Immune Response and Imperfect Vaccine in Malaria Dynamics

Abstract

The immune response to malaria and the effects of an imperfect vaccine for this disease are modelled incorporating an n stage parasite life cycle, immune cells, and antibodies. A globally asymptotically stable parasite-free equilibrium occurs when the associated reproduction number is less than unity. An imperfect malaria vaccine that reduces the number of merozoites released per bursting infected red blood cell (IRBC) and that boosts immune response can reduce the concentration of IRBCs in vivo. Numerical simulations show that a vaccine efficacy of at least 87% is necessary to eliminate IRBC in vivo. The concentration of IRBCs varies with the capacity of the vaccine to modify the total number of merozoites released per bursting IRBC.

Keywords:

• immune response
• malaria
• ordinary differential equations
• vaccine

ACKNOWLEDGMENTS

Abba B. Gumel acknowledges the support in part of the Natural Science and Engineering Research Council (NSERC) and Mathematics of Information Technology and Complex Systems (MITACS) of Canada. Ashrafi M. Niger acknowledges the support of the Department of Mathematics, University of Manitoba, and the Manitoba Graduate Scholarship. The authors are grateful to Professor Gauthier Sallet (University of Metz and INRIA Lorraine, France) for sending us his earlier articles. They are also grateful to the anonymous reviewers for their constructive comments and to Jane Heffernan for editorial assistance.