Computational and Mathematical Methods in Medicine
Volume 9 (2008), Issue 2, Pages 143-163
doi:10.1080/17486700701865661
Original Article

Modelling Immune Response and Drug Therapy in Human Malaria Infection

C. Chiyaka,1 W. Garira,1 and S. Dube2

1Department of Applied Mathematics, National University of Science and Technology, P.O. Box AC 939, Ascot, Bulawayo, Zimbabwe
2Department of Applied Biology/Biochemistry, National University of Science and Technology, P.O. Box AC 939, Ascot, Bulawayo, Zimbabwe

Received 14 December 2006; Accepted 12 December 2007

Copyright © 2008 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

A new intra-host model of malaria that describes the dynamics of the blood stages of the parasite and its interaction with red blood cells and immune effectors is proposed. Local and global stability of the disease free equilibrium are investigated. Conditions for existence and uniqueness of the endemic equilibrium are derived. An intra-host basic reproductive number is identified. We deduce that drugs based on inhibiting parasite production are more effective than those based on inhibiting merozoite invasion of erythrocytes. We extend the model to incorporate, in addition to immune response, drug therapy, following treatment with antimalarial drugs. Using stability analysis of the model, it is shown that infection can be eradicated within the host if the drug efficacy level exceeds a certain threshold value. It will persist if the efficacy is below this threshold. Numerical simulations are done to verify the analytic results and illustrate possible behaviour of the models.