, University of Bonn, Bonn, Germany
| | - Emad Alamoudi
- Faculty of Mathematics and Natural Sciences, University of Bonn, Bonn, Germany
| | - Simon Merkt
- Faculty of Mathematics and Natural Sciences, University of Bonn, Bonn, Germany
| | - Lara Fuhrmann
- Faculty of Mathematics and Natural Sciences, University of Bonn, Bonn, Germany
| | - Fan Bai
- Faculty of Mathematics and Natural Sciences, University of Bonn, Bonn, Germany
| | - Jan Hasenauer
- Faculty of Mathematics and Natural Sciences, University of Bonn, Bonn, Germany; Technische Universität München, Center for Mathematics, Garching, Germany; Helmholtz Zentrum München - German Research Center for Environmental Health, Institute of Computational Biology, Neuherberg, Germany.
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30
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Friston K, Costello A, Pillay D. 'Dark matter', second waves and epidemiological modelling. BMJ Glob Health 2020; 5:e003978. [PMID: 33328201 PMCID: PMC7745338 DOI: 10.1136/bmjgh-2020-003978] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2020] [Revised: 11/14/2020] [Accepted: 11/17/2020] [Indexed: 12/23/2022] Open
Abstract
Recent reports using conventional Susceptible, Exposed, Infected and Removed models suggest that the next wave of the COVID-19 pandemic in the UK could overwhelm health services, with fatalities exceeding the first wave. We used Bayesian model comparison to revisit these conclusions, allowing for heterogeneity of exposure, susceptibility and transmission. We used dynamic causal modelling to estimate the evidence for alternative models of daily cases and deaths from the USA, the UK, Brazil, Italy, France, Spain, Mexico, Belgium, Germany and Canada over the period 25 January 2020 to 15 June 2020. These data were used to estimate the proportions of people (i) not exposed to the virus, (ii) not susceptible to infection when exposed and (iii) not infectious when susceptible to infection. Bayesian model comparison furnished overwhelming evidence for heterogeneity of exposure, susceptibility and transmission. Furthermore, both lockdown and the build-up of population immunity contributed to viral transmission in all but one country. Small variations in heterogeneity were sufficient to explain large differences in mortality rates. The best model of UK data predicts a second surge of fatalities will be much less than the first peak. The size of the second wave depends sensitively on the loss of immunity and the efficacy of Find-Test-Trace-Isolate-Support programmes. In summary, accounting for heterogeneity of exposure, susceptibility and transmission suggests that the next wave of the SARS-CoV-2 pandemic will be much smaller than conventional models predict, with less economic and health disruption. This heterogeneity means that seroprevalence underestimates effective herd immunity and, crucially, the potential of public health programmes.
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Affiliation(s)
- Karl Friston
- Queen Square Institute of Neurology, University College London, London, UK
| | - Anthony Costello
- Institute of Global Health, University College London, London, UK
| | - Deenan Pillay
- University College London Faculty of Medical Sciences, London, UK
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31
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An evaluation of Hamiltonian Monte Carlo performance to calibrate age-structured compartmental SEIR models to incidence data. Epidemics 2020; 33:100415. [PMID: 33212347 DOI: 10.1016/j.epidem.2020.100415] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Revised: 10/28/2020] [Accepted: 10/28/2020] [Indexed: 11/20/2022] Open
Abstract
Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo method to estimate unknown quantities through sample generation from a target distribution for which an analytical solution is difficult. The strength of this method lies in its geometrical foundations, which render it efficient for traversing high-dimensional spaces. First, this paper analyses the performance of HMC in calibrating five variants of inputs to an age-structured SEIR model. Four of these variants are related to restriction assumptions that modellers devise to handle high-dimensional parameter spaces. The other one corresponds to the unrestricted symmetric variant. To provide a robust analysis, we compare HMC's performance to that of the Nelder-Mead algorithm (NMS), a common method for non-linear optimisation. Furthermore, the calibration is performed on synthetic data in order to avoid confounding effects from errors in model selection. Then, we explore the variation in the method's performance due to changes in the scale of the problem. Finally, we fit an SEIR model to real data. In all the experiments, the results show that HMC approximates both the synthetic and real data accurately, and provides reliable estimates for the basic reproduction number and the age-dependent transmission rates. HMC's performance is robust in the presence of underreported incidences and high-dimensional complexity. This study suggests that stringent assumptions on age-dependent transmission rates can be lifted in favour of more realistic representations. The supplementary section presents the full set of results.
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32
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Baguelin M, Medley GF, Nightingale ES, O’Reilly KM, Rees EM, Waterlow NR, Wagner M. Tooling-up for infectious disease transmission modelling. Epidemics 2020; 32:100395. [PMID: 32405321 PMCID: PMC7219405 DOI: 10.1016/j.epidem.2020.100395] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Accepted: 05/09/2020] [Indexed: 12/15/2022] Open
Abstract
In this introduction to the Special Issue on methods for modelling of infectious disease epidemiology we provide a commentary and overview of the field. We suggest that the field has been through three revolutions that have focussed on specific methodological developments; disease dynamics and heterogeneity, advanced computing and inference, and complexity and application to the real-world. Infectious disease dynamics and heterogeneity dominated until the 1980s where the use of analytical models illustrated fundamental concepts such as herd immunity. The second revolution embraced the integration of data with models and the increased use of computing. From the turn of the century an emergence of novel datasets enabled improved modelling of real-world complexity. The emergence of more complex data that reflect the real-world heterogeneities in transmission resulted in the development of improved inference methods such as particle filtering. Each of these three revolutions have always kept the understanding of infectious disease spread as its motivation but have been developed through the use of new techniques, tools and the availability of data. We conclude by providing a commentary on what the next revoluition in infectious disease modelling may be.
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Affiliation(s)
- Marc Baguelin
- School of Public Health, Infectious Disease Epidemiology, Imperial College London, United Kingdom
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK
| | - Graham F. Medley
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK
| | - Emily S. Nightingale
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK
| | - Kathleen M. O’Reilly
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK
| | - Eleanor M. Rees
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK
| | - Naomi R. Waterlow
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK
| | - Moritz Wagner
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK
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Forecasting the 2017/2018 seasonal influenza epidemic in England using multiple dynamic transmission models: a case study. BMC Public Health 2020; 20:486. [PMID: 32293372 PMCID: PMC7158152 DOI: 10.1186/s12889-020-8455-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2019] [Accepted: 03/04/2020] [Indexed: 01/13/2023] Open
Abstract
Background Since the 2009 A/H1N1 pandemic, Public Health England have developed a suite of real-time statistical models utilising enhanced pandemic surveillance data to nowcast and forecast a future pandemic. Their ability to track seasonal influenza and predict heightened winter healthcare burden in the light of high activity in Australia in 2017 was untested. Methods Four transmission models were used in forecasting the 2017/2018 seasonal influenza epidemic in England: a stratified primary care model using daily, region-specific, counts and virological swab positivity of influenza-like illness consultations in general practice (GP); a strain-specific (SS) model using weekly, national GP ILI and virological data; an intensive care model (ICU) using reports of ICU influenza admissions; and a synthesis model that included all data sources. For the first 12 weeks of 2018, each model was applied to the latest data to provide estimates of epidemic parameters and short-term influenza forecasts. The added value of pre-season population susceptibility data was explored. Results The combined results provided valuable nowcasts of the state of the epidemic. Short-term predictions of burden on primary and secondary health services were initially highly variable before reaching consensus beyond the observed peaks in activity between weeks 3–4 of 2018. Estimates for R0 were consistent over time for three of the four models until week 12 of 2018, and there was consistency in the estimation of R0 across the SPC and SS models, and in the ICU attack rates estimated by the ICU and the synthesis model. Estimation and predictions varied according to the assumed levels of pre-season immunity. Conclusions This exercise successfully applied a range of pandemic models to seasonal influenza. Forecasting early in the season remains challenging but represents a crucially important activity to inform planning. Improved knowledge of pre-existing levels of immunity would be valuable.
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Quinto EJ, Marín JM, Caro I, Mateo J, Schaffner DW. Modelling Growth and Decline in a Two-Species Model System: Pathogenic Escherichia coli O157:H7 and Psychrotrophic Spoilage Bacteria in Milk. Foods 2020; 9:E331. [PMID: 32178268 PMCID: PMC7142549 DOI: 10.3390/foods9030331] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2020] [Revised: 03/05/2020] [Accepted: 03/09/2020] [Indexed: 01/24/2023] Open
Abstract
Shiga toxin-producing Escherichia coli O157:H7 is a food-borne pathogen and the major cause of hemorrhagic colitis. Pseudomonas is the genus most frequent psychrotrophic spoilage microorganisms present in milk. Two-species bacterial systems with E. coli O157:H7, non-pathogenic E. coli, and P. fluorescens in skimmed milk at 7, 13, 19, or 25 °C were studied. Bacterial interactions were modelled after applying a Bayesian approach. No direct correlation between P. fluorescens's growth rate and its effect on the maximum population densities of E. coli species was found. The results show the complexity of the interactions between two species in a food model. The use of natural microbiota members to control foodborne pathogens could be useful to improve food safety during the processing and storage of refrigerated foods.
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Affiliation(s)
- Emiliano J. Quinto
- Department of Nutrition and Food Science, College of Medicine, University of Valladolid, 47005 Valladolid, Spain;
| | - Juan M. Marín
- Department of Statistics, University Carlos III de Madrid, 28903 Getafe, Madrid, Spain;
| | - Irma Caro
- Department of Nutrition and Food Science, College of Medicine, University of Valladolid, 47005 Valladolid, Spain;
| | - Javier Mateo
- Department of Food Hygiene and Food Technology, University of León, Campus de Vegazana s/n, 24071 León, Spain;
| | - Donald W. Schaffner
- Department of Food Science, Rutgers University, New Brunswick, NJ 08901, USA;
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