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异质环境中具有一般发病率的反应扩散SIRS模型的动力学

Dynamics of a reaction-diffusion SIRS model with general incidence rate in a heterogeneous environment.

作者信息

Avila-Vales Eric, Pérez Ángel G C

机构信息

Facultad de Matemáticas, Universidad Autónoma de Yucatán, Anillo Periférico Norte, Tablaje Catastral 13615, C.P. 97119 Mérida, Mexico.

出版信息

Z Angew Math Phys. 2022;73(1):9. doi: 10.1007/s00033-021-01645-0. Epub 2021 Nov 17.

DOI:10.1007/s00033-021-01645-0
PMID:34803189
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8596864/
Abstract

In this paper, we study a diffusive SIRS-type epidemic model with transfer from the infectious to the susceptible class. Our model includes a general nonlinear incidence rate and spatially heterogeneous diffusion coefficients. We compute the basic reproduction number of our model and establish the global stability of the disease-free steady state when . Furthermore, we study the uniform persistence when and perform a bifurcation analysis for a special case of our model. Some numerical simulations are presented to illustrate the dynamics of the solutions as the model parameters are varied.

摘要

在本文中，我们研究了一个具有从感染类向易感类转移的扩散SIRS型流行病模型。我们的模型包括一个一般的非线性发病率和空间异质扩散系数。我们计算了模型的基本再生数，并在 时建立了无病稳态的全局稳定性。此外，我们研究了 时的一致持久性，并对我们模型的一个特殊情况进行了分岔分析。给出了一些数值模拟来说明当模型参数变化时解的动态。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fda8/8596864/cf88c1ee8b3b/33_2021_1645_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fda8/8596864/ab1a547ac5e6/33_2021_1645_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fda8/8596864/acf20d4c1189/33_2021_1645_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fda8/8596864/a0f67abfc6a2/33_2021_1645_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fda8/8596864/62abff32f8bc/33_2021_1645_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fda8/8596864/cf88c1ee8b3b/33_2021_1645_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fda8/8596864/ab1a547ac5e6/33_2021_1645_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fda8/8596864/acf20d4c1189/33_2021_1645_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fda8/8596864/a0f67abfc6a2/33_2021_1645_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fda8/8596864/62abff32f8bc/33_2021_1645_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fda8/8596864/cf88c1ee8b3b/33_2021_1645_Fig5_HTML.jpg

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