Stability Analysis of a Staged Progression Susceptibility Model for Infectious Diseases

The aim of this paper is to provide a stability analysis for models with a general structure and mass action incidence; which include stage progression susceptibility, differential infectivity as well, and the loss of immunity induced by the vaccine also. We establish that the global dynamics are completely determined by the basic reproduction number R۰. More specifically, we prove that when R۰ is smaller or equal to one, the disease free equilibrium is globally asymptotically stable; while when it is greater than one, there exist a unique endemic equilibrium. We also provide sufficient conditions for the global asymptotic stability of the endemic equilibrium.

Keywords:

Differential susceptibility , differential infectivity , waning vaccine induced immunity , Lyapunov methods