A mathematical model for effective control and possible eradication of malaria

Abstract

In this study, a novel deterministic mathematical model for the transmission and control of malaria is formulated. The main innovation in the model is that, in addition to the natural death rate of the vector (mosquito) population, a proportion of the prevention effort also contributes to a reduction of the vector population. The model assumed that a proportion ca; 0 c 1 of the prevention effort a contributes to the death rate of the vector population. The study showed that there exists a domain where the model is epidemiologically and mathematically well-posed. The study showed that the model has a unique disease free and an endemic equilibrium points. It was established that the disease free equilibrium is locally and globally asymptotically stable when R0 < 1 and the endemic equilibrium is locally and globally asymptotically stable when R0 > 1: Parameters of the model were estimated from monthly confirmed malaria cases obtained from the Central Region of Ghana. A sensitivity analysis was carried out to determine the effects of each parameter on the basic reproduction number, R0: The result from the sensitivity analysis showed that the two most sensitive parameters in the reduction of R0 are prevention and treatment. Based on the result from the sensitivity analysis, numerical simulations were performed using various combinations of treatment and prevention to determine an optimal combination that reduces the incidence rate fastest. The result of the simulations showed that, with about 40% of effective prevention coupled with about 40% of treatment, will considerably reduce both the infected human and vector populations. The higher the prevention effort, the higher the reduction in the infected vector population. If the prevention efforts are implemented by all contiguous communities in the region, acting in concert, then a marked reduction should be seen in the infected vector population leading to a complete eradication of malaria in the region, by implication, through out Ghana.