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Hikari, Applied Mathematical Sciences, (8), p. 2701-2730, 2014

DOI: 10.12988/ams.2014.43197

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Optimal Control of Malaria Model with Drug Resistance in Presence of Parameter Uncertainty

Journal article published in 2014 by Gasper G. Mwanga, Heikki Haario, Betty K. Nannyonga
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

Plasmodium falciparum malaria has developed resistance to almost all available antimalarial drugs despite controlled antimalarial drug use. This study presents a mathematical model of spread of antimalarial drug resistance with control using treated bed nets, indoor residual spraying and treatment of symptomatic individuals. A common pitfall for such epidemiological models, however, is the absence of real data; model-based conclusions have to be based on uncertain parameter val-ues. Here we present an approach to study the robustness of optimal control solutions under such parameter uncertainty. For a given model simulation we create synthetic noisy data so that a plausible variability of the epidemiological dynamics is covered. By Markov chain Monte Carlo (MCMC) simulations this variability is mapped to model param-eter distributions. The optimal control algorithm is then run using different parameter values sampled from the MCMC parameter poste-rior. Moreover, the uncertainty of the cost function weights is accounted 2702 G. G. Mwanga, H. Haario, B. K. Nannyonga for by similar sampling. Numerical simulation results demonstrate the robustness of the approach: given the effective control strategy, the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the designing of cost-effective strategies for disease controls with multiple interventions, even under considerable uncertainty of model parameters and control costs.