Impact of Hygiene on Malaria Transmission Dynamics: A Mathematical Model

Abstract

Malaria continues to pose a major public health challenge, especially in developing countries, as 219 million cases of malaria were found in 89 countries. In this paper, a mathematical model using non-linear differential equations is formulated to describe the impact of hygiene on malaria transmission dynamics. The model is divided into seven compartments which includes five human compartments namely; unhygienic susceptible human population (Su), hygienic susceptible human population (Sn), unhygienic infected human population (Iu), hygienic infected human population (In) and the recovered human population (Rn) while the mosquito population is subdivided into susceptible mosquitoes (Sv) and infected mosquitoes Iv. The positivity of the solution shows that a domain exists where the model is biologically meaningful and mathematically well-posed. The Disease-Free Equilibrium (DFE) point of the model is obtained. Then, the basic reproduction number is computed using the next generation method and established the condition for local stability of the disease-free equilibrium. Thereafter the global stability of the disease-free equilibrium was obtained by constructing the Lyapunov function of the model system. Also, sensitivity analysis of the model system was carried out to identify the influence of the parameters on the basic reproduction number. The result shows that the natural death rate of the mosquitoes is most sensitive to the basic reproduction number.