<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>As the primary killer of health, the class of infectious diseases is the greatest threat to humanity. At present, international methods of studying the large-scale spatial transmission of sudden infectious diseases from the perspective of dynamics can be divided into two categories. On the one hand, top international biomedical and medical teams discuss the restraining effects of some prevention and control strategies on infectious diseases, such as smallpox, malaria, hand, foot and mouth disease and pandemic influenza, from the perspective of pragmatism. On the other hand, researchers in theoretical physics and network science tend to use compound population network models to explore the internal dynamic mechanism of spatial transmission of infectious diseases. This paper establishes a Lotka–Volterra dispersal predator–prey system in a patchy environment. It shows the existence of model boundary equilibria and asymptotic stability under an appropriate condition. This paper adopts the method of global Lyapunov function and the results of graph theory. We also consider a predator–prey dynamical model in a patchy environment, where the prey and predator individuals in each compartment can travel among <italic>n</italic> patches.</p>
</abstract>

As the primary killer of health, the class of infectious diseases is the greatest threat to humanity. At present, international methods of studying the large-scale spatial transmission of sudden infectious diseases from the perspective of dynamics can be divided into two categories. On the one hand, top international biomedical and medical teams discuss the restraining effects of some prevention and control strategies on infectious diseases, such as smallpox, malaria, hand, foot and mouth disease and pandemic influenza, from the perspective of pragmatism. On the other hand, researchers in theoretical physics and network science tend to use compound population network models to explore the internal dynamic mechanism of spatial transmission of infectious diseases. This paper establishes a Lotka–Volterra dispersal predator–prey system in a patchy environment. It shows the existence of model boundary equilibria and asymptotic stability under an appropriate condition. This paper adopts the method of global Lyapunov function and the results of graph theory. We also consider a predator–prey dynamical model in a patchy environment, where the prey and predator individuals in each compartment can travel among n patches.

Asymptotic stability problem of predator–prey system with linear diffusion

Department of Civil and Architectural Engineering, College of Engineering

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Asymptotic stability problem of predator\u2013prey system with linear diffusion"}

As the primary killer of health, the class of infectious diseases is the greatest threat to humanity. At present, international methods of studying the...

Asymptotic stability problem of predator–prey system with linear diffusion

Published Online: Sep 05, 2022

Page range: 15 - 26

Received: Nov 09, 2021

Accepted: May 15, 2022

DOI: https://doi.org/10.2478/amns.2022.1.00022

Keywords
Equilibria, patchyenvironments, graph theory, Lyapunov function

© 2022 Yanqiu Li et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Asymptotic stability problem of predator–prey system with linear diffusion

Published Online: Sep 05, 2022

Page range: 15 - 26

Received: Nov 09, 2021

Accepted: May 15, 2022

DOI: https://doi.org/10.2478/amns.2022.1.00022

KeywordsEquilibria, patchyenvironments, graph theory, Lyapunov function

© 2022 Yanqiu Li et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Equilibria, patchyenvironments, graph theory, Lyapunov function