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.