Controlling the Spread of a Vector Borne Epidemic: The Case of Malaria

As an application of the man–environment model presented in Section 1.3 , we shall consider a malaria epidemic system. In this case the environmental pollution is represented by the infective insect vector population, i.e., the infected mosquito population. We have considered a generalization of the classical Ross–Macdonald model, according to which malaria is an SIS system for which human infectives after recovery may go back to the susceptible state. We have extended the (linear) response of the Ross–Macdonald model, by using a possibly nonlinear functional response. This choice may allow possible saturation effects, \(\sigma -\) type responses, etc. For example behavioral changes can be taken into account; for a very large density of the infective population, the force of infection may tend to reduce itself because of the reduction of open exposure of the human population. We concentrate on a problem of diminishment of a spatially structured malaria epidemic, by acting on the segregation of the human and the mosquito populations via, e.g., treated bed nets. Optimal control problems have been analyzed with respect to both the parameters of the model and with respect to the region of intervention. All has been supported by a set of numerical simulations.