Mathematical Model for the Study of Malaria Transmission

Abstract

In this paper, an ordinary differential equation mathematical model is proposed to study the spread of malaria in human populations due to mosquitoes. Here we have considered compartments for the spread of malaria with a susceptible-infectious-recovered-susceptible (S-I-R-S) pattern for humans and a susceptible-infectious (S-I) pattern for mosquitoes. In addition, we have introduced the effect of applying control measures to reduce the concentration of waste material, household and industrial discharges to control the spread of the disease. It is found that if the control measures are applied then the concentration of waste material, population of infected humans and the population of infected mosquitoes reduce. In view of this a control epidemiological model has been proposed in this paper. We have used stability theory1-5 to obtain the criterion to control the spread of malaria. The results are illustrated with the help of a numerical example and its graphical representation.