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A Model of Perfect Pediatric Vaccination of Dengue with Delay and Optimal Control
College of Mathematics and Systems Science, Xinjiang University, Urumqi, China
College of Mathematics and Systems Science, Xinjiang University, Urumqi, China
- 1 College of Mathematics and Systems Science, Xinjiang University, Urumqi, China
- 2 College of Mathematics and Systems Science, Xinjiang University, Urumqi, China
International Journal of Modern Nonlinear Theory and Application·Volume 05 (2016)·Pages 133–146·Published 10 November 2016·DOI10.4236/ijmnta.2016.54014
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Abstract
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.
KeywordsDengue Model with VaccinationDelayDisease-Free Equilibria and Endemic EquilibrumStabilityOptimal Control
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