### Mathematical modeling of malaria disease with control strategy

Segun I. Oke, Michael M. Ojo, Michael O. Adeniyi, Maba B. Matadi

#### Abstract

This article suggested and analyzed the transmission dynamics of malaria disease in a population using a nonlinear mathematical model. The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. Moreso, the qualitatively evaluated model incorporates time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The optimal control problem was formulated using Pontryagin’s maximum principle, and three control strategies: disease prevention through bed nets, treatment and insecticides were incorporated. The optimality system was stimulated using an iterative technique of forward-backward Runge-Kutta fourth order scheme, so that the impacts of the control strategies on the infected individuals in the population can be determined. The possible influence of exploring a single control, the combination of two, and the three controls on the spread of the disease was also investigated. Numerical simulation was carried out and pertinent findings are displayed graphically.

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Published: 2020-07-16

Segun I. Oke, Michael M. Ojo, Michael O. Adeniyi, Maba B. Matadi, Mathematical modeling of malaria disease with control strategy, Commun. Math. Biol. Neurosci., 2020 (2020), Article ID 43

Copyright © 2020 Segun I. Oke, Michael M. Ojo, Michael O. Adeniyi, Maba B. Matadi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Commun. Math. Biol. Neurosci.

ISSN 2052-2541

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