Stability Analysis of a Staged Progression Susceptibility Model for Infectious Diseases

International Journal of Mathematical Modelling & Computations

مقاله 3، دوره 11، 4 (Fall) - شماره پیاپی 44، اسفند 2021، صفحه 1-37   

نوع مقاله: Full Length Article

شناسه دیجیتال (DOI): 10.30495/ijm2c.2021.685128

نویسندگان

Jean Pierre II KOUENKAM¹؛ Gilbert Chendjou¹؛ Jose MBANG^{* 2}؛ Yves EMVUDU¹

¹Department of Mathematics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon

²Laboratory of Applied Mathematics, Department of Mathematics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon

چکیده

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.

کلیدواژه‌ها

Differential susceptibility؛ Differential infectivity؛ Waning vaccine induced immunity؛ Lyapunov methods