Dynamical Behavior of a New Epidemiological Model

Zizi Wang and Zhiming Guo

Journal of Applied Mathematics, 2014, vol. 2014, 1-9

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 . The existence, uniqueness, and stability of the disease-free equilibrium and endemic equilibrium are discussed. The basic reproductive number 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 ; if , 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 is also addressed.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:854528

DOI: 10.1155/2014/854528

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