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Zbl 1162.92034
Blayneh, Kbenesh; Cao, Yanzhao; Kwon, Hee-Dae
Optimal control of vector-borne diseases: Treatment and prevention. (English)
[J] Discrete Contin. Dyn. Syst., Ser. B 11, No. 3, 587-611 (2009). ISSN 1531-3492; ISSN 1553-524X/e

Summary: We study the dynamics of a vector-transmitted disease using two deterministic models. First, we look at time dependent prevention and treatment efforts, where optimal control theory is applied. Using analytical and numerical techniques, it is shown that there are cost effective control efforts for treatment of hosts and prevention of host-vector contacts. Then, we considered the autonomous counter part of the model and we established global stability results based on the reproductive number. The model is applied to study the effects of prevention and treatment controls on a malaria disease while keeping the implementation cost at a minimum. Numerical results indicate the effects of the two controls (prevention and treatment) in lowering exposed and infected members of each of the populations. The study also highlights the effects of some model parameters on the results.

MSC 2000:: *92D30 Epidemiology
49J15 Optimal control problems with ODE (existence)
34D05 Asymptotic stability of ODE
49N90 Applications of optimal control and differential games
34D23 Global stability

Keywords: optimal control; autonomous; disease-free; numerical simulation

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