Mathematical study of a model with a density-dependent contact rate

Abstract

In this manuscript, we consider a parabolic epidemic system modelling the transmission of diseases like Hepatitis B
with a general density dependent rate in a closed population and bounded domain. Our model takes into account
diffusion of population as well as two classes of infected individuals: the chronic carriers and the acute infected humans.
Based on realistic assumptions, we study the existence of a
solution for the model and look for steady states using critical points or perturbation arguments.