Research article

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

  • Received: 14 April 2021 Accepted: 25 June 2021 Published: 05 July 2021
  • 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.

    Citation: Lin Zhao, Haifeng Huo. Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmission[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 6012-6033. doi: 10.3934/mbe.2021301

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  • 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.



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