Disease transmission dynamics of an epidemiological predator-prey system in open advective environments

Shuai Li; Sanling Yuan; Hao Wang

doi:10.3934/dcdsb.2022131

Article Contents

2023, Volume 28, Issue 2: 1480-1502. Doi: 10.3934/dcdsb.2022131

This issue Previous Article Characterizing the existence of positive periodic solutions in the weighted periodic-parabolic degenerate logistic equation Next Article Limit cycles in a switching Liénard system

Disease transmission dynamics of an epidemiological predator-prey system in open advective environments

1.
University of Shanghai for Science and Technology, Shanghai 200093, China
2.
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

^* Corresponding author: Sanling Yuan
^* Corresponding author: Sanling Yuan

Received: February 2022

Revised: May 2022

Early access: July 2022

Published: February 2023

The second author is partially supported by the National Natural Science Foundation of China (Grant 12071293). The third author is partially supported by the Natural Sciences and Engineering Research Council of Canada (Discovery Grant RGPIN-2020-03911 and Accelerator Grant RGPAS-2020-00090).

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Abstract

This paper delves into the dynamics of a spatial eco-epidemiological system with disease spread within the predator population in open advective environments. The disease-free subsystem is first discussed, and the net reproductive rate $ R_P $ is established to determine whether the predator can invade successfully. The impacts of advection rate on $ R_P $ are also discussed. Then for the scenario of successful invasion of the predator, sufficient conditions for the prevalence of disease and the local stability of disease-free attractor are obtained by dint of persistence theory and comparison theorem. Finally, we present a special numerical example, in which the basic reproduction ratio $ R_0 $ of the disease is established in the absence or presence of periodic perturbation. Our theoretical and numerical results both indicate that the advection rate in an intermediate interval can favor the coexistence of prey and healthy predator as well as the eradication of disease.

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Mathematics Subject Classification: Primary: 92D25, 92D30, 35A01, 35B35.

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Figure 1. The temporal-spatial evolution of system (1) with $ (\sigma,\vartheta,\beta) = (0.35,0.13,1) $

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Figure 2. The temporal-spatial evolution of system (1) with $ (\sigma,\vartheta,\beta) = (0.35,0.14,1) $

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Figure 3. Bifurcation diagram about $ \vartheta $ with $ \sigma = 0.35, \beta = 1 $

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Figure 4. The temporal-spatial evolution of system (1) with $ (\sigma,\vartheta,\beta) = (0.10,0.14,0.460) $

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Figure 5. The temporal-spatial evolution of system (1) with $ (\sigma,\vartheta,\beta) = (0.10,0.14,0.445) $

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Figure 6. Bifurcation diagram about $ \vartheta $ with $ \sigma = 0.1,\ \beta = 0.445 $

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Figure 7. Bifurcation diagram of $ I $ with respect to $ R_0 $ and $ \xi $

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