Individual behavior and epidemiological model

International audience In this paper, some results of existence and uniqueness of solution of a semi-linear parabolic problem describing the evolution of a population subjected to a disease are presented. The population is structured into two compartments the healthy individuals and the infected individuals who interact between them. A continuous variable representing a behavioral risk is introduced. The asymptotic in time of the problem is studied, and the existence of a non zero stationary state is proved. The question we would like to investigate is does it exist a segmentation of the population (here a safety group and a risky group) in the same way as in food models with two nutriments. To answer this question, some numerical results concerning the distribution of the population according to the variable representing a behavioral risk are presented within the disease of the HIV-AIDS in Mali.