Covid-19 Models and Model Fitting
Keywords:COVID-19 models, deterministic models, model ﬁtting, control relevance
AbstractThe paper discusses how to use cumulative conﬁrmed infected numbers to ﬁnd basic infection parameters. Next, an extension of the SEIR model, the SEICUR model from the literature (a renaming of the SEIRU model) is introduced, with details of how to compute the full set of model parameters, as well as the reproduction number R. A discussion is given of how the infection rate parameter relates to mitigation policy and various natural variations. Based on a simple mitigation model, an equivalent mitigation policy is found for Italy, Spain, and Norway. An indication of how to use feedback control theory to develop mitigation policy planning is given.
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, Oulu, Finland, September 21–23, 2021.
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.
Iman Rahimi, Fang Chen, and Amir H. Gandomi. A review on COVID-19 forecasting models. Neural Computing and Applications, 2021. doi:https://doi.org/10.1007/s00521-020-05626-8.
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.
Steven Sanche, Yen Ting Lin, Chonggang Xu, Ethan Romero-Severson, Nick Hengartner, and Ruian Ke. High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2. Emerging Infectious Diseases, 26(7), July 2020. ISSN 1080-6059. URL https://wwwnc.cdc.gov/eid/article/26/7/20-0282_article.
Yu Wu, Wenzhan Jing, Jue Liu, Qiujue Ma, Jie Yuan, Yaping Wang, Min Du, and Min Liu. Effects of temperature and humidity on the daily new cases and new deaths of COVID-19 in 166 countries. Science of the Total Environment, 729(139051), August 2020. doi:https://doi.org/10.1016/j.scitotenv.2020.139051.
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.
Copyright (c) 2022 Bernt Lie
This work is licensed under a Creative Commons Attribution 4.0 International License.