A Model of Perfect Pediatric Vaccination of Dengue with Delay and Optimal Control

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DOI: 10.4236/ijmnta.2016.54014    750 Downloads   907 Views  
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A delayed mathematical model of Dengue dynamical transmission between vector mosquitoes and human, incorporating a control strategy of perfect pediatric vaccination is proposed in this paper. By some analytical skills, we obtain the existence of disease-free equilibria and endemic equilibrium, the necessary conditions of global asymptotical stability about two disease-free equilibria. Further, by Pontryagin’s maximum principle, we obtain the optimal control of the disease. Finally, numerical simulations are carried out to verify the correctness of the theoretical results and feasibility of the control measure.

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Xue, Y. and Nie, L. (2016) A Model of Perfect Pediatric Vaccination of Dengue with Delay and Optimal Control. International Journal of Modern Nonlinear Theory and Application, 5, 133-146. doi: 10.4236/ijmnta.2016.54014.


[1] Kyle, J.L. and Harris, E. (2008) Global Spread and Persistence of Dengue. Annual Review of Microbiology, 62, 71-92.
[2] Rigau-Perez, J.G. (2006) Severe Dengue: The Need for New Case Definitions. Lancet Infectious Diseases, 6, 297-302.
[3] Keeling, M.J. and Rohani, P. (2008) Modeling Infectious Diseases in Humans and Animals, Princeton University Press, Printceton, 415.
[4] Scherer, A. and McLean, A. (2002) Mathematical Models of Vaccination. British Medical Bulletin, 62, 187-199.
[5] Murrel, S. and Butler, S.C.W. (2011) Review of Dengue Virus and the Development of a Vaccine. Biotechnology Advances, 29, 239-247.
[6] Clark, D.V., et al. (2005) Economic Impact of Dengue Fever/Dengue Hemorrhagic Fever in Thailand at the Family and Population Levels. American Journal of Tropical Medicine and Hygiene, 72, 786-791.
[7] Suaya, J.A., et al. (2009) Cost of Dengue Cases in Eight Countries in the Americas and Asia: A Prospective Study. American Journal of Tropical Medicine and Hygiene, 80, 846-855.
[8] Rodrigues, H.S., Monteiro, M.T.T. and Torres D.F.M. (2014) Vaccination Models and Optimal Control Strategies to Dengue. Mathematical Biosciences, 247, 1-12.
[9] Tridip, S., Sourav, R. and Joydev, C. (2015) Amathematical Model of Dengue Transmission with Memory. Communications in Nonlinear Science and Numerical Simulation, 22, 511-525.
[10] Fan, G.H., Wu, J.H. and Zhu, H.P. (2010) The Impact of Maturation Delay of Mosquitoes on Teh Transmission of West Nile Virus. Mathematical Biosciences, 228, 119-126.
[11] Silva, C.J. and Torres, D.F.M. (2012) Optimal Control Strategies for Tuberculosis Treatment: A Case Study in Angola. Numerical Algebra, Control and Optimization, 2, 601-617.
[12] Cesari, L. (1983) Optimization-Theory and Applications, Problems with Ordinary Differential Equations, Applications and Mathematics. Vol. 17, Springer-Verlag, New York, Heidelberg-Berlin.
[13] Pontryagin, L.S., Boltyanskii, V.G., et al. (1962) The Mathematical Theory of Optimal Processes. Interscience Publishers John Wiley & Sons, Inc., New York-London, Translated from the Russian by K.N., Trirogoff.

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