International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2569

Full Length Research Paper

Modelling the impact of drug resistance in malaria transmission and its optimal control analysis

K. O. Okosun* and O. D. Makinde
Institute for Advance Research in Mathematical Modelling and Computations, Cape Peninsula University of Technology, P. O. Box 1906, Bellville 7535, South Africa.
Email: [email protected]

  •  Accepted: 15 September 2011
  •  Published: 09 November 2011



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.