International Journal of Malaria and Tropical Diseases ISSN 2953-2108 Vol.  1 (12), pp. 063-071, December, 2017. © Advanced Scholars Journals

Full Length Research Paper

Effects of drug resistance in malaria transmission and its most favorable control analysis

*Steve Rhodes Tambo, Gary M. Botha and Jacob R. Makeba

Institute for Advance Research in Mathematical Modelling and Computations, Cape Peninsula University of Technology, P. O. Box 1906, Bellville 7535, South Africa.

E-mail: [email protected]

Accepted 15 October, 2017

Abstract

We derive and analyse a deterministic model for the transmission of malaria disease with drug resistance in the infectives. Firstly, we calculate the basic reproduction number, R, and investigate the existence and stability of equilibria. The system is found to exhibit backward bifurcation, with this occurrence, the classical epidemiological requirement for effective eradication of malaria, R < 1, is no longer sufficient, even though necessary. Secondly, by using optimal control theory, we derive the conditions for optimal control of the disease using Pontryagin’s Maximum Principle. Finally, numerical simulations are performed to illustrate the analytical results.

Key words: Malaria, bifurcation, stability, optimal control.