Optimal control in coupled within-host and between-host models

Abstract

We formulate an immuno-epidemiological model of coupled within-host model of ODEs and between-host model of ODE and PDE, using the Human Immunodeficiency Virus (HIV) for illustration. Existence and uniqueness of solution to the between-host model is established, and an explicit expression for the basic reproduction number of the between-host model derived. Stability of disease-free and endemic equilibria is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed; these results are novel for optimal control of ODEs linked with such first order PDEs. Numerical simulations based on the forward-backward sweep method are obtained. © EDP Sciences, 2014