Mathematical model for bird flu disease transmission with no bird migration

Abstract

In this paper a mathematical model for the transmission dynamics of bird flu among birds and humans is presented. The model assumes that there is no migration of birds in the susceptible bird population immediately the disease starts. The model formulated is analyzed using dynamical systems theory . The analysis of the steady state and its stability show that the system will be stable if there is a bound on the growth (birth) of birds in the community (αB). This means that the disease will die out after enough time if there is a bound on the growth rate of birds. We also looked at the endemic flu state and showed that the disease will persist if there is a bound on the infection transition rate from birds to birds (βB).

KEY WORDS: Mathematical model, bird – flu disease, transmission, steady state, stability