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The roles of maturation delay and vaccination on the spread of dengue virus and optimal control. (English) Zbl 1422.92161
Summary: A mathematical model of Dengue virus transmission between mosquitoes and humans, incorporating a control strategy of imperfect vaccination and vector maturation delay, is proposed in this paper. By using some analytical skills, we obtain the threshold conditions for the global attractiveness of two disease-free equilibria and prove the existence of a positive equilibrium for this model. Further, we investigate the sensitivity analysis of threshold conditions. Additionally, using the Pontryagin maximum principle, we obtain the optimal control strategy for the disease. Finally, numerical simulations are delivered to verify the correctness of the theoretical results, the feasibility of a vaccination control strategy, and the influences of the controlling parameters on the control and elimination of this disease. Theoretical results and numerical simulations show that the vaccination rate and effectiveness of vaccines are two key factors for the control of Dengue spread, and the manufacture of the Dengue vaccine is also architecturally significant.

92D30 Epidemiology
92C60 Medical epidemiology
37N25 Dynamical systems in biology
49N90 Applications of optimal control and differential games
49J15 Existence theories for optimal control problems involving ordinary differential equations
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