Global analysis of age-structured multi-stage epidemic models for infectious diseases

Suxia Zhang and Hongbin Guo

Applied Mathematics and Computation, 2018, vol. 337, issue C, 214-233

Abstract: We formulate a multi-stage SEIR model for infectious diseases with continuous age structure for each successive infectious stage during a long infective period. The model can describe disease progression through multiple infectious stages as in the case of HIV, hepatitis B and hepatitis C. Mathematical analysis shows that the global dynamics are completely determined by the basic reproductive number R0. If R0≤1, the disease-free equilibrium is globally asymptotically stable and the disease dies out. If R0>1, a unique endemic equilibrium is globally asymptotically stable, and the disease persists at the endemic equilibrium. The proof of global stability of endemic equilibria utilizes a Lyapunov functional. Numerical simulations are illustrated and model generalization is also discussed.

Keywords: Disease progression; Multiple stage; Age structure; Global stability; Lyapunov functional (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:337:y:2018:i:c:p:214-233

DOI: 10.1016/j.amc.2018.05.020

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