African Journal of Malaria and Tropical Diseases

African Journal of Malaria and Tropical Diseases ISSN 4123-0981 Vol. 1 (1), pp. 001-009, September, 2013. © International Scholars Journals

Full Length Research Paper

A study of the effect of drug resistance in malaria transmission and the most effective control measure

*Anyaoku K. Majid, Fayemi M. O. and Emeagwali H. R.

Department of Public health, Faculty of Medicine, University of South Africa, Pretoria, South Africa.

*Corresponding author. E-mail: [email protected]

Accepted 20 August, 2013

Abstract

We derive and analyze 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.