A cross-infection model with diffusion and incubation period

Danfeng Pang; Yanni Xiao; Xiao-Qiang Zhao

doi:10.3934/dcdsb.2021316

Article Contents

2022, Volume 27, Issue 11: 6269-6294. Doi: 10.3934/dcdsb.2021316

This issue Previous Article New insights to the Hide-Skeldon-Acheson dynamo Next Article Existence of ground states for Schrödinger-Poisson system with nonperiodic potentials

A cross-infection model with diffusion and incubation period

1.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China
2.
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada

^* Corresponding author
^* Corresponding author

Received: July 2021

Revised: December 2021

Early access: January 2022

Published: October 2022

This research was supported by the China Scholarship Council grant (Pang: 201906280199), the National Natural Science Foundation of China (Xiao: NSFC 11631012), and the NSERC of Canada (Zhao: RGPIN-2019-05648)

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Abstract

In this paper, we study a cross-infection model with diffusion and incubation period. Firstly, we prove the global attractivity of the infection-free equilibrium and infected equilibrium for the spatially homogeneous system. Secondly, we establish the threshold dynamics for the spatially heterogeneous system in terms of the basic reproduction number $ \mathcal{R}_0 $. It turns out that the infection-free steady state is globally attractive if $ \mathcal{R}_0<1 $; and the system is uniformly persistent if $ \mathcal{R}_0>1 $. Finally, we explore the influence of different diffusion coefficients, spatial heterogeneity of the disease transmission rate and the incubation period on $ \mathcal{R}_0 $. Our numerical results show that $ \mathcal{R}_0 $ are decreasing functions of the diffusion coefficients and the incubation period, respectively, while it is increasing with respect to the spatial heterogeneity.

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Mathematics Subject Classification: Primary: 35K57, 37N25; Secondary: 92D30.

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Figure 1. Schematic diagram for transmission of HCWs, patients and environmental bacteria in hospital

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Figure 2. Persistence of contaminated health-care workers, the infectious patients and the environmental bacteria when $ \mathcal{R}_0 = 1.5544>1 $

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Figure 3. Elimination of the contaminated health-care workers, the infectious patients and the environmental bacteria when $ \mathcal{R}_0 = 0.4984<1 $. Here $ \gamma = 240 $, $ c = 7 $

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Figure 4. $ \mathcal{R}_0 $ vs $ D_H, D_P $ and $ D_W $

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Figure 5. The effects of spatial heterogeneity and incubation period on $ \mathcal{R}_0 $

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