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.
Highlights
Avian Influenza, an acute infectious disease caused by influenza A virus, is a complicated disease that can infect poultry and infect humans who have direct exposure to infected birds or contaminated environments
Based on a recent avian influenza SI-SIR model with logistic growth for birds, we propose a stochastic model with generalized incidence rate
From the viewpoint of biology, the noise intensity in the infected birds plays a key role in the evolutionary dynamics
Summary
Avian Influenza, an acute infectious disease caused by influenza A virus, is a complicated disease that can infect poultry and infect humans who have direct exposure to infected birds or contaminated environments. Meng et al [14] showed that a large stochastic disturbance can cause infectious diseases to go to extinction, and Li et al [15] found that the average number of infected individuals always with the increase of noise intensity. These observations imply that stochastic disturbance is conductive to epidemic diseases control. Many researches choose white noise as an appropriate representation of environmental random fluctuations and study the effect of stochastic disturbance on the dynamics of epidemic models. Around the unique endemic equilibrium of system (2) is investigated
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