A mixed program for parasitic disease control

In this paper we are concerned with the control of a parasitic disease by a permanent, time-continuous mixed program of vector reduction (reduction of the contact rate) and drug application. We shall use the model developed in [1] with two control functions: one for the reduction of the contact rate and another for the administration of drugs to the population. This model takes into account the possibility that there may by a certain fraction of the population which cannot be covered by any drug application. Optimal control policies for reduction of the contact rate and for the protected proportion of the population by drugs are derived by using Pontryagin's maximum principle. A cost-optimal strategy is deduced for the maintenance of the affected proportion of the population below a given level. Some numerical examples are computed.