Annals of Communications in Mathematics

AbstractMalaria is one of the serious life-threatening diseases with negative effects on both the social and economic aspects of human life. Researching into its curtailment or eradication is necessary for elevating human health and social-economic status. In thisregard, this study focuses on the spatial non-linear mathematical model to investigate how vector control strategies are correlated with the dynamics of malaria transmission. The study employs a non-linear partial differential equations (NPDE) mathematical model to investigate malaria transmission. The model system incorporates human (host), mosquito (vector), and invasive alien plant populations. Some applicable epidemiological mathematical analyses were carried out on the model system, such as critical points, stability, the basic reproduction number, local asymptotic stability (LAS), bifurcation, global as- ymptotic stability (GAS), wave speed, and numerical analyses using relevant data were extensively analysed. Using the sharp threshold conditions imposed on the basic reproduction number, we were able to show that the model exhibited the backward bifurcation phenomenon and the DFE was shown to be globally asymptotic stable (GAS) under certain conditions. It was found that the invasive alien plants have significant effects on malaria transmission. This study suggests that mosquito repellent plants should be planted around the human environment to replace the invasive plants so as to reduce mosquito shelters andfeeding opportunities for mosquitoes.

AbstractA spatial mathematical model to study the impact of vector control strategies on the dynamics of malaria transmission and its analysis is considered in this paper. The resulting model equations are divided into homogeneous and non-homogeneous equations. The homogeneous equations are solved to determine their disease-free equilibrium (DFE) and their stability. A basic reproduction number was determined from the DFE. It was found that when basic reproduction number is less one, the disease will die out, when the basic reproduction number is exactly one, the model undergoes a backward bifurcation, when the basic reproduction number is exactly zero, the model undergoes forward bifur- cation and whenever the basic reproduction is greater than one, the disease will persist in the population. A quantitative sensitivity analysis of the model parameters was also conducted through the disease’s basic reproduction number to determine the parameters that are sensitive to malaria transmission. A travelling wave equation and solutions were also provided for a possible understanding of the behaviour of mosquitoes’ mobility in the human environment. Finally, we carried out a simulation of our formulated partial differ- ential model and quantitatively assessed and investigated the twin effect of the presence of invasive plants and the spatial dispersion of vectors on malaria dynamics. Sensitivity analysis was also carried out, and the quantitative effect of diffusion and advection on the wave front was demonstrated. The speed of the disease propagation by using travelling wave solutions of the model was also investigated numerically.