The identification of the periodic behaviour in an epidemic model

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.