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

<p>In this paper, we propose a multi-group SEIR epidemic model with spatial diffusion, where the model parameters are spatially heterogeneous. The positivity and ultimate boundedness of the solution, as well as the existence of a global attractor of the associated solution semiflow, are established. The definition of the basic reproduction number is given by utilizing the next generation operator approach, whereby threshold-type results on the global dynamics in terms of this number are established. That is, when the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable, while if it is greater than one, uniform persistence of this model is proved. Finally, the feasibility of the main theoretical results is shown with the aid of numerical examples for a model with two groups.</p>
</abstract>

In this paper, we propose a multi-group SEIR epidemic model with spatial diffusion, where the model parameters are spatially heterogeneous. The positivity and ultimate boundedness of the solution, as well as the existence of a global attractor of the associated solution semiflow, are established. The definition of the basic reproduction number is given by utilizing the next generation operator approach, whereby threshold-type results on the global dynamics in terms of this number are established. That is, when the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable, while if it is greater than one, uniform persistence of this model is proved. Finally, the feasibility of the main theoretical results is shown with the aid of numerical examples for a model with two groups.

Global Behavior of a Multi–Group Seir Epidemic Model with Spatial Diffusion in a Heterogeneous Environment

Tianjin University of Technology and Education

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper, we propose a multi-group SEIR epidemic model with spatial diffusion, where the model parameters are spatially heterogeneous. The positivity and...

Global Behavior of a Multi–Group Seir Epidemic Model with Spatial Diffusion in a Heterogeneous Environment

Online veröffentlicht: 04. Juli 2022

Seitenbereich: 271 - 283

Eingereicht: 14. Nov. 2021

Akzeptiert: 18. März 2022

DOI: https://doi.org/10.34768/amcs-2022-0020

Schlüsselwörter
global stability, multi-group epidemic model, spatial heterogeneity, spatial diffusion

© 2022 Pengyan Liu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Global Behavior of a Multi–Group Seir Epidemic Model with Spatial Diffusion in a Heterogeneous Environment

Online veröffentlicht: 04. Juli 2022

Seitenbereich: 271 - 283

Eingereicht: 14. Nov. 2021

Akzeptiert: 18. März 2022

DOI: https://doi.org/10.34768/amcs-2022-0020

Schlüsselwörterglobal stability, multi-group epidemic model, spatial heterogeneity, spatial diffusion

© 2022 Pengyan Liu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Schlüsselwörter
global stability, multi-group epidemic model, spatial heterogeneity, spatial diffusion