| Dengue virus is mainly transmitted by Aedes aegypti and Aedes albopictus,leading to great economic cost in many tropical and subtropical regions,and posting threat to people's health.The purpose of this work is to develop an ordinary differential equation model to assess the effectiveness of vaccination for humans against dengue virus transmissionWe derived the expression of the basic reproduction number R0 by using the next generation matrix approach.We proved that the disease-free equilibrium point is locally asymptotically stable in the domain by Routh-Hurwitz criterion if R0<1.We also proved that the global asymptotic stability of the disease-free equilibrium point in the domain D by constructing Lyapunov function.Similarly,if R0>1,we proved that the global asymptotic stability of endemic equilibrium pointThe target reproduction number is used to measure the control efforts,and the effective reproduction number to quantify the number of secondary cases for partially susceptible populations.Furthermore,we used sensitivity analysis to compare the relative significance of the model parameters to R0.The results show that R0 is most sensitive to the average number of times that one mosquito would bite a person per day,?v.The least sensitive parameter is the per capita rate for humans from the exposed state to the infected state,?hWe compared different scenarios of vaccination for humans.The numerical results show that the cumulative number of humans is the smallest when vaccinating humans before the outbreak compared with that when vaccinating humans during any other periods.If we vaccinate humans during two periods,then it is more effective to vaccinate humans before and during the outbreak than vaccinating humans during any of the other two periods.Finally,we proposed ten various control schemes to combat dengue,and the necessary conditions for an optimal control are derived using Pontryagin's maximum principle.The numerical results were presented to find the optimal control scheme. |
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