On a seasonally responsive malaria model

Authors

  • Kenneth Njengele Dukuza University of Pretoria

DOI:

https://doi.org/10.11145/539

Abstract

Entomological studies suggest that mosquito population is a function of time and rainfall in areas where malaria disease is hyperendemic. In this research work we propose a mathematical model to capture this phenomenon. A malaria disease transmission model is formulated and studied. The epidemic threshold parameter which is generally known as the basic reproduction number and usually denoted by $R_{0}$ is obtained. The existence of equilibria is considered. We use the Center Manifold Theory to show the possibility of occurrence of a Backward Bifurcation at $R_{0}=1$. Finally our model is modified to incorporate the seasonal response of the mosquito population, and the model equivalent of the basic reproduction number is determined.

Author Biography

Kenneth Njengele Dukuza, University of Pretoria

Applied mathematics PhD Student.

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Published

2015-05-29

Issue

Vol. 2 No. 1 (2015)

Section

Conference Contributions (Pretoria)

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