### Mathematical Biosciences and Engineering

2020, Issue 5: 4678-4705. doi: 10.3934/mbe.2020257
Research article Special Issues

# Global dynamics of a delayed diffusive virus infection model with cell-mediated immunity and cell-to-cell transmission

• Received: 09 May 2020 Accepted: 03 July 2020 Published: 08 July 2020
• In this paper, we propose and analyze a delayed diffusive viral dynamic model incorporating cell-mediated immunity and both cell-free and cell-to-cell transmission. After discussing the well-posedness, we provide some preliminary results on solutions. Then we study the existence and uniqueness of homogeneous steady states, which turned out to be completely determined by the basic reproduction number of infection R0 and the basic reproduction number of immunity R1. Note that when R1 is defined, it is necessary that R0 > 1. The main result is a threefold dynamics. Roughly speaking, when R0 < 1 the infection-free steady state is globally asymptotically stable; when R1 ≤ 1 < R0 the immunity-free infected steady state is globally asymptotically stable; when R1 > 1 the infected-immune steady state is globally asymptotically stable. The approaches are linearization technique and the Lyapunov functional method. The theoretical results are also illustrated with numerical simulations.

Citation: Chunyang Qin, Yuming Chen, Xia Wang. Global dynamics of a delayed diffusive virus infection model with cell-mediated immunity and cell-to-cell transmission[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 4678-4705. doi: 10.3934/mbe.2020257

### Related Papers:

• In this paper, we propose and analyze a delayed diffusive viral dynamic model incorporating cell-mediated immunity and both cell-free and cell-to-cell transmission. After discussing the well-posedness, we provide some preliminary results on solutions. Then we study the existence and uniqueness of homogeneous steady states, which turned out to be completely determined by the basic reproduction number of infection R0 and the basic reproduction number of immunity R1. Note that when R1 is defined, it is necessary that R0 > 1. The main result is a threefold dynamics. Roughly speaking, when R0 < 1 the infection-free steady state is globally asymptotically stable; when R1 ≤ 1 < R0 the immunity-free infected steady state is globally asymptotically stable; when R1 > 1 the infected-immune steady state is globally asymptotically stable. The approaches are linearization technique and the Lyapunov functional method. The theoretical results are also illustrated with numerical simulations.

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

2.6 3.9

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