Spatial dynamics of an epidemic model in time almost periodic and space periodic media

Ming-Zhen Xin; Bin-Guo Wang

doi:10.3934/dcdsb.2022116

Article Contents

2023, Volume 28, Issue 2: 1159-1184. Doi: 10.3934/dcdsb.2022116

This issue Previous Article Global attractor for the periodic generalized Korteweg-De Vries equation through smoothing Next Article Stability and dynamics of spike-type solutions to delayed Gierer-Meinhardt equations

Spatial dynamics of an epidemic model in time almost periodic and space periodic media

Ming-Zhen Xin and
Bin-Guo Wang^,

School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China

^* Corresponding author: Bin-Guo Wang
^* Corresponding author: Bin-Guo Wang

Received: March 2022

Revised: May 2022

Early access: June 2022

Published: February 2023

Research supported by NSF of China 11501269 and Natural Science Foundation of Gansu Province of China (grant number: 21JR7RA535)

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Abstract

This paper is devoted to the study of a reaction-diffusion-advection epidemic model in time almost periodic and space periodic media. First, we obtain a threshold result on the global stability of either zero or the positive time almost periodic solution in terms of the basic reproduction ratio $ \mathcal{R}_0 $. Second, we prove the existence of spreading speeds in the partially spatially homogeneous case and the general case. At last, we use numerical simulations to investigate the influence of model parameters on spreading speeds.

Keywords:

Epidemic model,
time almost periodic and space periodic,
basic reproduction ratio,
spreading speeds.

Mathematics Subject Classification: Primary: 35K15, 35K57, 35C07; Secondary: 92D30.

Citation:

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Figure 1. The evolution of $ u_1 $ and $ u_2 $

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Figure 2. The relationship between $ c_-^* $, $ c_+^* $ and $ k_{d_1}, k_{d_2}, k_q, k_p $

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Figure 3. The evolution of $ u_1 $ and $ u_2 $

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Figure 4. The relationship between $ c_-^* $, $ c_+^* $ and $ k_{d_1}, k_{d_2}, k_q, k_p $

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