Abstract:
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.
Keywords ,mathematical model.
