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Stability of Disease Free Equilibria in Epidemiological Models

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Abstract.

In this paper we study the structural properties of epidemiological models and we derive a necessary and sufficient condition for the stability of their disease free equilibria. We then show that for a large class of models our condition may be explicitly obtained by using symbolic computation tools. We also give a sufficient condition for the global stability of the disease free equilibrium.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, P.O. Box 2390, Marrakech, Morocco

    M’hammed El Kahoui

  2. IRMAR, Université de Rennes 1, Campus de Beaulieu, F-35042, Rennes, CEDEX France

    Adamou Otto

  3. Département de Mathématiques et Informatique, FS de l’U.A.M de Niamey, BP 10662, Niamey, Niger

    Adamou Otto

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  1. M’hammed El Kahoui
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  2. Adamou Otto
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Correspondence to M’hammed El Kahoui.

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Kahoui, M.E., Otto, A. Stability of Disease Free Equilibria in Epidemiological Models. Math.Comput.Sci. 2, 517–533 (2009). https://doi.org/10.1007/s11786-008-0068-0

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  • DOI: https://doi.org/10.1007/s11786-008-0068-0

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