Optimal control of vector-borne diseases: Treatment and prevention

Pages: 587 - 611, Volume 11, Issue 3, May 2009

doi:10.3934/dcdsb.2009.11.587       Abstract        Full Text (596.7K)       Related Articles

Kbenesh Blayneh - Department of Mathematics, Florida A & M University, Tallahassee, FL 32307-5200, United States (email)
Yanzhao Cao - Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849, United States (email)
Hee-Dae Kwon - Department of Mathematics, Inha University, Incheon, 402-751, South Korea (email)

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.

Keywords:  Optimal Control, Autonomous, Disease-free, Numerical Simulation.
Mathematics Subject Classification:  Primary: 92D25, Secondary: 49J15.

Received: January 2008;      Revised: October 2008;      Published: March 2009.