Basic Reproduction Ratios for Almost Periodic Compartmental Epidemic Models

By Bin-Guo Wang, Xiao-Qiang Zhao. Journal of Dynamics and Differential Equations, 2013

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The theory of the basic reproduction ratio R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}$$\end{document} and its computation formulae for almost periodic compartmental epidemic models are established. It is shown that the disease-free almost periodic solution is stable if R0<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}<1$$\end{document}, and unstable if R0>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}>1$$\end{document}. We also apply the developed theory to a patchy model with almost periodic population dispersal and disease transmission coefficients to obtain a threshold type result for uniform persistence and global extinction of the disease.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/daea3b8a69b719e2a5612c6d1363f04af15351ed