Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmission

Mathematical Biosciences and Engineering

Lin Zhao¹  Haifeng Huo¹ 

[1] Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China;

关键词: non-monotone system;    si epidemic model;    vertical transmission;    spreading speed;   

DOI  :  10.3934/mbe.2021301

来源: DOAJ

【 摘 要 】

In this paper, we focus on spreading speed of a reaction-diffusion SI epidemic model with vertical transmission, which is a non-monotone system. More specifically, we prove that the solution of the system converges to the disease-free equilibrium as $ t \rightarrow \infty $ if $ R_{0} \leqslant 1 $ and if $ R_0 > 1 $, there exists a critical speed $ c^\diamond > 0 $ such that if $ \|x\| = ct $ with $ c \in (0, c^\diamond) $, the disease is persistent and if $ \|x\| \geqslant ct $ with $ c > c^\diamond $, the infection dies out. Finally, we illustrate the asymptotic behaviour of the solution of the system via numerical simulations.

【 授权许可】

Unknown