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

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  • Zhang, Suxia
  • Guo, Hongbin

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.

Suggested Citation

  • Zhang, Suxia & Guo, Hongbin, 2018. "Global analysis of age-structured multi-stage epidemic models for infectious diseases," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 214-233.
    • Handle: RePEc:eee:apmaco:v:337:y:2018:i:c:p:214-233
    DOI: 10.1016/j.amc.2018.05.020
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    Cited by:

    1. Chao Liu & Peng Chen & Qiyu Jia & Lora Cheung, 2022. "Effects of Media Coverage on Global Stability Analysis and Optimal Control of an Age-Structured Epidemic Model with Multi-Staged Progression," Mathematics, MDPI, vol. 10(15), pages 1-28, August.

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