Mathematical analysis for the dynamics of Feline immunodeficiency virus in cats population

Abstract

In this paper, we present an extended version of the deterministic model of feline immunodeficiency virus (FIV) within cats population to carry out the stability analysis with regards to the total population of cats and disease prevalence. For the extension, we incorporate the compartment of latently infected domestic cats since it is evident that such cats transmit the virus as well. Stability analysis of the presented model is carried out. The analysis reveals that the retrovirus cannot invades the population at carrying capacity state if the threshold parameter, R0 is less than unity. Indeed, we obtain an additional equilibrium point known as semi-trivial state for which the disease exterminate the host population. Moreover, the carrying capacity state can exchange stability with non-trivial equilibrium at R0 = 1 so that the latter will be the only attractor when R_0 > 1, a phenomenon called transcritical bifurcation.