Journal of Applied Mathematics
Volume 2012 (2012), Article ID 854723, 20 pages
Research Article

Optimal Control of a Spatio-Temporal Model for Malaria: Synergy Treatment and Prevention

1Laboratoire d'Hydrologie et Ressources en Eau, Institut International d'Ingénierie de l'Eau et de l'Environnement (2iE), 01 Rue de la Science, BP 594, Ouagadougou, Burkina Faso
2Laboratoire CEREGMIA, Université des Antilles et de la Guyane, 2091 Route de Baduel, 97157 Pointe-à-Pitre, France
3CIRAD, UMR G-EAU, 34398 Montpellier, France

Received 29 January 2012; Revised 10 May 2012; Accepted 10 May 2012

Academic Editor: Zhiwei Gao

Copyright © 2012 Malicki Zorom et al. 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.


We propose a metapopulation model for malaria with two control variables, treatment and prevention, distributed between 𝑛 different patches (localities). Malaria spreads between these localities through human travel. We used the theory of optimal control and applied a mathematical model for three connected patches. From previous studies with the same data, two patches were identified as reservoirs of malaria infection, namely, the patches that sustain malaria epidemic in the other patches. We argue that to reduce the number of infections and semi-immunes (i.e., asymptomatic carriers of parasites) in overall population, two considerations are needed, (a) For the reservoir patches, we need to apply both treatment and prevention to reduce the number of infections and to reduce the number of semi-immunes; neither the treatment nor prevention were specified at the beginning of the control application, except prevention that seems to be effective at the end. (b) For unreservoir patches, we should apply the treatment to reduce the number of infections, and the same strategy should be applied to semi-immune as in (a).