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

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 co...

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Bibliographic Details
Published in:Journal of applied mathematics 2012-01, Vol.2012 (2012), p.1-20
Main Authors: Somé, Blaise, Barbier, Bruno, Zongo, Pascal, Zorom, Malicki
Format: Article
Language:English
Subjects:
Biomathematics
Budgets
Care and treatment
Infections
Malaria
Mathematical models
Meta-analysis
Mosquitoes
Physiological aspects
Population biology
Prevention
Sensitivity analysis
Studies
Variables
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Summary: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).
ISSN:1110-757X
1687-0042
DOI:10.1155/2012/854723