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

Optimal control of vector-borne diseases: Treatment and prevention


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


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


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.
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

Ovide Arino, Manuel Delgado, Mónica Molina-Becerra. Asymptotic behavior of disease-free equilibriums of an age-structured predator-prey model with disease in the prey. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 501-515. doi: 10.3934/dcdsb.2004.4.501


Djamila Moulay, M. A. Aziz-Alaoui, Hee-Dae Kwon. Optimal control of chikungunya disease: Larvae reduction, treatment and prevention. Mathematical Biosciences & Engineering, 2012, 9 (2) : 369-392. doi: 10.3934/mbe.2012.9.369


Wandi Ding. Optimal control on hybrid ODE Systems with application to a tick disease model. Mathematical Biosciences & Engineering, 2007, 4 (4) : 633-659. doi: 10.3934/mbe.2007.4.633


Radoslaw Pytlak. Numerical procedure for optimal control of higher index DAEs. Discrete and Continuous Dynamical Systems, 2011, 29 (2) : 647-670. doi: 10.3934/dcds.2011.29.647


Emmanuel Trélat. Optimal control of a space shuttle, and numerical simulations. Conference Publications, 2003, 2003 (Special) : 842-851. doi: 10.3934/proc.2003.2003.842


Kamil Aida-Zade, Jamila Asadova. Numerical solution to optimal control problems of oscillatory processes. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021166


Joaquim P. Mateus, Paulo Rebelo, Silvério Rosa, César M. Silva, Delfim F. M. Torres. Optimal control of non-autonomous SEIRS models with vaccination and treatment. Discrete and Continuous Dynamical Systems - S, 2018, 11 (6) : 1179-1199. doi: 10.3934/dcdss.2018067


Yves Dumont, Frederic Chiroleu. Vector control for the Chikungunya disease. Mathematical Biosciences & Engineering, 2010, 7 (2) : 313-345. doi: 10.3934/mbe.2010.7.313


Gong Chen, Peter J. Olver. Numerical simulation of nonlinear dispersive quantization. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 991-1008. doi: 10.3934/dcds.2014.34.991


Nicolas Vauchelet. Numerical simulation of a kinetic model for chemotaxis. Kinetic and Related Models, 2010, 3 (3) : 501-528. doi: 10.3934/krm.2010.3.501


Petr Bauer, Michal Beneš, Radek Fučík, Hung Hoang Dieu, Vladimír Klement, Radek Máca, Jan Mach, Tomáš Oberhuber, Pavel Strachota, Vítězslav Žabka, Vladimír Havlena. Numerical simulation of flow in fluidized beds. Discrete and Continuous Dynamical Systems - S, 2015, 8 (5) : 833-846. doi: 10.3934/dcdss.2015.8.833


Ugur G. Abdulla, Evan Cosgrove, Jonathan Goldfarb. On the Frechet differentiability in optimal control of coefficients in parabolic free boundary problems. Evolution Equations and Control Theory, 2017, 6 (3) : 319-344. doi: 10.3934/eect.2017017


Shakoor Pooseh, Ricardo Almeida, Delfim F. M. Torres. Fractional order optimal control problems with free terminal time. Journal of Industrial and Management Optimization, 2014, 10 (2) : 363-381. doi: 10.3934/jimo.2014.10.363


Lorena Bociu, Lucas Castle, Kristina Martin, Daniel Toundykov. Optimal control in a free boundary fluid-elasticity interaction. Conference Publications, 2015, 2015 (special) : 122-131. doi: 10.3934/proc.2015.0122


Jésus Ildefonso Díaz, Tommaso Mingazzini, Ángel Manuel Ramos. On the optimal control for a semilinear equation with cost depending on the free boundary. Networks and Heterogeneous Media, 2012, 7 (4) : 605-615. doi: 10.3934/nhm.2012.7.605


Bruno Buonomo, Eleonora Messina. Impact of vaccine arrival on the optimal control of a newly emerging infectious disease: A theoretical study. Mathematical Biosciences & Engineering, 2012, 9 (3) : 539-552. doi: 10.3934/mbe.2012.9.539


Yue Liu, Wing-Cheong Lo. Stability analysis and optimal control of production-limiting disease in farm with two vaccines. Discrete and Continuous Dynamical Systems - B, 2022, 27 (2) : 619-638. doi: 10.3934/dcdsb.2021058


Z. Foroozandeh, Maria do rosário de Pinho, M. Shamsi. On numerical methods for singular optimal control problems: An application to an AUV problem. Discrete and Continuous Dynamical Systems - B, 2019, 24 (5) : 2219-2235. doi: 10.3934/dcdsb.2019092


Enrique Fernández-Cara, Irene Marín-Gayte. Theoretical and numerical results for some bi-objective optimal control problems. Communications on Pure and Applied Analysis, 2020, 19 (4) : 2101-2126. doi: 10.3934/cpaa.2020093


Martin Benning, Elena Celledoni, Matthias J. Ehrhardt, Brynjulf Owren, Carola-Bibiane Schönlieb. Deep learning as optimal control problems: Models and numerical methods. Journal of Computational Dynamics, 2019, 6 (2) : 171-198. doi: 10.3934/jcd.2019009

2021 Impact Factor: 1.497


  • PDF downloads (571)
  • HTML views (0)
  • Cited by (79)

Other articles
by authors

[Back to Top]