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Abstract
Mathematical models have been used as one of the important tools in understanding the dynamics of malaria in many human communities. A review of relevant mathematical models of malaria epidemic in different human communities, taking note of the specific questions each of the models was designed to answer were carried out. In this work, we propose a non-linear mathematical model, to study the spatial dynamics of malaria in a localized population that has a significant presence of invasive plants that harbours adult mosquitoes. Significant qualitative properties of the spatially homogeneous model are derived. We also characterized the travelling wave velocity for the spatial model which includes the dispersal of vectors. It is imperative to investigate the twin effect of invasive plants and spatial dispersion of vectors on the dynamics of malaria as these can have significant effect on the formulation of robust control measures that will result in the reduction of malaria burden in the target population. We therefore carried out simulation of the non-linear model and quantitatively assess and investigate the twin effect of the presence of invasive plants and the spatial dispersion of vectors on malaria dynamics.Sensitivity analysis was carried out and the quantitative effect of diffusion and advection on the wave front was demonstrated. It was found that malaria persists where there are invasive plants than where there are no invasive alien plants. The speed of the disease propagation by using travelling wave solutions of the model was also investigated numerically. The result shows that the diffusion and advection forces increase the speed of the disease transmission due to mosquito flight speed.
