Stability Analysis of a Mathematical Model for Endemic Malaria Transmission Dynamics
DOI:
https://doi.org/10.63561/jmns.v3i1.1158Keywords:
Mathematical Model, Model Properties, Equilibrium Points, Basic Reproduction Number, Backward Bifurcation.Abstract
Malaria is a mosquito-borne disease that continues to affect people worldwide and remains a serious public health problem. It is caused by parasites from the Plasmodium genus and is transmitted through the bites of infected female Anopheles mosquitoes. In 2017, about 219 million malaria cases were recorded globally, with children accounting for a large number of related deaths. This study develops a mathematical model to understand how malaria spreads and how it can be controlled. The model examines important features such as the basic reproduction number and the conditions for disease-free and endemic states. It also investigates the occurrence of backward bifurcation using the center manifold theory to better understand how the disease behaves under certain conditions. The findings show that when specific conditions (Z1-Z2 ) > 0 and U3 > 0 are met, both A and B are positive, and the model shows backward bifurcation. In another case if (Z1 - Z2 ) < 0 and U3 > 0, A is positive while B is negative, and the model still exhibits backward bifurcation. This means that malaria can remain in the population even when the basic reproduction number is less than one.
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