Permanence and extinction for a nonautonomous avian-human influenza epidemic model with distributed time delay

In this paper we have constructed a mathematical model to interpret the spread of wild avian influenza from the birds to the humans, after the emergence of mutant avian influenza, with nonautonomous ordinary differential equations and distributed time delay due to the intracellular delay between initial infection of a cell and the release of new virus particles. The bird population is divided into two classes: susceptible birds and infected birds with wild avian influenza, by a S I compartmental model. The human population is divided into four classes, namely susceptible humans, humans infected with wild avian influenza, humans infected with mutant avian influenza, and recovered humans from mutant avian influenza, by a S I R compartmental model. Here, we have established some sufficient conditions on the permanence and extinction of the disease by using inequality analytical techniques. By a Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.