基于Beverton-Holt模型下Wolbachia传播动力学分析

The analysis of Wolbachia propagation dynamics based on Beverton-Holt model

登革热是由登革病毒经蚊媒传播引发的一种急性传染病,目前一种新型的生物控制策略是向野外释放感染Wolbachia的蚊子,这种蚊子能够有效抑制登革热病毒在人群之间的传播。基于经典的Beverton-Holt模型,文章假设在完全CI的条件下,建立一个具有世代重叠的扩展的Beverton-Holt模型,研究在4种不同的释放策略下该模型的动力学行为。通过应用差分方程稳定性与分支理论,证明该模型平衡点的存在性条件、稳定性性态和吸引域,成功找到了Wolbachia在野生蚊子种群中成功传播的释放阈值r^(*),并且当r=r^(*)时,模型存在一个鞍结点分支,最后利用数值模拟证明所得出的结论。

Dengue fever is an acute infectious disease caused by the mosquito-borne transmission of dengue virus.At present,a novel biological control strategy is to release Wolbachia-infected mosquitoes into the wild,which can effectively inhibit the transmission of dengue virus between humans.Based on the classical Beverton-Holt model and the assumption of complete cytoplasmic incompatibility(CI),this paper establishes an extended Beverton-Holt model with overlapping generations to study the dynamics of the model under four different release strategies.By applying the stability and bifurcation theory of difference equations,the existence condition,stability and attraction domain of the equilibrium point in this model are proved.The release threshold r^(*)for Wolbachia to spread successfully in the wild mosquito populations is found.Moreover,the model has a saddle node bifurcation when r=r^(*).Finally,the results were proven by numerical simulation.