Journal
MATHEMATICAL BIOSCIENCES
Volume 261, Issue -, Pages 1-12Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.mbs.2014.11.005
Keywords
Malaria; Nonlinear ODE models; Optimal control; Parameter uncertainty; MCMC
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Funding
- World Bank through Ministry of Education and Vocational training of United Republic of Tanzania
- Finnish Center of Excellence in Inverse Problems
- Chair of Excellence at the Carlos III University in Madrid Spain
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The main scope of this paper is to study the optimal control practices of malaria, by discussing the implementation of a catalog of optimal control strategies in presence of parameter uncertainties, which is typical of infectious diseases data. In this study we focus on a deterministic mathematical model for the transmission of malaria, including in particular asymptomatic carriers and two age classes in the human population. A partial qualitative analysis of the relevant ODE system has been carried out, leading to a realistic threshold parameter. For the deterministic model under consideration, four possible control strategies have been analyzed: the use of Long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic and asymptomatic individuals. The numerical results show that using optimal control the disease,can be brought to a stable disease free equilibrium when all four controls are used. The Incremental Cost-Effectiveness Ratio (ICER) for all possible combinations of the disease-control measures is determined. The numerical simulations of the optimal control in the presence of parameter uncertainty demonstrate the robustness of the optimal control: 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. (C) 2014 Elsevier Inc. All rights reserved.
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