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With the consideration of the mechanism of prevention and control for the spread of dengue fever, a mathematical model of dengue fever dynamical transmission between mosquitoes and humans, incorporating a vector control strategy of impulsive culling of mosquitoes, is proposed in this paper. By using the comparison principle, Floquet theory and some of analytical methods, we obtain the basic reproductive number R0 for this infectious disease, which illustrates the stability of the disease-free periodic solution and the uniform persistence of the disease. Further, the explicit conditions determining the backward or forward bifurcation are obtained and we show that the culling rate φ has a major effect on the occurrence of backward bifurcation. Finally, numerical simulations are given to verify the correctness of theoretical results and the highest efficiency of vector control strategy.

The effect of vector control strategy against Dengue transmission between mosquitoes and humans