SVEIR MODEL OF AN INFECTIOUS DISEASE AMONG INFECTED IMMIGRANTS WITH NONLINEAR INCIDENCE RATE

Abstract

In this paper, the effect of a saturated incidence rate and infectious immigrants on the transmission dynamics of an infectious disease is studied using an SVEIR model. The model exhibits three equilibrium states: the disease-free and endemic equilibrium states when there is no influx of infective immigrants and the endemic equilibrium state when there is an influx of infective immigrants in the population. Besides, the model shows a forward bifurcation when there is no entry of infective immigrants and this aid in establishing the local and global asymptotically stability when the basic reproduction number, R0<1 and R0>1 respectively. Numerical results are performed to examine the effect of the saturated incidence rate and the infective immigrants on disease transmission. The results indicate that the disease could be controlled or eradicated if there is a strict check to ensure that the infected immigrants are treated before they join the population.