On A Model For The Cross Protection Of Two Infectious Diseases

Abstract

This paper studies the effects of the spread of two similarly transmitted infectious diseases with cross protection in an unvaccinated population using a basic SEIR model with vital dynamics (births and deaths). A basic Mathematical model is built-up to study the joint transmission dynamics of diseases in the population. The equilibriums of these models as well as their stabilities are studied. Specifically, the stability results for disease-free and endemic steady states are proven. Finally, numerical simulations of the models are carried out with Matlab / Mathematica to study the behavior of the solutions in different regions of the parameter space.

Keywords: cross protection, infectious diseases, disease-free and endemic equilibria, numerical simulations, joint modeling