<p>This paper proposes a reaction-diffusion epidemic model incorporating media coverage and vaccination strategies, and analyzes the transmission dynamics of diseases in spatially heterogeneous environments. The model innovatively considers the impact of environmental pollution on disease transmission and introduces nonlinear incidence rate functions to more accurately describe the disease transmission process. The study establishes the well-posedness of the model solution and calculates the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">$\mathcal{R}_{0}$</EquationSource> </InlineEquation> using the next generation infection operator. We derive the corresponding threshold results and prove that the disease-free equilibrium is globally asymptotically stable when <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo><</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$\mathcal{R}_{0}<1$</EquationSource> </InlineEquation>, while the disease persists when <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo>></mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$\mathcal{R}_{0}>1$</EquationSource> </InlineEquation>. In particular, for the spatially homogeneous case, we establish the existence and uniqueness of an endemic equilibrium when <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo>></mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$\mathcal{R}_{0}>1$</EquationSource> </InlineEquation>. Finally, numerical simulations validate the theoretical results and intuitively demonstrate the inhibitory effect of media coverage on disease transmission.</p>

Global Dynamics of a Reaction-Diffusion Epidemic Model in a Spatially Heterogeneous Environment

期刊论文
发表日期：

2026年1月19日

查看全文

Youhui Su,
Jing Zhang,
Weimin Hu,
Qian Wen

摘要

This paper proposes a reaction-diffusion epidemic model incorporating media coverage and vaccination strategies, and analyzes the transmission dynamics of diseases in spatially heterogeneous environments. The model innovatively considers the impact of environmental pollution on disease transmission and introduces nonlinear incidence rate functions to more accurately describe the disease transmission process. The study establishes the well-posedness of the model solution and calculates the basic reproduction number $R_{0}$ $\mathcal{R}_{0}$ using the next generation infection operator. We derive the corresponding threshold results and prove that the disease-free equilibrium is globally asymptotically stable when $R_{0} < 1$ $\mathcal{R}_{0}<1$ , while the disease persists when $R_{0} > 1$ $\mathcal{R}_{0}>1$ . In particular, for the spatially homogeneous case, we establish the existence and uniqueness of an endemic equilibrium when $R_{0} > 1$ $\mathcal{R}_{0}>1$ . Finally, numerical simulations validate the theoretical results and intuitively demonstrate the inhibitory effect of media coverage on disease transmission.