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2009, Volume 11, Issue 3: 587-611. Doi: 10.3934/dcdsb.2009.11.587
This issue Previous Article Coagulation, fragmentation and growth processes in a size structured population Next Article Equilibria of a cyclin structured cell population model

Optimal control of vector-borne diseases: Treatment and prevention

  • 1.

    Department of Mathematics, Florida A & M University, Tallahassee, FL 32307-5200

  • 2.

    Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849

  • 3.

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

Received:  December 31, 2007
Revised:  September 30, 2008
Published:  April 2009
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: Primary: 92D25, Secondary: 49J15.

    Citation:
    shu

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