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Stollenwerk N, Estadilla CDS, Mar J, Bidaurrazaga Van-Dierdonck J, Ibarrondo O, Blasco-Aguado R, Aguiar M. The effect of mixed vaccination rollout strategy: A modelling study. Infect Dis Model 2023; 8:318-340. [PMID: 36945695 PMCID: PMC9998287 DOI: 10.1016/j.idm.2023.03.002] [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: 10/20/2022] [Revised: 02/11/2023] [Accepted: 03/07/2023] [Indexed: 03/12/2023] Open
Abstract
Vaccines have measurable efficacy obtained first from vaccine trials. However, vaccine efficacy (VE) is not a static measure and long-term population studies are needed to evaluate its performance and impact. COVID-19 vaccines have been developed in record time and the currently licensed vaccines are extremely effective against severe disease with higher VE after the full immunization schedule. To assess the impact of the initial phase of the COVID-19 vaccination rollout programmes, we used an extended Susceptible - Hospitalized - Asymptomatic/mild - Recovered (SHAR) model. Vaccination models were proposed to evaluate different vaccine types: vaccine type 1 which protects against severe disease only but fails to block disease transmission, and vaccine type 2 which protects against both severe disease and infection. VE was assumed as reported by the vaccine trials incorporating the difference in efficacy between one and two doses of vaccine administration. We described the performance of the vaccine in reducing hospitalizations during a momentary scenario in the Basque Country, Spain. With a population in a mixed vaccination setting, our results have shown that reductions in hospitalized COVID-19 cases were observed five months after the vaccination rollout started, from May to June 2021. Specifically in June, a good agreement between modelling simulation and empirical data was well pronounced.
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Affiliation(s)
- Nico Stollenwerk
- BCAM-Basque Center for Applied Mathematics, Bilbao, Basque Country, Spain
- Dipartimento di Matematica, Universitá degli Studi di Trento, Povo, Trento, Italy
| | - Carlo Delfin S Estadilla
- BCAM-Basque Center for Applied Mathematics, Bilbao, Basque Country, Spain
- Preventive Medicine and Public Health Department, University of the Basque Country, Leioa, Basque Country, Spain
| | - Javier Mar
- Osakidetza Basque Health Service, Guipúzcoa, Basque Country, Spain
- Biodonostia Health Research Institute, Guipúzcoa, Basque Country, Spain
| | | | - Oliver Ibarrondo
- Osakidetza Basque Health Service, Guipúzcoa, Basque Country, Spain
| | | | - Maíra Aguiar
- BCAM-Basque Center for Applied Mathematics, Bilbao, Basque Country, Spain
- Dipartimento di Matematica, Universitá degli Studi di Trento, Povo, Trento, Italy
- Ikerbasque, Basque Foundation for Science, Bilbao, Basque Country, Spain
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Georgiev SG, Vulkov LG. Coefficient identification in a SIS fractional-order modelling of economic losses in the propagation of COVID-19. JOURNAL OF COMPUTATIONAL SCIENCE 2023; 69:102007. [PMID: 37041821 PMCID: PMC10062717 DOI: 10.1016/j.jocs.2023.102007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/23/2021] [Revised: 11/02/2022] [Accepted: 03/27/2023] [Indexed: 06/19/2023]
Abstract
A fractional-order SIS (Susceptible-Infectious-Susceptible) model with time-dependent coefficients is used to analyse some effects of the novel coronavirus 2019 (COVID-19). This generalized model is suitable for describing the COVID dynamics since it does not presume permanent immunity after contagion. The fractional derivative activates the memory property of the dynamics of the susceptible and infectious population time series. A coefficient identification inverse problem is posed, which consists of reconstructing the time-varying transmission and recovery rates, which are of paramount importance in practice for both medics and politicians. The inverse problem is reduced to a minimization problem, which is solved in a least squares sense. The iterative predictor-corrector algorithm reconstructs the time-dependent parameters in a piecewise-linear fashion. The economic losses emerging from social distancing using the calibrated model are also discussed. A comparison between the results obtained by the classical model and the fractional-order model is included, which is validated by ample tests with synthetic and real data.
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Affiliation(s)
- Slavi G Georgiev
- Department of Informational Modeling, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. Georgi Bonchev Str., 1113 Sofia, Bulgaria
- Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Str., 7004 Ruse, Bulgaria
| | - Lubin G Vulkov
- Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Str., 7004 Ruse, Bulgaria
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Critical fluctuations in epidemic models explain COVID-19 post-lockdown dynamics. Sci Rep 2021; 11:13839. [PMID: 34226646 PMCID: PMC8257671 DOI: 10.1038/s41598-021-93366-7] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2021] [Accepted: 06/24/2021] [Indexed: 11/09/2022] Open
Abstract
As the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. The momentary reproduction ratio r(t) of an epidemic is used as a public health guiding tool to evaluate the course of the epidemic, with the evolution of r(t) being the reasoning behind tightening and relaxing control measures over time. Here we investigate critical fluctuations around the epidemiological threshold, resembling new waves,
even when the community disease transmission rate \documentclass[12pt]{minimal}
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\begin{document}$$\beta$$\end{document}β is not significantly changing. Without loss of generality, we use simple models that can be treated analytically and results are applied to more complex models describing COVID-19 epidemics. Our analysis shows that, rather than the supercritical regime (infectivity larger than a critical value, \documentclass[12pt]{minimal}
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\begin{document}$$\beta > \beta _c$$\end{document}β>βc) leading to new exponential growth of infection, the subcritical regime (infectivity smaller than a critical value, \documentclass[12pt]{minimal}
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\begin{document}$$\beta < \beta _c$$\end{document}β<βc) with small import is able to explain the dynamic behaviour of COVID-19 spreading after a lockdown lifting, with \documentclass[12pt]{minimal}
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\begin{document}$$r(t) \approx 1$$\end{document}r(t)≈1 hovering around its threshold value.
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Krause AL, Kurowski L, Yawar K, Van Gorder RA. Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies. J Theor Biol 2018; 449:35-52. [PMID: 29673907 DOI: 10.1016/j.jtbi.2018.04.023] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2017] [Revised: 02/17/2018] [Accepted: 04/15/2018] [Indexed: 10/17/2022]
Abstract
While deterministic metapopulation models for the spread of epidemics between populations have been well-studied in the literature, variability in disease transmission rates and interaction rates between individual agents or populations suggests the need to consider stochastic fluctuations in model parameters in order to more fully represent realistic epidemics. In the present paper, we have extended a stochastic SIS epidemic model - which introduces stochastic perturbations in the form of white noise to the force of infection (the rate of disease transmission from classes of infected to susceptible populations) - to spatial networks, thereby obtaining a stochastic epidemic metapopulation model. We solved the stochastic model numerically and found that white noise terms do not drastically change the overall long-term dynamics of the system (for sufficiently small variance of the noise) relative to the dynamics of a corresponding deterministic system. The primary difference between the stochastic and deterministic metapopulation models is that for large time, solutions tend to quasi-stationary distributions in the stochastic setting, rather than to constant steady states in the deterministic setting. We then considered different approaches to controlling the spread of a stochastic SIS epidemic over spatial networks, comparing results for a spectrum of controls utilizing local to global information about the state of the epidemic. Variation in white noise was shown to be able to counteract the treatment rate (treated curing rate) of the epidemic, requiring greater treatment rates on the part of the control and suggesting that in real-life epidemics one should be mindful of such random variations in order for a treatment to be effective. Additionally, we point out some problems using white noise perturbations as a model, but show that a truncated noise process gives qualitatively comparable behaviors without these issues.
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Affiliation(s)
- Andrew L Krause
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
| | - Lawrence Kurowski
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
| | - Kamran Yawar
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
| | - Robert A Van Gorder
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK.
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