A mathematical model for the control of malaria

Abstract

Many infectious diseases including malaria are preventable, yet they remain endemic in many communities due to lack of proper, adequate and timely control policies. Strategies for controlling the spread of any infectious disease include a rapid reduction in both the infected and susceptible populations. (if a cure is available) as well as a rapid reduction in the susceptible class if a vaccine is available. For diseases like malaria where there is no vaccine, it is still possible to reduce the susceptible class through a variety of control measures. In this dissertation, we have developed a mathematical model for the transmission of malaria. We have shown that the model has a unique disease-free and endemic equilibria. The disease-free equilibrium Is locally and globally asymptotically stable, if R <_ 1, and that the endemic equilibrium exist provided Ro > 1. Simulation of the model clearly shows that, with a proper combination of treatment and a concerted effort aimed at prevention, malaria can be eliminated from our community. It is not necessary (or impossible) to kill all mosquitoes in order to eliminate malaria. In fact, effective treatment offered to about 50% of the infected population, together with about 50% prevention rate is all that is required to eliminate the disease.