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Modeling and dynamics analysis of Zika transmission with contaminated aquatic environments
Nonlinear Dynamics ( IF 5.6 ) Pub Date : 2021-02-23 , DOI: 10.1007/s11071-021-06289-3
Liping Wang , Hongyong Zhao

Since the outbreak in Brazil, Zika has received the worldwide attention. Zika virus is mainly transmitted via the bites of Aedes mosquito. Recently, experimental evidence demonstrates that Zika virus in contaminated aquatic environments can be transmitted to aquatic mosquitoes through breeding. To study the effects of contaminated aquatic environments on Zika transmission, we propose a new Zika model by introducing a general incidence function. For a general incidence function, we calculate the basic reproduction number \(R_0\), analyze the stability of disease-free equilibria and give general conditions with the occurrence of backward bifurcation. For the two special sublinear incidence functions, \(R_0=1\) is a sharp threshold. It means that the disease can be eradicated by reducing \(R_{0}\) below 1. For the special nonlinear incidence function, we investigate theoretically backward bifurcation and saddle-node bifurcation and simulate numerically Hopf bifurcation. Analysis results suggest that transmission force from contaminated aquatic environments to aquatic mosquitoes plays an important role in generating complex dynamics. Furthermore, our model is extended to explore the effects of temperature variability on spread of Zika disease.



中文翻译:

水污染环境下寨卡病毒传播的建模和动力学分析

自巴西爆发以来,寨卡病毒已受到全世界的关注。寨卡病毒主要通过伊蚊的叮咬传播。最近,实验证据表明,受污染的水生环境中的寨卡病毒可通过繁殖传播给水生蚊子。为了研究受污染的水生环境对寨卡病毒传播的影响,我们通过引入一般入射函数来提出一个新的寨卡病毒模型。对于一般的发病函数,我们计算基本繁殖数\(R_0 \),分析无病平衡的稳定性,并给出发生反向分叉的一般条件。对于两个特殊的亚线性入射函数,\(R_0 = 1 \)是一个敏锐的门槛。这意味着可以通过将\(R_ {0} \)减小到1以下来根除该疾病。对于特殊的非线性入射函数,我们在理论上研究反向分叉和鞍形节点分叉,并通过数值模拟Hopf分叉。分析结果表明,从受污染的水生环境到水生蚊子的传播力在产生复杂的动力学过程中起着重要作用。此外,我们的模型被扩展以探索温度变异性对寨卡病传播的影响。

更新日期:2021-02-23
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