Numerical Simulation for the Transmission Dynamics of Avian Influenza

Abstract

This paper presents numerical simulations for the transmission dynamics of avian influenza using the model formulated and analysed by Kimbir etal (2014). It is proved that the disease free equilibrium state is locally asymptotically stable whenever the reproduction number is less than unity. The implication is that if the reproduction number is less than unity, the infection is controlled or eradicated and the disease persists otherwise. The numerical simulations are consistent with the local stability of the disease-free states. The simulations further reveals that the infection transmission rate constitutes an essential parameter for an epidemic to occur, thus efforts should be geared at bringing the infection transmission to the lowest level in order to ensure eradication. It was also shown from the study that increasing culling of infected birds, will reduce the disease progression within the birds’ population thereby, reducing the transmission of avian influenza. Effective isolation of infected individuals without culling is vital to eradicating the disease transmission, but a combined effective use of culling of infected birds and isolation of infected humans is a strong control measure against pandemics.

Key words: Avian influenza, Mathematical model, Basic reproduction number, Numerical simulations