Extended Covid-19 Models

Authors

  • Bernt Lie

DOI:

https://doi.org/10.3384/ecp21185497

Keywords:

COVID-19 models, deterministic models, complex models, vaccination policy

Abstract

The paper discusses how to extend the SEICUR model with a description of migration. Next, the SEICUR model is extended with a description of age distribution, for the case that infection and serious illness depends on age. Finally, the SEICUR model is extended with models of vaccination. Simulation of the SEICUR model for Italy and Spain indicated that the number of migrants per day between the two countries need to be relatively large before a significant change in infection is noticed. However, this was based on the assumption of average spreaders among the migrants. The age distribution model is mainly of use when considering serious illness and death, and was not pursued further. Vaccination data for Italy, Spain, and Norway, shows that for countries with a low fraction of infected (e.g., Norway), vaccination allows for a noticeable relaxation in mitigation, while for countries which already have a high fraction of infected (e.g., Spain), the effect of vaccination is relatively smaller due to the larger fraction of people already recovered. The extended models allow for a more realistic study of COVID-19 spread, and how to optimize mitigation policies vs. vaccination.

References

Fred Brauer, Carlos Castillo-Chavez, and Zhilan Feng. Mathematical Models in Epidemiology. Number 69 in Texts in Applied Mathematics. Springer, New York, 2019. ISBN 978-1-4939-9826-5.

Bernt Lie. Epidemiological Models and Process Engineering. In Proceedings, SIMS EUROSIM 2021, Oulo Finland, September 21–23., 2021a.

Bernt Lie. COVID-19 Models and Model Fitting. In Proceedings, SIMS EUROSIM 2021, Oulo Finland, September 21–23., 2021b.

Z. Liu, P. Magal, O. Seydi, and G.Webb. A COVID-19 epidemic model with latency period. Infectious Disease Modelling, 5: 323–337, 2020a. doi:10.1016/j.idm.2020.03.003.

Zhihua Liu, Pierre Magal, Ousmane Seydi, and Glenn Webb. A model to predict covid-19 epidemics with applications to south korea, italy and spain. SIAM News, 2020b. https://sinews.siam.org/Details-Page/a-model-to-predictcovid-19-epidemics-with-applications-to-south-korea-italyand-spain.

Zhihua Liu, Pierre Magal, and Glenn F Webb. Predicting the number of reported and unreported cases for the COVID-19 epidemics in china, south korea, italy, france, germany and united kingdom. apr 2020c. doi:10.1101/2020.04.09.20058974.

Leonardo López and Xavier Rodó. A modified SEIR model to predict the COVID-19 outbreak in Spain and Italy: simulating control scenarios and multi-scale epidemics. Results in Physics, 2020. doi:10.1016/j.rinp.2020.103746. URL https://pubmed.ncbi.nlm.nih.gov/ 33391984/.

Stig Øyvann. Jakten på en presis beskrivelse av epidemien. Computerworld, 38(6):26–30, December 2020.

Christopher Rackauckas and Qing Nie. DifferentialEquations.jl — A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia. Journal of Open Research Software, 5(15), 2017a. doi:10.5334/jors.151.

Christopher Rackauckas and Qing Nie. Adaptive methods for stochastic differential equations via natural embeddings and rejection sampling with memory. Discrete and continuous dynamical systems. Series B, 22(7):2731, 2017b.

Christopher Rackauckas and Qing Nie. Stability-Optimized High Order Methods and Stiffness Detection for Pathwise Stiff Stochastic Differential Equations. arXiv:1804.04344 [math], 2018. URL http://arxiv.org/abs/1804. 04344.

Jr. Reiner, Robert C., Ryan M. Barber, James K. Collins, and more. Modeling COVID-19 scenarios for the United States. Nature Medicine, 27:94–105, 2021. doi:https://doi.org/10.1038/s41591-020-1132-9.

Aleksa Zlojutro, David Rey, and Lauren Gardner. A decisionsupport framework to optimize border control for global outbreak mitigation. Scientific Reports, (2216), 2019. doi:https://doi.org/10.1038/s41598-019-38665-w.

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Published

2022-03-31