%0 Journal Article
%T Study on a Stochastic Avian Influenza Epidemic Model with Generalized Incidence Rate
%A Shasha Ma
%J Open Journal of Applied Sciences
%P 228-245
%@ 2165-3925
%D 2020
%I Scientific Research Publishing
%R 10.4236/ojapps.2020.105018
%X <span style=\"font-family:Verdana;\">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 </span><span></span><span style=\"font-family:Verdana;\">&nbsp;</span><span style=\"font-family:Verdana;\">is established, and
hence the extinction of disease is investigated. From the viewpoint of biology,
the noise intensity in the infected birds</span><span><span><span style=\"font-family:&quot;\"> </span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">plays
a key role in the evolutionary dynamics. Moreover, we also analyze the
asymptotic behavior around the endemic equilibrium of the corresponding
deterministic model.</span></span></span>
%K Avian Influenza
%K Extinction
%K Ergodic Stationary Distribution
%K Asymptotic Behavior
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=100478