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May  2009, 11(3): 587-611. doi: 10.3934/dcdsb.2009.11.587

Optimal control of vector-borne diseases: Treatment and prevention

Kbenesh Blayneh 1, , Yanzhao Cao 2, and  Hee-Dae Kwon 3,

1. 

Department of Mathematics, Florida A & M University, Tallahassee, FL 32307-5200, United States
2. 

Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849, United States
3. 

Department of Mathematics, Inha University, Incheon, 402-751, South Korea

Received  January 2008 Revised  October 2008 Published  March 2009

In this paper 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 mode 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.
Keywords: Disease-free, Numerical Simulation., Autonomous, Optimal Control.
Mathematics Subject Classification: Primary: 92D25, Secondary: 49J1.
Citation: Kbenesh Blayneh, Yanzhao Cao, Hee-Dae Kwon. Optimal control of vector-borne diseases: Treatment and prevention. Discrete and Continuous Dynamical Systems - B, 2009, 11 (3) : 587-611. doi: 10.3934/dcdsb.2009.11.587
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