Epidemic Models Structured by Immunological Variables

We develop a differential-integral equation model of epidemics in an animal population structured by immunological variables such as mean viral load and mean T-cell density. The population is subdivided into susceptible individuals whose dynamics is modeled by an ordinary differential equation, and infected/infectious individuals structured by immunological state summarized in a vector variable, Y say, whose evolution is described by a dynamical system. The dynamics of the infected population is modeled by a partial differential equation of the so-called “size-structured” type, with boundary condition corresponding to newly acquired infections.

We present some theoretical results about existence and uniqueness of solutions in a simplified setting. The general question of well-posedness for the model is an open problem. We finally present the results of some numerical experiments corresponding to HIV infection.