A voltage-based Event-Timing-Dependent Plasticity rule accounts for LTP subthreshold and suprathreshold for dendritic spikes in CA1 pyramidal neurons

Long-term potentiation (LTP) is a synaptic mechanism involved in learning and memory. Experiments have shown that dendritic sodium spikes (Na-dSpikes) are required for LTP in the distal apical dendrites of CA1 pyramidal cells. On the other hand, LTP in perisomatic dendrites can be induced by synaptic input patterns that can be both subthreshold and suprathreshold for Na-dSpikes. It is unclear whether these results can be explained by one unifying plasticity mechanism. Here, we show in biophysically and morphologically realistic compartmental models of the CA1 pyramidal cell that these forms of LTP can be fully accounted for by a simple plasticity rule. We call it the voltage-based Event-Timing-Dependent Plasticity (ETDP) rule. The presynaptic event is the presynaptic spike or release of glutamate. The postsynaptic event is the local depolarization that exceeds a certain plasticity threshold. Our model reproduced the experimentally observed LTP in a variety of protocols, including local pharmacological inhibition of dendritic spikes by tetrodotoxin (TTX). In summary, we have provided a validation of the voltage-based ETDP, suggesting that this simple plasticity rule can be used to model even complex spatiotemporal patterns of long-term synaptic plasticity in neuronal dendrites.

Data-driven mechanistic framework with stratified immunity and effective transmissibility for COVID-19 scenario projections

Scenario-based modeling frameworks have been widely used to support policy-making at state and federal levels in the United States during the COVID-19 response. While custom-built models can be used to support one-off studies, sustained updates to projections under changing pandemic conditions requires a robust, integrated, and adaptive framework. In this paper, we describe one such framework, UVA-adaptive, that was built to support the CDC-aligned Scenario Modeling Hub (SMH) across multiple rounds, as well as weekly/biweekly projections to Virginia Department of Health (VDH) and US Department of Defense during the COVID-19 response. Building upon an existing metapopulation framework, PatchSim, UVA-adaptive uses a calibration mechanism relying on adjustable effective transmissibility as a basis for scenario definition while also incorporating real-time datasets on case incidence, seroprevalence, variant characteristics, and vaccine uptake. Through the pandemic, our framework evolved by incorporating available data sources and was extended to capture complexities of multiple strains and heterogeneous immunity of the population. Here we present the version of the model that was used for the recent projections for SMH and VDH, describe the calibration and projection framework, and demonstrate that the calibrated transmissibility correlates with the evolution of the pathogen as well as associated societal dynamics.

flepiMoP: The evolution of a flexible infectious disease modeling pipeline during the COVID-19 pandemic

The COVID-19 pandemic led to an unprecedented demand for projections of disease burden and healthcare utilization under scenarios ranging from unmitigated spread to strict social distancing policies. In response, members of the Johns Hopkins Infectious Disease Dynamics Group developed flepiMoP (formerly called the COVID Scenario Modeling Pipeline), a comprehensive open-source software pipeline designed for creating and simulating compartmental models of infectious disease transmission and inferring parameters through these models. The framework has been used extensively to produce short-term forecasts and longer-term scenario projections of COVID-19 at the state and county level in the US, for COVID-19 in other countries at various geographic scales, and more recently for seasonal influenza. In this paper, we highlight how the flepiMoP has evolved throughout the COVID-19 pandemic to address changing epidemiological dynamics, new interventions, and shifts in policy-relevant model outputs. As the framework has reached a mature state, we provide a detailed overview of flepiMoP's key features and remaining limitations, thereby distributing flepiMoP and its documentation as a flexible and powerful tool for researchers and public health professionals to rapidly build and deploy large-scale complex infectious disease models for any pathogen and demographic setup.

Glucagon-like peptide-1 and interleukin-6 interaction in response to physical exercise: An in-silico model in the framework of immunometabolism

BACKGROUND AND OBJECTIVE

Glucagon-like peptide 1 (GLP-1) is classically identified as an incretin hormone, secreted in response to nutrient ingestion and able to enhance glucose-stimulated insulin secretion. However, other stimuli, such as physical exercise, may enhance GLP-1 plasma levels, and this exercise-induced GLP-1 secretion is mediated by interleukin-6 (IL-6), a cytokine secreted by contracting skeletal muscle. The aim of the study is to propose a mathematical model of IL-6-induced GLP-1 secretion and kinetics in response to physical exercise of moderate intensity.

METHODS

The model includes the GLP-1 subsystem (with two pools: gut and plasma) and the IL-6 subsystem (again with two pools: skeletal muscle and plasma); it provides a parameter of possible clinical relevance representing the sensitivity of GLP-1 to IL-6 (k0). The model was validated on mean IL-6 and GLP-1 data derived from the scientific literature and on a total of 100 virtual subjects.

RESULTS

Model validation provided mean residuals between 0.0051 and 0.5493 pg⋅mL-1 for IL-6 (in view of concentration values ranging from 0.8405 to 3.9718 pg⋅mL-1) and between 0.0133 and 4.1540 pmol⋅L-1 for GLP-1 (in view of concentration values ranging from 0.9387 to 17.9714 pmol⋅L-1); a positive significant linear correlation (r = 0.85, p<0.001) was found between k0 and the ratio between areas under GLP-1 and IL-6 curve, over the virtual subjects.

CONCLUSIONS

The model accurately captures IL-6-induced GLP-1 kinetics in response to physical exercise.

Reconstruction of incidence reporting rate for SARS-CoV-2 Delta variant of COVID-19 pandemic in the US

In recent years, advanced regularization techniques have emerged as a powerful tool aimed at stable estimation of infectious disease parameters that are crucial for future projections, prevention, and control. Unlike other system parameters, i.e., incubation and recovery rates, the case reporting rate, Ψ, and the time-dependent effective reproduction number, R e ( t ) , are directly influenced by a large number of factors making it impossible to pre-estimate these parameters in any meaningful way. In this study, we propose a novel iteratively-regularized trust-region optimization algorithm, combined with SuSvIuIvRD compartmental model, for stable reconstruction of Ψ and R e ( t ) from reported epidemic data on vaccination percentages, incidence cases, and daily deaths. The innovative regularization procedure exploits (and takes full advantage of) a unique structure of the Jacobian and Hessian approximation for the nonlinear observation operator. The proposed inversion method is thoroughly tested with synthetic and real SARS-CoV-2 Delta variant data for different regions in the United States of America from July 9, 2021, to November 25, 2021. Our study shows that case reporting rate during the Delta wave of COVID-19 pandemic in the US is between 12% and 37%, with most states being in the range from 15% to 25%. This confirms earlier accounts on considerable under-reporting of COVID-19 cases due to the impact of "silent spreaders" and the limitations of testing.

Predicting Covid-19 pandemic waves with biologically and behaviorally informed universal differential equations

During the COVID-19 pandemic, it became clear that pandemic waves and population responses were locked in a mutual feedback loop in a classic example of a coupled behavior-disease system. We demonstrate for the first time that universal differential equation (UDE) models are able to extract this interplay from data. We develop a UDE model for COVID-19 and test its ability to make predictions of second pandemic waves. We find that UDEs are capable of learning coupled behavior-disease dynamics and predicting second waves in a variety of populations, provided they are supplied with learning biases describing simple assumptions about disease transmission and population response. Though not yet suitable for deployment as a policy-guiding tool, our results demonstrate potential benefits, drawbacks, and useful techniques when applying universal differential equations to coupled systems.

Comparison of tracer kinetic models for 68Ga-PSMA-11 PET in intermediate-risk primary prostate cancer patients

BACKGROUND

68Ga-PSMA-11 positron emission tomography enables the detection of primary, recurrent, and metastatic prostate cancer. Regional radiopharmaceutical uptake is generally evaluated in static images and quantified as standard uptake values (SUVs) for clinical decision-making. However, analysis of dynamic images characterizing both tracer uptake and pharmacokinetics may offer added insights into the underlying tissue pathophysiology. This study was undertaken to evaluate the suitability of various kinetic models for 68Ga-PSMA-11 PET analysis. Twenty-three lesions in 18 patients were included in a retrospective kinetic evaluation of 55-min dynamic 68Ga-PSMA-11 pre-prostatectomy PET scans from patients with biopsy-demonstrated intermediate- to high-risk prostate cancer. Three kinetic models-a reversible one-tissue compartment model, an irreversible two-tissue compartment model, and a reversible two-tissue compartment model, were evaluated for their goodness of fit to lesion and normal reference prostate time-activity curves. Kinetic parameters obtained through graphical analysis and tracer kinetic modeling techniques were compared for reference prostate tissue and lesion regions of interest.

RESULTS

Supported by goodness of fit and information loss criteria, the irreversible two-tissue compartment model optimally fit the time-activity curves. Lesions exhibited significant differences in kinetic rate constants (K1, k2, k3, Ki) and semiquantitative measures (SUV and %ID/kg) when compared with reference prostatic tissue. The two-tissue irreversible tracer kinetic model was consistently appropriate across prostatic zones.

CONCLUSIONS

An irreversible tracer kinetic model is appropriate for dynamic analysis of 68Ga-PSMA-11 PET images. Kinetic parameters estimated by Patlak graphical analysis or full compartmental analysis can distinguish tumor from normal prostate tissue.

Variation in pneumococcal invasiveness metrics is driven by serotype carriage duration and initial risk of disease

Streptococcus pneumoniae is an opportunistic pathogen that, while usually carried asymptomatically, can cause severe invasive diseases like meningitis and bacteremic pneumonia. A central goal in S. pneumoniae public health management is to identify which serotypes (immunologically distinct strains) pose the most risk of invasive disease. The most common invasiveness metrics use cross-sectional data (i.e., invasive odds ratios (IOR)), or longitudinal data (i.e., attack rates (AR)). To assess the reliability of these metrics we developed an epidemiological model of carriage and invasive disease. Our mathematical analyses illustrate qualitative failures with the IOR metric (e.g., IOR can decline with increasing invasiveness parameters). Fitting the model to both longitudinal and cross-sectional data, our analysis supports previous work indicating that invasion risk is maximal at or near time of colonization. This pattern of early invasive disease risk leads to substantial (up to 5-fold) biases when estimating underlying differences in invasiveness from IOR metrics, due to the impact of carriage duration on IOR. Together, these results raise serious concerns with the IOR metric as a basis for public health decision-making and lend support for multiple alternate metrics including AR.

Bayesian modeling of dynamic behavioral change during an epidemic

For many infectious disease outbreaks, the at-risk population changes their behavior in response to the outbreak severity, causing the transmission dynamics to change in real-time. Behavioral change is often ignored in epidemic modeling efforts, making these models less useful than they could be. We address this by introducing a novel class of data-driven epidemic models which characterize and accurately estimate behavioral change. Our proposed model allows time-varying transmission to be captured by the level of "alarm" in the population, with alarm specified as a function of the past epidemic trajectory. We investigate the estimability of the population alarm across a wide range of scenarios, applying both parametric functions and non-parametric functions using splines and Gaussian processes. The model is set in the data-augmented Bayesian framework to allow estimation on partially observed epidemic data. The benefit and utility of the proposed approach is illustrated through applications to data from real epidemics.

Effective population size in simple infectious disease models

Almost all models used in analysis of infectious disease outbreaks contain some notion of population size, usually taken as the census population size of the community in question. In many settings, however, the census population is not equivalent to the population likely to be exposed, for example if there are population structures, outbreak controls or other heterogeneities. Although these factors may be taken into account in the model: adding compartments to a compartmental model, variable mixing rates and so on, this makes fitting more challenging, especially if the population complexities are not fully known. In this work we consider the concept of effective population size in outbreak modelling, which we define as the size of the population involved in an outbreak, as an alternative to use of more complex models. Effective population size is an important quantity in genetics for estimation of genetic diversity loss in populations, but it has not been widely applied in epidemiology. Through simulation studies and application to data from outbreaks of COVID-19 in China, we find that simple SIR models with effective population size can provide a good fit to data which are not themselves simple or SIR.

Global dynamics of a compartmental model to assess the effect of transmission from deceased

During several epidemics, transmission from deceased people significantly contributed to disease spread, but mathematical analysis of this transmission has not been seen in the literature numerously. Transmission of Ebola during traditional burials was the most well-known example; however, there are several other diseases, such as hepatitis, plague or Nipah virus, that can potentially be transmitted from disease victims. This is especially true in the case of serious epidemics when healthcare is overwhelmed and the operative capacity of the health sector is diminished, such as seen during the COVID-19 pandemic. We present a compartmental model for the spread of a disease with an imperfect vaccine available, also considering transmission from deceased infected in general. The global dynamics of the system are completely described by constructing appropriate Lyapunov functions. To support our analytical results, we perform numerical simulations to assess the importance of transmission from the deceased, considering the data collected from three infectious diseases, Ebola virus disease, COVID-19, and Nipah fever.

An optimal control model for Covid-19 spread with impacts of vaccination and facemask

A non-linear system of differential equations was used to explain the spread of the COVID-19 virus and a SEIQR model was developed and tested to provide insights into the spread of the pandemic. This article, which is related to the aforementioned work as well as other work covering variations of SIR models, Hermite Wavelets Transform, and also the Generalized Compartmental COVID-19 model, we develop a mathematical control model and apply it to represent optimal vaccination strategy against COVID-19 using Pontryagin's Maximum Principle and also factoring in the effect of facemasks on the spread of the virus. As background work, we analyze the mathematical epidemiology model with the facemask effect on both reproduction number and stability, we also analyze the difference between confirmed COVID-19 cases of the Quarantine class and anonymous cases of the Infectious class that is expected to recover. We also apply control theory to mine insights for effective virus spread prevention strategies. Our models are validated using Matlab mathematical model validation tools. Statistical tests against data from Jordan are used to validate our work including the modeling of the relation between the facemask effect and COVID-19 spread. Furthermore, the relation between control measure ξ, cost, and Infected cases is also studied.

The potential impact of a vaccine on Neisseria gonorrhoeae prevalence among heterosexuals living in a high prevalence setting

BACKGROUND

Treatment of Neisseria gonorrhoeae is under threat with the emergence and spread of antimicrobial resistance. Thus, there is a growing interest in the development of a gonorrhoea vaccine. We used mathematical modelling to assess the impact of a hypothetical vaccine in controlling gonorrhoea among heterosexuals living in a setting of relatively high N. gonorrhoeae prevalence (∼3 %).

METHODS

We developed a mathematical model of N. gonorrhoeae transmission among 15-49-year-old heterosexuals, stratified by age and sex, and calibrated to prevalence and sexual behaviour data from South Africa as an example of a high prevalence setting for which we have data available. Using this model, we assessed the potential impact of a vaccine on N. gonorrhoeae prevalence in the entire population. We considered gonorrhoea vaccines having differing impacts on N. gonorrhoeae infection and transmission and offered to different age-groups.

RESULTS

The model predicts that N. gonorrhoeae prevalence can be reduced by ∼50 % in 10 years following introduction of a vaccine if annual vaccination uptake is 10 %, vaccine efficacy against acquisition of infection is 25 % and duration of protection is 5 years, with vaccination available to the entire population of 15-49-year-olds. If only 15-24-year-olds are vaccinated, the predicted reduction in prevalence in the entire population is 25 % with equivalent vaccine characteristics and uptake. Although predicted reductions in prevalence for vaccination programmes targeting only high-activity individuals and the entire population are similar over the same period, vaccinating only high-activity individuals is more efficient as the cumulative number of vaccinations needed to reduce prevalence in the entire population by 50 % is ∼3 times lower for this programme.

CONCLUSION

Provision of a gonorrhoea vaccine could lead to substantial reductions in N. gonorrhoeae prevalence in a high prevalence heterosexual setting, even with moderate annual vaccination uptake of a vaccine with partial efficacy.

Analysis of the COVID-19 pandemic using a compartmental model with time-varying parameters fitted by a genetic algorithm

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%.

SIRSi-vaccine dynamical model for the Covid-19 pandemic

Covid-19, caused by severe acute respiratory syndrome coronavirus 2, broke out as a pandemic during the beginning of 2020. The rapid spread of the disease prompted an unprecedented global response involving academic institutions, regulatory agencies, and industries. Vaccination and nonpharmaceutical interventions including social distancing have proven to be the most effective strategies to combat the pandemic. In this context, it is crucial to understand the dynamic behavior of the Covid-19 spread together with possible vaccination strategies. In this study, a susceptible-infected-removed-sick model with vaccination (SIRSi-vaccine) was proposed, accounting for the unreported yet infectious. The model considered the possibility of temporary immunity following infection or vaccination. Both situations contribute toward the spread of diseases. The transcritical bifurcation diagram of alternating and mutually exclusive stabilities for both disease-free and endemic equilibria were determined in the parameter space of vaccination rate and isolation index. The existing equilibrium conditions for both points were determined in terms of the epidemiological parameters of the model. The bifurcation diagram allowed us to estimate the maximum number of confirmed cases expected for each set of parameters. The model was fitted with data from São Paulo, the state capital of SP, Brazil, which describes the number of confirmed infected cases and the isolation index for the considered data window. Furthermore, simulation results demonstrate the possibility of periodic undamped oscillatory behavior of the susceptible population and the number of confirmed cases forced by the periodic small-amplitude oscillations in the isolation index. The main contributions of the proposed model are as follows: A minimum effort was required when vaccination was combined with social isolation, while additionally ensuring the existence of equilibrium points. The model could provide valuable information for policymakers, helping define disease prevention mitigation strategies that combine vaccination and non-pharmaceutical interventions, such as social distancing and the use of masks. In addition, the SIRSi-vaccine model facilitated the qualitative assessment of information regarding the unreported infected yet infectious cases, while considering temporary immunity, vaccination, and social isolation index.

A Stochastic Mobility-Driven Spatially Explicit SEIQRD covid-19 Model with VOCs, Seasonality, and Vaccines

In this work, we extend our previously developed compartmental SEIQRD model for sars-cov-2 in Belgium. We introduce sars-cov-2 variants of concern, vaccines, and seasonality in our model, as their addition has proven necessary for modelling sars-cov-2 transmission dynamics during the 2020-2021 covid-19 pandemic in Belgium. The model is geographically stratified into eleven spatial patches (provinces), and a telecommunication dataset provided by Belgium's biggest operator is used to incorporate interprovincial mobility. We calibrate the model using the daily number of hospitalisations in each province and serological data. We find the model adequately describes these data, but the addition of interprovincial mobility was not necessary to obtain an accurate description of the 2020-2021 sars-cov-2 pandemic in Belgium. We further demonstrate how our model can be used to help policymakers decide on the optimal timing of the release of social restrictions.We find that adding spatial heterogeneity by geographically stratifying the model results in more uncertain model projections as compared to an equivalent nation-level model, which has both communicative advantages and disadvantages. We finally discuss the impact of imposing local mobility or social contact restrictions to contain an epidemic in a given province and find that lowering social contact is a more effective strategy than lowering mobility.

Epidemic Management via Imperfect Testing: A Multi-criterial Perspective

Diagnostic testing may represent a key component in response to an ongoing epidemic, especially if coupled with containment measures, such as mandatory self-isolation, aimed to prevent infectious individuals from furthering onward transmission while allowing non-infected individuals to go about their lives. However, by its own nature as an imperfect binary classifier, testing can produce false negative or false positive results. Both types of misclassification are problematic: while the former may exacerbate the spread of disease, the latter may result in unnecessary isolation mandates and socioeconomic burden. As clearly shown by the COVID-19 pandemic, achieving adequate protection for both people and society is a crucial, yet highly challenging task that needs to be addressed in managing large-scale epidemic transmission. To explore the trade-offs imposed by diagnostic testing and mandatory isolation as tools for epidemic containment, here we present an extension of the classical Susceptible-Infected-Recovered model that accounts for an additional stratification of the population based on the results of diagnostic testing. We show that, under suitable epidemiological conditions, a careful assessment of testing and isolation protocols can contribute to epidemic containment, even in the presence of false negative/positive results. Also, using a multi-criterial framework, we identify simple, yet Pareto-efficient testing and isolation scenarios that can minimize case count, isolation time, or seek a trade-off solution for these often contrasting epidemic management objectives.

Short-term PET-derived kinetic estimation for the diagnosis of hepatocellular carcinoma: a combination of the maximum-slope method and dual-input three-compartment model

BACKGROUND

Kinetic estimation provides fitted parameters related to blood flow perfusion and fluorine-18-fluorodeoxyglucose (¹⁸F-FDG) transport and intracellular metabolism to characterize hepatocellular carcinoma (HCC) but usually requires 60 min or more for dynamic PET, which is time-consuming and impractical in a busy clinical setting and has poor patient tolerance.

METHODS

This study preliminarily evaluated the equivalence of liver kinetic estimation between short-term (5-min dynamic data supplemented with 1-min static data at 60 min postinjection) and fully 60-min dynamic protocols and whether short-term ¹⁸F-FDG PET-derived kinetic parameters using a three-compartment model can be used to discriminate HCC from the background liver tissue. Then, we proposed a combined model, a combination of the maximum-slope method and a three-compartment model, to improve kinetic estimation.

RESULTS

There is a strong correlation between the kinetic parameters K₁ ~ k₃, HPI and [Formula: see text] in the short-term and fully dynamic protocols. With the three-compartment model, HCCs were found to have higher k₂, HPI and k₃ values than background liver tissues, while K₁, k₄ and [Formula: see text] values were not significantly different between HCCs and background liver tissues. With the combined model, HCCs were found to have higher HPI, K₁ and k₂, k₃ and [Formula: see text] values than background liver tissues; however, the k₄ value was not significantly different between HCCs and the background liver tissues.

CONCLUSIONS

Short-term PET is closely equivalent to fully dynamic PET for liver kinetic estimation. Short-term PET-derived kinetic parameters can be used to distinguish HCC from background liver tissue, and the combined model improves the kinetic estimation.

CLINICAL RELEVANCE STATEMENT

Short-term PET could be used for hepatic kinetic parameter estimation. The combined model could improve the estimation of liver kinetic parameters.

Quantitative Assessment of a Dual Epidemic Caused by Tuberculosis and HIV in the Philippines

Tuberculosis (TB) and human immunodeficiency virus (HIV) are the two major public health emergencies in the Philippines. The country is ranked fourth worldwide in TB incidence cases despite national efforts and initiatives to mitigate the disease. Concurrently, the Philippines has the fastest-growing HIV epidemic in Asia and the Pacific region. The TB-HIV dual epidemic forms a lethal combination enhancing each other's progress, driving the deterioration of immune responses. In order to understand and describe the transmission dynamics and epidemiological patterns of the co-infection, a compartmental model for TB-HIV is developed. A class of people living with HIV (PLHIV) who did not know their HIV status is incorporated into the model. These unaware PLHIV who do not seek medical treatment are potential sources of new HIV infections that could significantly influence the disease transmission dynamics. Sensitivity analysis using the partial rank correlation coefficient is performed to assess model parameters that are influential to the output of interests. The model is calibrated using available Philippine data on TB, HIV, and TB-HIV. Parameters that are identified include TB and HIV transmission rates, progression rates from exposed to active TB, and from TB-latent with HIV to active infectious TB with HIV in the AIDS stage. Uncertainty analysis is performed to identify the degree of accuracy of the estimates. Simulations predict an alarming increase of 180% and 194% in new HIV and TB-HIV infections in 2025, respectively, relative to 2019 data. These projections underscore an ongoing health crisis in the Philippines that calls for a combined and collective effort by the government and the public to take action against the lethal combination of TB and HIV.

Integrative modelling of reported case numbers and seroprevalence reveals time-dependent test efficiency and infectious contacts

Mathematical models have been widely used during the ongoing SARS-CoV-2 pandemic for data interpretation, forecasting, and policy making. However, most models are based on officially reported case numbers, which depend on test availability and test strategies. The time dependence of these factors renders interpretation difficult and might even result in estimation biases. Here, we present a computational modelling framework that allows for the integration of reported case numbers with seroprevalence estimates obtained from representative population cohorts. To account for the time dependence of infection and testing rates, we embed flexible splines in an epidemiological model. The parameters of these splines are estimated, along with the other parameters, from the available data using a Bayesian approach. The application of this approach to the official case numbers reported for Munich (Germany) and the seroprevalence reported by the prospective COVID-19 Cohort Munich (KoCo19) provides first estimates for the time dependence of the under-reporting factor. Furthermore, we estimate how the effectiveness of non-pharmaceutical interventions and of the testing strategy evolves over time. Overall, our results show that the integration of temporally highly resolved and representative data is beneficial for accurate epidemiological analyses.

Validation of a compartmental model to predict drug release from porous structures produced by ScCO(2) techniques

A global release model is proposed to study the drug release from porous materials for pharmaceutical applications. This model is defined by implementing a compartmental model where the release profile could be explained as the combination of mass transfer phenomena through three compartments as well as a desorption process or dissolution process from the support. This model was validated with five different systems produced with supercritical CO₂ (aerogels, membranes, and fibers), showing different release processes. Numerical results indicate that this compartmental approach can be useful to determine adsorption and desorption constants as well as mass transfer resistances within the material. Likewise, this model can predict lag phases and imbibition phenomena. Therefore, the development of compartmental models can be an alternative to traditional models to successfully predict the drug profile of porous materials, achieving a complete understanding of the involved phenomena regardless of the material characteristics.

Data Assimilation Predictive GAN (DA-PredGAN) Applied to a Spatio-Temporal Compartmental Model in Epidemiology

We propose a novel use of generative adversarial networks (GANs) (i) to make predictions in time (PredGAN) and (ii) to assimilate measurements (DA-PredGAN). In the latter case, we take advantage of the natural adjoint-like properties of generative models and the ability to simulate forwards and backwards in time. GANs have received much attention recently, after achieving excellent results for their generation of realistic-looking images. We wish to explore how this property translates to new applications in computational modelling and to exploit the adjoint-like properties for efficient data assimilation. We apply these methods to a compartmental model in epidemiology that is able to model space and time variations, and that mimics the spread of COVID-19 in an idealised town. To do this, the GAN is set within a reduced-order model, which uses a low-dimensional space for the spatial distribution of the simulation states. Then the GAN learns the evolution of the low-dimensional states over time. The results show that the proposed methods can accurately predict the evolution of the high-fidelity numerical simulation, and can efficiently assimilate observed data and determine the corresponding model parameters.

Transmissibility of tuberculosis among students and non-students: an occupational-specific mathematical modelling

BACKGROUND

Recently, despite the steady decline in the tuberculosis (TB) epidemic globally, school TB outbreaks have been frequently reported in China. This study aimed to quantify the transmissibility of Mycobacterium tuberculosis (MTB) among students and non-students using a mathematical model to determine characteristics of TB transmission.

METHODS

We constructed a dataset of reported TB cases from four regions (Jilin Province, Xiamen City, Chuxiong Prefecture, and Wuhan City) in China from 2005 to 2019. We classified the population and the reported cases under student and non-student groups, and developed two mathematical models [nonseasonal model (Model A) and seasonal model (Model B)] based on the natural history and transmission features of TB. The effective reproduction number (R_eff) of TB between groups were calculated using the collected data.

RESULTS

During the study period, data on 456,423 TB cases were collected from four regions: students accounted for 6.1% of cases. The goodness-of-fit analysis showed that Model A had a better fitting effect (P < 0.001). The average R_eff of TB estimated from Model A was 1.68 [interquartile range (IQR): 1.20-1.96] in Chuxiong Prefecture, 1.67 (IQR: 1.40-1.93) in Xiamen City, 1.75 (IQR: 1.37-2.02) in Jilin Province, and 1.79 (IQR: 1.56-2.02) in Wuhan City. The average R_eff of TB in the non-student population was 23.30 times (1.65/0.07) higher than that in the student population.

CONCLUSIONS

The transmissibility of MTB remains high in the non-student population of the areas studied, which is still dominant in the spread of TB. TB transmissibility from the non-student-to-student-population had a strong influence on students. Specific interventions, such as TB screening, should be applied rigorously to control and to prevent TB transmission among students.

Modeling of the effect of cerebrospinal fluid flow modulation on locally delivered drugs in the brain

Cerebrospinal fluid (CSF) plays a vital role in maintaining brain homeostasis and recent research has focused on elucidating the role that convective flow of CSF plays in brain health. This paper describes a computational compartmental model of how CSF dynamics affect drug pharmacokinetics in the rat brain. Our model implements a local, sustained release approach for drug delivery to the brain. Simulation outputs highlight the potential for modulating CSF flow to improve overall drug pharmacokinetics in the central nervous system and suggest that concomitant CSF modulation and optimized drug release rates from implantable depots can be used to engineer the duration of action of chemotherapeutics. As an example, the tissue exposure of temozolomide, the standard of care treatment for glioblastoma, was modeled in conjunction with two CSF-modulating drugs: acetazolamide and verapamil. Simulations indicate that temozolomide exposure in the interstitial fluid is increased by 25% when using local sustained release delivery systems and concomitant acetazolamide delivery to reduce CSF production. This computational model can be used to produce insight on how to appropriately modulate CSF production and engineer drug release to tailor drug exposure in the brain while limiting off-target effects. As new research continues to elucidate the dynamic roles of CSF, this model can be further improved and leveraged to provide information on how CSF modulation may play a beneficial role in treating a wide variety of neurological disease.

A general modeling framework for exploring the impact of individual concern and personal protection on vector-borne disease dynamics

BACKGROUND

As climate variability and extreme weather events associated with climate change become more prevalent, public health authorities can expect to face an expanding spectrum of vector-borne diseases with increasing incidence and geographical spread. Common interventions include the use of larvicides and adulticides, as well as targeted communications to increase public awareness regarding the need for personal protective measures, such as mosquito repellant, protective clothing, and mosquito nets. Here, we propose a simplified compartmental model of mosquito-borne disease dynamics that incorporates the use of personal protection against mosquito bites influenced by two key individual-level behavioral drivers-concern for being bitten by mosquitos as a nuisance and concern for mosquito-borne disease transmission.

METHODS

We propose a modified compartmental model that describes the dynamics of vector-borne disease spread in a naïve population while considering the public demand for community-level control and, importantly, the effects of personal-level protection on population-level outbreak dynamics. We consider scenarios at low, medium, and high levels of community-level vector control, and at each level, we consider combinations of low, medium, and high levels of motivation to use personal protection, namely concern for disease transmission and concern for being bitten in general.

RESULTS

When there is very little community-level vector control, nearly the entire population is quickly infected, regardless of personal protection use. When vector control is at an intermediate level, both concerns that motivate the use of personal protection play an important role in reducing disease burden. When authorities have the capacity for high-level community vector control through pesticide use, the motivation to use personal protection to reduce disease transmission has little additional effect on the outbreak.

CONCLUSIONS

While results show that personal-level protection alone is not enough to significantly impact an outbreak, personal protective measures can significantly reduce the severity of an outbreak in conjunction with community-level control. Furthermore, the model provides insight for targeting public health messaging to increase the use of personal protection based on concerns related to being bitten by mosquitos or vector-borne disease transmission.

A decision analytic approach for social distancing policies during early stages of COVID-19 pandemic

The COVID-19 pandemic has become a crucial public health problem in the world that disrupted the lives of millions in many countries including the United States. In this study, we present a decision analytic approach which is an efficient tool to assess the effectiveness of early social distancing measures in communities with different population characteristics. First, we empirically estimate the reproduction numbers for two different states. Then, we develop an age-structured compartmental simulation model for the disease spread to demonstrate the variation in the observed outbreak. Finally, we analyze the computational results and show that early trigger social distancing strategies result in smaller death tolls; however, there are relatively larger second waves. Conversely, late trigger social distancing strategies result in higher initial death tolls but relatively smaller second waves. This study shows that decision analytic tools can help policy makers simulate different social distancing scenarios at the early stages of a global outbreak. Policy makers should expect multiple waves of cases as a result of the social distancing policies implemented when there are no vaccines available for mass immunization and appropriate antiviral treatments.

Evaluating the impact of stay-at-home and quarantine measures on COVID-19 spread

BACKGROUND

During the early stage of the COVID-19 pandemic, many countries implemented non-pharmaceutical interventions (NPIs) to control the transmission of SARS-CoV-2, the causative pathogen of COVID-19. Among those NPIs, stay-at-home and quarantine measures were widely adopted and enforced. Understanding the effectiveness of stay-at-home and quarantine measures can inform decision-making and control planning during the ongoing COVID-19 pandemic and for future disease outbreaks.

METHODS

In this study, we use mathematical models to evaluate the impact of stay-at-home and quarantine measures on COVID-19 spread in four cities that experienced large-scale outbreaks in the spring of 2020: Wuhan, New York, Milan, and London. We develop a susceptible-exposed-infected-removed (SEIR)-type model with components of self-isolation and quarantine and couple this disease transmission model with a data assimilation method. By calibrating the model to case data, we estimate key epidemiological parameters before lockdown in each city. We further examine the impact of stay-at-home and quarantine rates on COVID-19 spread after lockdown using counterfactual model simulations.

RESULTS

Results indicate that self-isolation of susceptible population is necessary to contain the outbreak. At a given rate, self-isolation of susceptible population induced by stay-at-home orders is more effective than quarantine of SARS-CoV-2 contacts in reducing effective reproductive numbers [Formula: see text]. Variation in self-isolation and quarantine rates can also considerably affect the duration of outbreaks, attack rates and peak timing. We generate counterfactual simulations to estimate effectiveness of stay-at-home and quarantine measures. Without these two measures, the cumulative confirmed cases could be much higher than reported numbers within 40 days after lockdown in Wuhan, New York, Milan, and London.

CONCLUSIONS

Our findings underscore the essential role of stay-at-home orders and quarantine of SARS-CoV-2 contacts during the early phase of the pandemic.

Policy-driven mathematical modeling for COVID-19 pandemic response in the Philippines

Around the world, disease surveillance and mathematical modeling have been vital tools for government responses to the COVID-19 pandemic. In the face of a volatile crisis, modeling efforts have had to evolve over time in proposing policies for pandemic interventions. In this paper, we document how mathematical modeling contributed to guiding the trajectory of pandemic policies in the Philippines. We present the mathematical specifications of the FASSSTER COVID-19 compartmental model at the core of the FASSSTER platform, the scenario-based disease modeling and analytics toolkit used in the Philippines. We trace how evolving epidemiological analysis at the national, regional, and provincial levels guided government actions; and conversely, how emergent policy questions prompted subsequent model development and analysis. At various stages of the pandemic, simulated outputs of the FASSSTER model strongly correlated with empirically observed case trajectories (r=94%-99%, p<.001). Model simulations were subsequently utilized to predict the outcomes of proposed interventions, including the calibration of community quarantine levels alongside improvements to healthcare system capacity. This study shows how the FASSSTER model enabled the implementation of a phased approach toward gradually expanding economic activity while limiting the spread of COVID-19. This work points to the importance of locally contextualized, flexible, and responsive mathematical modeling, as applied to pandemic intelligence and for data-driven policy-making in general.

Impact of vaccine effectiveness and coverage on preventing large mumps outbreaks on college campuses: Implications for vaccination strategy

Recent mumps outbreaks among highly vaccinated populations, including college students, have called into question the vaccine effectiveness (VE) of routine two-dose measles, mumps, and rubella (MMR2) immunization. We aimed to estimate the VE required for a novel vaccination strategy (e.g., MMR booster dose, novel vaccine) to prevent large mumps outbreaks on college campuses. Using mumps college outbreak data reported to the U.S. Centers for Disease Control and Prevention during 2016-2017, we estimated current MMR2 VE using the screening method and implemented a compartmental model of mumps transmission. We performed 2000 outbreak simulations, following introduction of an infectious person to a population of 10,000, over ranges of MMR2 vaccine coverage (VC) and VE (30.0-99.0%). We compared the impact of varying VC and VE on mumps and mumps orchitis case counts and determined VE thresholds that ensured < 5.0% and < 2.0% of the outbreak simulations exceeded 20 and 100 mumps cases. Median estimated MMR2 VE in reported mumps outbreaks was 60.5% and median reported MMR2 VC was 97.5%. Simulated mumps case count was more sensitive to changes in VE than in VC. The opposite was true for simulated mumps orchitis case count, though orchitis case count was small (mean <10 cases across simulations for VE near 60.5% and VC near 97.5%). At 97.5% VC, 73.1% and 78.2% VE were required for < 5.0% and < 2.0% of outbreaks, respectively, to exceed 100 mumps cases. Maintaining 97.5% VC, 82.4% and 85.9% VE were required for < 5.0% and < 2.0% of outbreaks, respectively, to exceed 20 cases. We conclude that maintaining current levels of MMR2 VC, a novel vaccination strategy aimed at reducing mumps transmission must achieve at least 73.1-85.9% VE among young adults to prevent large mumps outbreaks on college campuses.

Compartmental modeling of skin absorption and desorption kinetics: Donor solvent evaporation, variable diffusion/partition coefficients, and slow equilibration process within stratum corneum

This work expands the recently developed compartmental model for skin transport to model variable diffusion and/or partition coefficients, and the presence of slow equilibration/slow binding kinetics within stratum corneum. The model was validated by comparing it with the diffusion model which was solved numerically using the finite element method. It was found that the new compartmental model predictions agreed well with that of the diffusion model, providing a sufficient number of compartments was used. The compartmental model was applied to two previously published experimental data sets: water penetration and desorption data and the finite dose dermal penetration of testosterone. Significant improvement of the fitting quality for all these data sets was achieved using the compartmental model.

Global prediction model for COVID-19 pandemic with the characteristics of the multiple peaks and local fluctuations

Background

With the spread of COVID-19, the time-series prediction of COVID-19 has become a research hotspot. Unlike previous epidemics, COVID-19 has a new pattern of long-time series, large fluctuations, and multiple peaks. Traditional dynamical models are limited to curves with short-time series, single peak, smoothness, and symmetry. Secondly, most of these models have unknown parameters, which bring greater ambiguity and uncertainty. There are still major shortcomings in the integration of multiple factors, such as human interventions, environmental factors, and transmission mechanisms.

Methods

A dynamical model with only infected humans and removed humans was established. Then the process of COVID-19 spread was segmented using a local smoother. The change of infection rate at different stages was quantified using the continuous and periodic Logistic growth function to quantitatively describe the comprehensive effects of natural and human factors. Then, a non-linear variable and NO₂ concentrations were introduced to qualify the number of people who have been prevented from infection through human interventions.

Results

The experiments and analysis showed the R² of fitting for the US, UK, India, Brazil, Russia, and Germany was 0.841, 0.977, 0.974, 0.659, 0.992, and 0.753, respectively. The prediction accuracy of the US, UK, India, Brazil, Russia, and Germany in October was 0.331, 0.127, 0.112, 0.376, 0.043, and 0.445, respectively.

Conclusion

The model can not only better describe the effects of human interventions but also better simulate the temporal evolution of COVID-19 with local fluctuations and multiple peaks, which can provide valuable assistant decision-making information.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-022-01604-x.

Fractional optimal control of compartmental SIR model of COVID-19: Showing the impact of effective vaccination

In this work a compartmental SIR model has been proposed for describing the dynamics of COVID-19 with Caputo's fractional derivative(FD). SIR compartmental model has been used here with fractional differential equations(FDEs). The mathematical model of the pandemic consists of three compartments namely susceptible, infected and recovered individuals. The dynamics of the pandemic COVID-19 with FDEs for showing the effect of memory as most of the cell biological systems can be described accurately by FDEs Time dependent control(Effective vaccination) has been applied model to formulated fractional optimal control problem(FOCP) to reduce the viral load. Pontryagin's Maximum Principle(PMP) has been used to formulate FOCP. An effective vaccination is very helpful for controlling the pandemic, which is observed through the numerical simulation via Grunwald-Letnikov(G-L) approximation. All numerical simulation work has been carried in MATLAB platform.

Modelling the COVID-19 epidemic and the vaccination campaign in Italy by the SUIHTER model

Several epidemiological models have been proposed to study the evolution of COVID-19 pandemic. In this paper, we propose an extension of the SUIHTER model, to analyse the COVID-19 spreading in Italy, which accounts for the vaccination campaign and the presence of new variants when they become dominant. In particular, the specific features of the variants (e.g. their increased transmission rate) and vaccines (e.g. their efficacy to prevent transmission, hospitalization and death) are modeled, based on clinical evidence. The new model is validated comparing its near-future forecast capabilities with other epidemiological models and exploring different scenario analyses.

Modeling the Dynamics of Heroin and Illicit Opioid Use Disorder, Treatment, and Recovery

Opioid use disorder (OUD) has become a serious leading health issue in the USA leading to addiction, disability, or death by overdose. Research has shown that OUD can lead to a chronic lifelong disorder with greater risk for relapse and accidental overdose deaths. While the prescription opioid epidemic is a relatively new phenomenon, illicit opioid use via heroin has been around for decades. Recently, additional illicit opioids such as fentanyl have become increasingly available and problematic. We propose a mathematical model that focuses on illicit OUD and includes a class for recovered users but allows for individuals to either remain in or relapse back to the illicit OUD class. Therefore, in our model, individuals may cycle in and out of three different classes: illicit OUD, treatment, and recovered. We additionally include a treatment function with saturation, as it has been shown there is limited accessibility to specialty treatment facilities. We used 2002–2019 SAMHSA and CDC data for the US population, scaled to a medium-sized city, to obtain parameter estimates for the specific case of heroin. We found that the overdose death rate has been increasing linearly since around 2011, likely due to the increased presence of fentanyl in the heroin supply. Extrapolation of this overdose death rate, together with the obtained parameter estimates, predict that by 2038 no endemic equilibrium will exist and the only stable equilibrium will correspond to the absence of heroin use disorder in the population. There is a range of parameter values that will give rise to a backward bifurcation above a critical saturation of treatment availability. We show this for a range of overdose death rate values, thus illustrating the critical role played by the availability of specialty treatment facilities. Sensitivity analysis consistently shows the significant role of people entering treatment on their own accord, which suggests the importance of removing two of the most prevalent SAMHSA-determined reasons that individuals do not enter treatment: financial constraints and the stigma of seeking treatment for heroin use disorder.

A random forest model for forecasting regional COVID-19 cases utilizing reproduction number estimates and demographic data

During the COVID-19 pandemic, predicting case spikes at the local level is important for a precise, targeted public health response and is generally done with compartmental models. The performance of compartmental models is highly dependent on the accuracy of their assumptions about disease dynamics within a population; thus, such models are susceptible to human error, unexpected events, or unknown characteristics of a novel infectious agent like COVID-19. We present a relatively non-parametric random forest model that forecasts the number of COVID-19 cases at the U.S. county level. Its most prioritized training features are derived from easily accessible, standard epidemiological data (i.e., regional test positivity rate) and the effective reproduction number ( R t ) from compartmental models. A novel input training feature is case projections generated by aligning estimated effective reproduction number (pre-computed by COVIDActNow.org) with real time testing data until maximally correlated, helping our model fit better to the epidemic's trajectory as ascertained by traditional models. Poor reliability of R t is partially mitigated with dynamic population mobility and prevalence and mortality of non-COVID-19 diseases to gauge population disease susceptibility. The model was used to generate forecasts for 1, 2, 3, and 4 weeks into the future for each reference week within 11/01/2020 - 01/10/2021 for 3068 counties. Over this time period, it maintained a mean absolute error (MAE) of less than 300 weekly cases/100,000 and consistently outperformed or performed comparably with gold-standard compartmental models. Furthermore, it holds great potential in ensemble modeling due to its potential for a more expansive training feature set while maintaining good performance and limited resource utilization.

COVID-19 outbreak: A data-driven optimization model for allocation of patients

COVID-19 is an unprecedented pandemic that puts the entire world at stake and the healthcare systems across the globe have faced pressing challenges. The number of COVID-19 patients increases rapidly every day. The hospitals across many countries are starving to provide adequate service to the patients due to the shortage of resources and as a consequence, patients do not get admitted to hospitals on time, which in turn creates panic and might contribute to the spread of the pandemic. Under this resource constraint situation, this study proposes a data-driven optimization model for patient allocation in hospitals. First, a compartmental model is developed for characterizing the spread of the COVID-19 virus. Then, Pareto analysis is carried out to identify the most COVID-affected cities. An optimization model is then developed for optimal patient allocation in hospitals in different cities. Finally, a sensitivity analysis is also conducted to investigate the robustness of our decision model. Using published data for Indian cities, obtained from different websites, the proposed methodology has been validated. Experimental results reveal that the proposed model offers some efficient strategies for optimal allocation of patients. A total of ten cities are identified as the most affected. Besides, four factors, namely cooperation, distances between cities, number of patients, and bed capacity per city emerge as important determinants.

Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities

We propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in ∼ 1500 dimensions after discretization. To infer these parameters, we use reported data on the number of confirmed, hospitalized, and deceased cases with suitable post-processing in both a deterministic inversion approach with appropriate regularization as a first step, followed by Bayesian inversion with proper prior distributions. To address the curse of dimensionality and the ill-posedness of the high-dimensional inference problem, we propose use of a dimension-independent projected Stein variational gradient descent method, and demonstrate the intrinsic low-dimensionality of the inverse problem. We present inference results with quantified uncertainties for both New Jersey and Texas, which experienced different epidemic phases and patterns. Moreover, we also present forecasting and validation results based on the empirical posterior samples of our inference for the future trajectory of COVID-19.

Age-stratified transmission model of COVID-19 in Ontario with human mobility during pandemic's first wave

In this work, we employ a data-fitted compartmental model to visualize the progression and behavioral response to COVID-19 that match provincial case data in Ontario, Canada from February to June of 2020. This is a "rear-view mirror" glance at how this region has responded to the 1st wave of the pandemic, when testing was sparse and NPI measures were the only remedy to stave off the pandemic. We use an SEIR-type model with age-stratified subpopulations and their corresponding contact rates and asymptomatic rates in order to incorporate heterogeneity in our population and to calibrate the time-dependent reduction of Ontario-specific contact rates to reflect intervention measures in the province throughout lockdown and various stages of social-distancing measures. Cellphone mobility data taken from Google, combining several mobility categories, allows us to investigate the effects of mobility reduction and other NPI measures on the evolution of the pandemic. Of interest here is our quantification of the effectiveness of Ontario's response to COVID-19 before and after provincial measures and our conclusion that the sharp decrease in mobility has had a pronounced effect in the first few weeks of the lockdown, while its effect is harder to infer once other NPI measures took hold.

Wastewater monitoring outperforms case numbers as a tool to track COVID-19 incidence dynamics when test positivity rates are high

Wastewater-based epidemiology (WBE) has been shown to coincide with, or anticipate, confirmed COVID-19 case numbers. During periods with high test positivity rates, however, case numbers may be underreported, whereas wastewater does not suffer from this limitation. Here we investigated how the dynamics of new COVID-19 infections estimated based on wastewater monitoring or confirmed cases compare to true COVID-19 incidence dynamics. We focused on the first pandemic wave in Switzerland (February to April, 2020), when test positivity ranged up to 26%. SARS-CoV-2 RNA loads were determined 2-4 times per week in three Swiss wastewater treatment plants (Lugano, Lausanne and Zurich). Wastewater and case data were combined with a shedding load distribution and an infection-to-case confirmation delay distribution, respectively, to estimate infection incidence dynamics. Finally, the estimates were compared to reference incidence dynamics determined by a validated compartmental model. Incidence dynamics estimated based on wastewater data were found to better track the timing and shape of the reference infection peak compared to estimates based on confirmed cases. In contrast, case confirmations provided a better estimate of the subsequent decline in infections. Under a regime of high-test positivity rates, WBE thus provides critical information that is complementary to clinical data to monitor the pandemic trajectory.

Wastewater monitoring outperforms case numbers as a tool to track COVID-19 incidence dynamics when test positivity rates are high

Wastewater-based epidemiology (WBE) has been shown to coincide with, or anticipate, confirmed COVID-19 case numbers. During periods with high test positivity rates, however, case numbers may be underreported, whereas wastewater does not suffer from this limitation. Here we investigated how the dynamics of new COVID-19 infections estimated based on wastewater monitoring or confirmed cases compare to true COVID-19 incidence dynamics. We focused on the first pandemic wave in Switzerland (February to April, 2020), when test positivity ranged up to 26%. SARS-CoV-2 RNA loads were determined 2-4 times per week in three Swiss wastewater treatment plants (Lugano, Lausanne and Zurich). Wastewater and case data were combined with a shedding load distribution and an infection-to-case confirmation delay distribution, respectively, to estimate infection incidence dynamics. Finally, the estimates were compared to reference incidence dynamics determined by a validated compartmental model. Incidence dynamics estimated based on wastewater data were found to better track the timing and shape of the reference infection peak compared to estimates based on confirmed cases. In contrast, case confirmations provided a better estimate of the subsequent decline in infections. Under a regime of high-test positivity rates, WBE thus provides critical information that is complementary to clinical data to monitor the pandemic trajectory.

Scheduling fixed length quarantines to minimize the total number of fatalities during an epidemic

We consider a susceptible, infected, removed (SIR) system where the transmission rate may be temporarily reduced for a fixed amount of time. We show that in order to minimize the total number of fatalities, the transmission rate should be reduced on a single contiguous time interval, and we characterize this interval via an integral condition. We conclude with a few numerical simulations showing the actual reduction obtained.

An integrated framework for modelling quantitative effects of entry restrictions and travel quarantine on importation risk of COVID-19

OBJECTIVE

As the potential spread of COVID-19 sparked by imported cases from overseas will pose continuous challenges, it is essential to estimate the effects of control measures on reducing the importation risk of COVID-19. Our objective is to provide a framework of methodology for quantifying the combined effects of entry restrictions and travel quarantine on managing the importation risk of COVID-19 and other pandemics by leveraging different sets of parameters.

METHODS

Three major categories of control measures on controlling importation risk were parameterized and modelled by the framework: 1) entry restrictions, 2) travel quarantine, and 3) domestic containment measures. Integrating the parameterized intensity of control measures, a modified SEIR model was developed to simulate the case importation and local epidemic under different scenarios of global epidemic dynamics. A web-based tool was also provided to enable interactive visualization of epidemic simulation.

RESULTS

The simulated number of case importation and local spread modelled by the proposed framework of methods fitted well to the historical epidemic curve of China and Singapore. Based on the simulation results, the total numbers of infected cases when reducing 30% of visitor arrivals would be 88·4 (IQR 87·5-89·6) and 58·8 (IQR 58·3-59·5) times more than those when reducing 99% of visitor arrivals in mainland China and Singapore respectively, assuming actual time-varying R_t and travel quarantine policy. If the number of global daily new infections reached 100,000, 85%-91% of inbound travels should be reduced to keep the daily new infected number below 100 for a country with a similar travel volume as Singapore (daily 52,000 tourist arrivals in 2019). Whereas if the number was lower than 10,000, the daily new infected case would be less than 100 even with no entry restrictions.

DISCUSSIONS

We proposed a framework that first estimated the intensity of travel restrictions and local containment measures for countries since the first overseas imported case. Our approach then quantified the combined effects of entry restrictions and travel quarantine using a modified SEIR model to simulate the potential epidemic spread under hypothetical intensities of these control measures. We also developed a web-based system that enables interactive simulation, which could serve as a valuable tool for health system administrators to assess policy effects on managing the importation risk. By leveraging different sets of parameters, it could adapt to any specific country and specific type of epidemic.

CONCLUSIONS

This framework has provided a valuable tool to parameterize the intensity of control measures, simulate both the case importation and local epidemic, and quantify the combined effects of entry restrictions and travel quarantine on managing the importation risk.

Partnership dynamics in mathematical models and implications for representation of sexually transmitted infections: a review

Mathematical models of sexually transmitted disease (STI) are increasingly relied on to inform policy, practice, and resource allocation. Because STI transmission requires sexual contact between two or more people, a model's ability to represent the dynamics of sexual partnerships can influence the validity of findings. This ability is to a large extent constrained by the model type, as different modeling frameworks vary in their capability to capture patterns of sexual contact at individual, partnership, and network levels. In this paper, we classify models into three groups: compartmental, individual-based, and statistical network models. For each framework, we describe the basic model structure and discuss key aspects of sexual partnership dynamics: how and with whom partnerships are formed, partnership duration and dissolution, and temporal overlap in partnerships (concurrency). We illustrate the potential implications of accurately accounting for partnership dynamics, but these effects depend on characteristics of both the population and pathogen; the combined impact of these partnership and epidemiologic dynamics can be difficult to predict. While each of the reviewed model frameworks may be appropriate to inform certain research or policy questions, modelers and consumers of models should carefully consider the implications of sexual partnership dynamics for the questions under study.

A Deterministic Compartmental Modeling Framework for Disease Transmission

Mathematical models for the spread of diseases help us understand the mechanisms on how diseases spread, evaluate the possible effects of interventions, predict outcomes of epidemics, and forecast the course of outbreaks. Compartmental models are widely used in synthetic biology since they can represent a biological system as an assembly of various parts or compartments with different functions. Here we present a framework for the analysis of a compartmental model for the transmission of diseases using ordinary differential equations. We apply this method on a study about the spread of tuberculosis.

Flattening the curve is flattening the complexity of covid-19

Since the February 2020 publication of the article 'Flattening the curve' in The Economist, political leaders worldwide have used this expression to legitimize the introduction of social distancing measures in fighting Covid-19. In fact, this expression represents a complex combination of three components: the shape of the epidemic curve, the social distancing measures and the reproduction number [Formula: see text]. Each component has its own history, each with a different history of control. Presenting the control of the epidemic as flattening the curve is in fact flattening the underlying natural-social complexity. The curve that needs to be flattened is presented as a bell-shaped curve, implicitly suggesting that the pathogen's spread is subject only to natural laws. The [Formula: see text] value, however, is, fundamentally, a metric of how a pathogen behaves within a social context, namely its numerical value is affected by sociopolitical influences. The jagged and erratic empirical curve of Covid-19 illustrates this. Although the virus has most likely infected only a small portion of the total susceptible population, it is clear its shape has changed drastically. This changing shape is largely due to sociopolitical factors. These include shifting formal laws and policies, shifting individual behaviors as well as shifting various other social norms and practices. This makes the course of Covid-19 curve both erratic and unpredictable.

Infection dynamics and persistence of hepatitis E virus on pig farms - a review

Background

Hepatitis E virus (HEV) genotype 3 and 4 is a zoonosis that causes hepatitis in humans. Humans can become infected by consumption of pork or contact with pigs. Pigs are the main reservoir of the virus worldwide and the virus is present on most pig farms.

Main body

Though HEV is present on most farms, the proportion of infected pigs at slaughter and thus the level of exposure to consumers differs between farms and countries. Understanding the cause of that difference is necessary to install effective measures to lower HEV in pigs at slaughter. Here, HEV studies are reviewed that include infection dynamics of HEV in pigs and on farms, risk factors for HEV farm prevalence, and that describe mechanisms and sources that could generate persistence on farms. Most pigs become infected after maternal immunity has waned, at the end of the nursing or beginning of the fattening phase. Risk factors increasing the likelihood of a high farm prevalence or proportion of actively infected slaughter pigs comprise of factors such as farm demographics, internal and external biosecurity and immunomodulating coinfections. On-farm persistence of HEV is plausible, because of a high transmission rate and a constant influx of susceptible pigs. Environmental sources of HEV that enhance persistence are contaminated manure storages, water and fomites.

Conclusion

As HEV is persistently present on most pig farms, current risk mitigation should focus on lowering transmission within farms, especially between farm compartments. Yet, one should be aware of the paradox of increasing the proportion of actively infected pigs at slaughter by reducing transmission insufficiently. Vaccination of pigs may aid HEV control in the future.

Mathematical modeling with optimal control analysis of social media addiction

In this paper, we developed a deterministic mathematical model of social media addiction (SMA) with an optimal control strategy. Major qualitative analysis like the social media addiction free equilibrium point (E ₀), endemic equilibrium point (E∗), basic reproduction number ( R 0 ) , were computed. From the stability analysis, we found that the social media addiction free equilibrium point (SMAFEP) is locally asymptotically stable if R 0 < 1 . The global asymptotic stablity of SMAFEP is stablished using Castillo-Chavez theorem. If R 0 > 1 the unique endemic equilibruim is locally assymptotically stable. Also using Center Manifold theorem, the model exhabits a forward bifurcation at R 0 = 1 . The sensitivity of model parameters is done using the normalized forward sensitivity index definition. Secondly, we introduced two time dependent controls on the basic model and formulated an optimal control model. Then, we used the Pontryagin's maximum principle to find the optimal system of the model. Numerical simulations, on the optimal control problem using the fourth-order Range-Kutta forward-backward sweep method, on the suggested strategies for SMA is performed. We found that to effectively control SMA at a specified period of time, stakeholders and policymakers must apply the integrated control strategies C.

A metapopulation network model for the spreading of SARS-CoV-2: Case study for Ireland

We present preliminary results on an all-Ireland network modelling approach to simulate the spreading the Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS-CoV-2), commonly known as the coronavirus. In the model, nodes correspond to locations or communities that are connected by links indicating travel and commuting between different locations. While this proposed modelling framework can be applied on all levels of spatial granularity and different countries, we consider Ireland as a case study. The network comprises 3440 electoral divisions (EDs) of the Republic of Ireland and 890 superoutput areas (SOAs) for Northern Ireland, which corresponds to local administrative units below the NUTS 3 regions. The local dynamics within each node follows a phenomenological SIRX compartmental model including classes of Susceptibles, Infected, Recovered and Quarantined (X) inspired from Science 368, 742 (2020). For better comparison to empirical data, we extended that model by a class of Deaths. We consider various scenarios including the 5-phase roadmap for Ireland. In addition, as proof of concept, we investigate the effect of dynamic interventions that aim to keep the number of infected below a given threshold. This is achieved by dynamically adjusting containment measures on a national scale, which could also be implemented at a regional (county) or local (ED/SOA) level. We find that - in principle - dynamic interventions are capable to limit the impact of future waves of outbreaks, but on the downside, in the absence of a vaccine, such a strategy can last several years until herd immunity is reached.

A metapopulation network model for the spreading of SARS-CoV-2: Case study for Ireland

We present preliminary results on an all-Ireland network modelling approach to simulate the spreading the Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS-CoV-2), commonly known as the coronavirus. In the model, nodes correspond to locations or communities that are connected by links indicating travel and commuting between different locations. While this proposed modelling framework can be applied on all levels of spatial granularity and different countries, we consider Ireland as a case study. The network comprises 3440 electoral divisions (EDs) of the Republic of Ireland and 890 superoutput areas (SOAs) for Northern Ireland, which corresponds to local administrative units below the NUTS 3 regions. The local dynamics within each node follows a phenomenological SIRX compartmental model including classes of Susceptibles, Infected, Recovered and Quarantined (X) inspired from Science 368, 742 (2020). For better comparison to empirical data, we extended that model by a class of Deaths. We consider various scenarios including the 5-phase roadmap for Ireland. In addition, as proof of concept, we investigate the effect of dynamic interventions that aim to keep the number of infected below a given threshold. This is achieved by dynamically adjusting containment measures on a national scale, which could also be implemented at a regional (county) or local (ED/SOA) level. We find that - in principle - dynamic interventions are capable to limit the impact of future waves of outbreaks, but on the downside, in the absence of a vaccine, such a strategy can last several years until herd immunity is reached.

SARS-COV-2 outbreak and control in Kenya - Mathematical model analysis

The coronavirus disease 2019 (COVID-19) pandemic reached Kenya in March 2020 with the initial cases reported in the capital city Nairobi and in the coastal area Mombasa. As reported by the World Health Organization, the outbreak of COVID-19 has spread across the world, killed many, collapsed economies and changed the way people live since it was first reported in Wuhan, China, in the end of 2019. As at the end of December 2020, it had led to over 2.8 million confirmed cases in Africa with over 67 thousand deaths. The trend poses a huge threat to global public health. Understanding the early transmission dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas. We employed a SEIHCRD mathematical transmission model with reported Kenyan data on cases of COVID-19 to estimate how transmission varies over time. The model is concise in structure, and successfully captures the course of the COVID-19 outbreak, and thus sheds light on understanding the trends of the outbreak. The next generation matrix approach was adopted to calculate the basic reproduction number (R 0) from the model to assess the factors driving the infection. The model illustrates the effect of mass testing on COVID-19 as well as individual self initiated behavioral change. The results have significant impact on the management of COVID-19 and implementation of prevention policies. The results from the model analysis shows that aggressive and effective mass testing as well as individual self initiated behaviour change play a big role in getting rid of the COVID-19 epidemic otherwise the rate of infection will continue to increase despite the increased rate of recovery.