Abstract
We present a compartmental model in ordinary differential equations of malaria disease transmission, accommodating the effect of indoor residual spraying on the vector population. The model allows for influx of infected migrants into the host population and for outflow of recovered migrants. The system is shown to have positive solutions. In the special case of no infected immigrants, we prove global stability of the disease-free equilibrium. Existence of a unique endemic equilibrium point is also established for the case of positive influx of infected migrants. As a case study we consider the combined South African malaria region. Using data covering 31 years, we quantify the effect of malaria infected immigrants on the South African malaria region.
Highlights
Malaria disease has been a major cause of morbidity and mortality in many regions of the world, in Africa where year after year we see millions of people suffering of malaria
We present a compartmental model in ordinary differential equations of malaria disease transmission, accommodating the effect of indoor residual spraying on the vector population
In this article we study the effect of infected migrants into a given population for the case of malaria, using a new compartmental model in ordinary differential equations (ODEs) designed for this purpose
Summary
Malaria disease has been a major cause of morbidity and mortality in many regions of the world, in Africa where year after year we see millions of people suffering of malaria. The model can be applied to test and quantify the effect of disease resulting from infected tourists, infected business travellers, traveling sports people, touring musicians or cultural groups, and similar traveling people from elsewhere, visiting a local population. This is important in particular when the disease in point is well under control in the local population. Our model is utilized to determine the extent to which the upsurge is due to a combination of influx of malaria infected migrants into the region and the effect of IRS.
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