The identification of the periodic behaviour in an epidemic model |
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Authors: | Giovanni Di Lena Gabriella Serio |
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Affiliation: | (1) Dipartimento di Matematica, Palazzo Ateneo, 70121 Bari, Italy;(2) Istituto di Igiene Policlinico, Università di Bari, 70121 Bari, Italy |
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Abstract: | In this paper we study a method for the identification of the unknown parameter of the periodic function and also the first component of the state vector, in a mathematical model which describes the evolution of some diseases with an oro-fecal transmission.To solve the identification problem we use a numerical method to integrate the differential equations system, which reproduces the stability properties of the above mentioned continuous system.The numerical methods which we propose can be applied also to a spatial semi discretization of the reaction-diffusion model which is a diffusive generalization of the system that we consider in this paper.Finally, through an analysis on both the continuous and the discrete system we also obtain a necessary condition on the experimental data in order that a periodic trajectory of the system exists.Work supported by: Progetto Finalizzato Controllo Malattie da Infezione-CNR and by Ministero Pubblica Istruzione |
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Keywords: | Identification epidemic model periodic solution numerical analysis |
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