# MATHEMATICAL MODELING OF THE EFFECT OF IVERMECTIN AND CATTLE AVAILABILITY ON MALARIA CONTROL

## Keywords:

Disease-free equilibrium points, Next Generation Matrix, Stability, Reproduction Number## Abstract

The fight against malaria is still on with the 2030 elimination goal in view. Several control tools have been in use to achieve the goal and a current attention under research is on the use of some endectocides one of which is known as ivermectin (IVM) drug that serves as mosquitocidal tool. In this study, a mathematical model is formulated for the control of this disease considering IVM with cattle availability. The model consists of ordinary differential equation from which we obtained the basic reproduction number, R0 and then investigated the existence and stability of the disease-free equilibrium (DFE). Analytical estimate based on sensitivity index analysis showed that a 25% reduction in the proportion of vector blood meal on humans with cattle availability corresponds to a 25% reduction in the basic reproduction number. This finding is supported with the result of the numerical simulation. Applying four different combinations of control tools as strategies while varying the degrees of effort, the contribution of cattle availability through the parameter that controls the proportion of vector blood-meal on human is further seen to be positive on malaria control even when no measure of control is applied.

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*64*, 127–138. https://nampjournals.org.ng/index.php/home/article/view/99