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.