Journal of Advances in Applied Mathematics

Download PDF (337.4 KB) PP. 211 - 221 Pub. Date: October 1, 2016

DOI: 10.22606/jaam.2016.14002

• Amine Bernoussi^*
  Université Ibn Tofail, Faculté des Sciences, Département de Mathématiques, Kénitra, Morocco
• Abdelilah Kaddar
  Université Mohammed V de Rabat, Faculté des Sciences Juridiques, Economiques et Sociales - Salé, Morocco
• Said Asserda
  Université Ibn Tofail, Faculté des Sciences, Département de Mathématiques, Kénitra, Morocco

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.

Epidemic model, distributed time delay, Lyapunov function, global stability

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