Study on a Stochastic Avian Influenza Epidemic Model with Generalized Incidence Rate ()
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.
Share and Cite:
Ma, S. (2020) Study on a Stochastic Avian Influenza Epidemic Model with Generalized Incidence Rate.
Open Journal of Applied Sciences,
10, 228-245. doi:
10.4236/ojapps.2020.105018.
Cited by
No relevant information.