[Back]

I. Zeiler:
"Optimal Control in a SI Model for HIV";
Talk: Advanced Course on Epidemiology of Infectious Diseases, Oeiras, Portugal; 2006-04-10 - 2006-04-14.

We discuss an epidemiological SI model of the sexual transmission of HIV/AIDS with a constant recruitment rate and varying population size. In contrast to previous work done the effect of prevalence on the incidence rate is assumed to be twofold. Like in classical models it increases the per-susceptible incidence, but additionally it is assumed that a higher prevalence itself leads to an increased awareness of the disease and therewith to an incidence rate that is marginally decreasing or, after reaching a maximum, actually decreasing with prevalence. We derive a threshold for such behaviour depending on a factor of risk perception and do some numerical analysis.

With this dynamics a non-linear, autonomous, infinite time horizon optimal control problem with two states and one control is formulated. The decision maker seeks to minimize the discounted stream of the total costs of a HIV epidemic, which are consisting of the social costs caused by the disease and the monetary costs for the control instrument, which describes the optimal policy of screening out a certain fraction of infected individuals from the sexually active population and taking them into treatment. The optimal control problem is solved by applying Pontryagin´s Minimum Principle.