Fluctuations in a SIS epidemic model with variable size population

Abderrahman Iggidr 1 Khadija Niri 2, * Elkhomeini Ould Moulay Ely 2
* Auteur correspondant
1 MASAIE - Tools and models of nonlinear control theory for epidemiology and immunology
LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : In an epidemiological model, time spent in one compartment is often modeled by a delay in the model. In general the presence of delay in differential equations can change the stability of an equilibrium to instability and causes the appearance of oscillatory solutions. In this paper we consider a SIS epidemiological model with demographic effects: birth, mortality and mortality caused by infection. The delay is the period of infection. We define the concept of oscillation in the sense that solutions of the model studied fluctuate around a steady state. Our goal is to show that in this model, there are oscillating solutions for certain parameters values. We determine a large set of initial data for which solutions of this model are slowly oscillating.
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Abderrahman Iggidr, Khadija Niri, Elkhomeini Ould Moulay Ely. Fluctuations in a SIS epidemic model with variable size population. Applied Mathematics and Computation, Elsevier, 2010, 217 (1), pp.55-64. 〈http://www.sciencedirect.com/science/article/B6TY8-4YKGJ16-3/2/994381a120a4a11cfc4e5726c8c5cff3〉. 〈10.1016/j.amc.2010.03.040〉. 〈inria-00551771〉

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