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

Abstract

With the consideration of 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 theorem and some of analytical methods, we obtain the basic reproductive number $\mathcal{R}_0$ 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 the culling rate $\phi$ is a major effect on the occurrence of backward bifurcation. Finally, numerical simulations are given to verify the correctness of theoretical results and the most efficiency of vector control strategy.

Keywords

• dengue fever
• impulsive culling
• extinction
• uniform persistence
• bifurcation