Stability Analysis of an SIRI Epidemic Model with Distributed Latent Period

Abstract

In this paper, we investigate the global asymptotic stability of the possible equilibria for an SIRI epidemic model with a distributed latent period and a general incidence function. By using the method of Lyapunov functions and the LaSalle invariance principle, we show that the global asymptotic stability is completely determined by the basic reproduction number R0. The originality of this work is to have a basic reproduction number R0 which depends on the distribution of the latent period. Finally, we use a nonstandard discretization method of Mickens to illustrate numerically our theoretical results.

Global Stability of an Sirsi Epidemic Model With a Distributed Delayed and Generalized Incidence Function Amine Bernoussi

“…The latency period is the period during which an individual exposed to the disease can not pass it on to another individual. In the literature, several types of representation are presented, namely the introduction of an additional variable or the inclusion of a deviation in time: the discrete delay or the distributed delay (see [1,2,5,6,7,8,11,12,14,16,20,23,24,25,27,28]). Recently, considerable attention has been paid to model the relapse phenomenon, i.e.…”

“…the return of signs and symptoms of a disease after a remission. Hence, the recovered individual can return to the infectious class (see [5,6]). For the biological explanations of the relapse phenomena, we cite two examples: Malaria and Tuberculosis.…”