Liu, M., Huang, J., Ruan, S. and Yu, P. (2019) Bifurcation Analysis of an SIRS Epidemic Model with a Generalized Nonmonotone and Saturated Incidence Rate. Journal of Differential Equations, 267, 1859-1898.
https://doi.org/10.1016/j.jde.2019.03.005

has been cited by the following article:

• TITLE: Study on a Stochastic Avian Influenza Epidemic Model with Generalized Incidence Rate

  AUTHORS: Shasha Ma

  KEYWORDS: Avian Influenza, Extinction, Ergodic Stationary Distribution, Asymptotic Behavior

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.10 No.5, May 27, 2020

  ABSTRACT: Avian Influenza, with a high mortality rate in human population, is considered to be one of the most significant potential threats to human beings. Based on a recent avian influenza SI-SIR model with logistic growth for birds, we propose a stochastic model with generalized incidence rate. For the stochastic avian-only system, sufficient conditions for the extinction of infected birds are established, and the existence of a unique ergodic stationary distribution is also obtained. For the stochastic avian-human system, a threshold number is established, and hence the extinction of disease is investigated. From the viewpoint of biology, the noise intensity in the infected birds plays a key role in the evolutionary dynamics. Moreover, we also analyze the asymptotic behavior around the endemic equilibrium of the corresponding deterministic model.