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

We formulate and then analyze a multi-group coupled within-host model of ODEs and between-host model of ODE and first-order PDEs, using the Human Immunodeficiency Virus (HIV) for illustration. The basic reproduction number of the multi-group coupled epidemiological model is derived, steady states solutions are calculated and stability analysis of equilbria is investigated. An optimal control problem for our model with drug treatment on the multi-group within-host system is formulated and analyzed. Ekeland's principle is used in proving existence and uniqueness of an optimal control pair. Numerical simulations based on the semi-implicit finite difference schemes and the forward-backward sweep iterative method are obtained.