THE ROLE OF MOSQUITO TRAP IN MALARIA CONTROL- A MATHEMATICAL APPROACH)

Abstract

We propose a simple mathematical model of malaria transmission involving a system of five ordinary differential equations with only susceptible and infectious classes of both humans and mosquitoes and a new class of trapped mosquitoes. The motivation is to use mathematical approach to analyze the role of mosquito trap in malaria control. We obtain the basic reproduction number, R₀ and found that the trap effectiveness is a key parameter that drives the dynamics of the disease. The analytical results show that, for R₀ < 1 , the disease-free equilibrium point is locally asymptotically stable and globally asymptotically stable in the absence of disease related death, and unstable for R₀ > 1. We found from the numerical solution that with the given parameter values in the absence of mosquito trap, malaria infection may be as high as 80% within six months of introduction of few infected mosquitoes into an entirely susceptible population. Although, other parameters like the infection rates of both humans and mosquitoes can cause the disease to invade the population when the level of trap effectiveness is low but trap effectiveness very close to 1 may likely lead to disease eradication.