Biological control of malaria: A mathematical model

摘要

This paper presents a mathematical model to evaluate the impact of the larval control method of biological control of malaria in an endemic area by considering both human and mosquitoes populations variable. The different equilibria of the model are found and stability of these equilibria are discussed in-detail. Also, the presented model exhibits backward bifurcation under certain restriction on parameters, which gives rise to existence of multiple endemic equilibrium for R0<1. This suggests that an accurate estimation of parameters and the level of control measures is important to reduce the infection prevalence of malaria in endemic region and R0<1 is not enough to eliminate the disease from the population under consideration. Finally the presented model is extended to include optimal control which helps in implementing time dependent anti-malaria control techniques while minimizing the cost of implementation of such measures.