title: Optimal control problems of epidemic systems with parameter uncertainties: application to a malaria two-age-classes transmission model with asymptomatic carriers.
abstract: 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.
authors.affiliation: Department of Mathematics and Physics, Lappeenranta University of Technology, P.O.Box 20, Lappeenranta FI-53851, Finland. Electronic address: mwanga.gasper@gmail.com.
authors.forename: Gasper G
authors.initials: GG
authors.lastname: Mwanga
authors.affiliation: Department of Mathematics and Physics, Lappeenranta University of Technology, P.O.Box 20, Lappeenranta FI-53851, Finland.
authors.forename: Heikki
authors.initials: H
authors.lastname: Haario
authors.affiliation: Department of Mathematics and Physics, Lappeenranta University of Technology, P.O.Box 20, Lappeenranta FI-53851, Finland; Gregorio Millan Institute Fluid Dynamics, Nanoscience and Industrial Mathematics, Escuela Politecnica Superior, Universidad Carlos III de Madrid, Av. de la Universidad, 30, Leganes 28911, Spain.
authors.forename: Vicenzo
authors.initials: V
authors.lastname: Capasso
mesh_terms: D000818:Animals; D000852:Anopheles / Q000469:parasitology; D002353:Carrier State / Q000453:epidemiology / Q000517:prevention & control; D003362:Cost-Benefit Analysis; D058872:Epidemics / Q000191:economics / Q000517:prevention & control / Q000706:statistics & numerical data; D006801:Humans; D008288:Malaria / Q000453:epidemiology* / Q000517:prevention & control / Q000635:transmission*; D008390:Markov Chains; D055641:Mathematical Concepts; D008954:Models, Biological; D009010:Monte Carlo Method; D009032:Mosquito Control; D035501:Uncertainty
keywords: MCMC; Malaria; Nonlinear ODE models; Optimal control; Parameter uncertainty