A mathematical model to study resistance and non-resistance strains of influenza

Abstract

Recently, cases of influenza virus resistance are being observed. Resistance is deadly and can cause many pandemics in future. That is why, here we investigate the situation on which the strains exist side – by – side and the difference in their mode of transmission. This paper studies two strain (resistance and non - resistance) flu model. The non-resistant strain mutates to give the resistant strain. These strains are differentiated by their incidence rates which are; bilinear and saturated for the non-resistant and saturated resistant strain respectively. This will help in studying the difference in the mode of transmission of the two strains. Equilibrium solutions are computed and Lyapunov functions are used to show their global stability. It is clear from the analysis that disease – free equilibrium is globally asymptotically stable if maxRR,RN<1. On the other hand endemic equilibrium is globally asymptotically stable if minRR,RN>1. Any strain with biggest basic reproduction ratio out performs the other. In order to support the analytic results some numerical simulations are carried out.