Yoichi Enatsu (University of Tokyo): On the stability of SIRS epidemic models with age of infection and its applications |
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Szerda, 24. Szeptember 2014, 08:45 - 10:00
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| Abstract. In order to investigate the influence of impermanent immunity of diseases on the asymptotic behavior of disease transmission, we consider the dynamics of SIRS epidemic models with age of infection. Choosing an appropriate age-specific transmission coefficient, we provide examples such that the models are re-written as a system of differential equations incorporating distributed delays. When the recovered individuals attain permanent immunity, the global dynamics has been well-understood by formulating epidemic models without cyclic structures such as SIR models. However, if this is not the case, there is still an open problem for the stability of an endemic equilibrium. Between the delayed models and age-structured models, we aim to fill the gap of the local and global asymptotic stability of the endemic equilibrium by giving recent results when the basic reproduction number is greater than unity. |
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