A Model Analysis for the Transmission Dynamics of Avian Influenza

Abstract

This paper examines the transmission dynamics of avian influenza. A nonlinear mathematical model for the problem is formulated and analysed. For the prevalence of the disease and the ease of analysis, we considered the model in proportions of susceptible, infectious, isolated and recovered compartments. The basic reproduction number was computed and used to prove the stability of the disease free equilibrium states. It is proved that the basic reproduction number is a decreasing function of the culling rate of infected birds. It is further proved that the disease free equilibrium state is locally asymptotically stable whenever the basic reproduction number is less than unity.

Key words: Avian influenza, Mathematical model, Basic reproduction number. Disease free equilibrium