Stability Analysis of a Staged Progression Susceptibility Model for Infectious Diseases

Subject Areas : International Journal of Mathematical Modelling & Computations

Jean Pierre II KOUENKAM ¹ , Gilbert Chendjou ² , Jose MBANG ³ , Yves EMVUDU ⁴

1 - Department of Mathematics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
2 - Department of Mathematics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
3 - Laboratory of Applied Mathematics, Department of Mathematics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
4 - Department of Mathematics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon

Received: 2021-06-03 Accepted : 2021-09-13 Published : 2021-12-01

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

Abstract :

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 R0. More specifically, we prove that when R0 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.