A diffusive virus infection dynamic model with nonlinear functional response, absorption effect and chemotaxis

作者：Wang, Wei; Ma, Wanbiao^*; Lai, Xiulan

来源：Communications in Nonlinear Science & Numerical Simulation, 2017, 42: 585-606.

DOI：10.1016/j.cnsns.2016.05.010

• Virus infection dynamic model
• Absorption effect
• Basic reproduction number
• Travelling wave solutions
• Chemotaxis

From a biological perspective, a diffusive virus infection dynamic model with nonlinear functional response, absorption effect and chemotaxis is proposed. In the model, the diffusion of virus consists of two parts, the random diffusion and the chemotactic movement. The chemotaxis flux of virus depends not only on their own density, but also on the density of infected cells, and the density gradient of infected cells. The well posedness of the proposed model is deeply investigated. For the proposed model, the linear stabilities of the infection-free steady state E-0 and the infection steady state E* are extensively performed. We show that the threshold dynamics can be expressed by the basic reproduction number R-0 of the model without chemotaxis. That is, the infection-free steady state E-0 is globally asymptotically stable if R-0 < 1, and the virus is uniformly persistent if R-0 > 1. In addition, we use the cross iteration method and the Schauder's fixed point theorem to prove the existence of travelling wave solutions connecting the infection-free steady state E-0 and the infection steady state E* by constructing a pair of upper-lower solutions. At last, numerical simulations are presented to confirm theoretical findings.

• 出版日期2017-1
• 单位北京科技大学; 中国人民大学