Computational and Mathematical Methods in Medicine
Volume 8 (2007), Issue 3, Pages 191-203
doi:10.1080/17486700701529002
Original Article

On Oscillatory Pattern of Malaria Dynamics in a Population with Temporary Immunity

J. Tumwiine,1 J. Y. T. Mugisha,2 and L. S. Luboobi2

1Department of Mathematics, Mbarara University, P.O. Box 1410, Mbarara, Uganda
2Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, Uganda

Received 2 October 2006; Revised 1 February 2007; Accepted 20 June 2007

Copyright © 2007 Hindawi Publishing Corporation. 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.

Abstract

We use a model to study the dynamics of malaria in the human and mosquito population to explain the stability patterns of malaria. The model results show that the disease-free equilibrium is globally asymptotically stable and occurs whenever the basic reproduction number, R0 is less than unity. We also note that when R0>1, the disease-free equilibrium is unstable and the endemic equilibrium is stable. Numerical simulations show that recoveries and temporary immunity keep the populations at oscillation patterns and eventually converge to a steady state.