Dynamical Behavior of a New Epidemiological Model

Zizi Wang and Zhiming Guo

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

Abstract: A new epidemiological model is introduced with nonlinear incidence, in which the infected disease may lose infectiousness and then evolves to a chronic noninfectious disease when the infected disease has not been cured for a certain time τ. The existence, uniqueness, and stability of the disease‐free equilibrium and endemic equilibrium are discussed. The basic reproductive number R0 is given. The model is studied in two cases: with and without time delay. For the model without time delay, the disease‐free equilibrium is globally asymptotically stable provided that R0 ≤ 1; if R0 > 1, then there exists a unique endemic equilibrium, and it is globally asymptotically stable. For the model with time delay, a sufficient condition is given to ensure that the disease‐free equilibrium is locally asymptotically stable. Hopf bifurcation in endemic equilibrium with respect to the time τ is also addressed.

Date: 2014
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https://doi.org/10.1155/2014/854528

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:854528

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