Inverse problem for a coupling model of reaction-diffusion and ordinary differential equations systems. Application to an epidemiological model

Abstract

This paper investigates an identifiability method for a class of systems of reaction diffusion equations in the L2 framework. This class is composed of a master system of ordinary differential equations coupled with a slave system of diffusion equations. It can model two populations, the second one being diffusive contrary to the first one. The identifiability method is based on an elimination procedure providing relations called input-output polynomials and linking the unknown parameters, the inputs and the outputs of the model. These polynomials can also be used to estimate the parameters as shown in this article. To our best knowledge, such an identifiability method and a parameter estimation procedure have not yet been explored for such a system in the L2 framework. This work is applied on an epidemiological model describing the propagation of the chikungunya in a local population.