<p>A nonlocal delay reaction-diffusion Cholera model is developed to consider the effects of the latency delay of infected host and the phage-bacteria interaction. We prove, firstly, the well-posedness of solutions for this model, which includes the existence, uniqueness, boundedness and the existence of global attractor. And then, by using the next generation operator, the basic reproduction number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_10938_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathcal {R}}_{0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> is defined. Further, the disease-free steady state is globally asymptotically stable if <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_10938_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathcal {R}}_{0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> is less than one. And, the uniform persistence of model without phage is studied for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_10938_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathcal {R}}_0>1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Besides, the exact expression of the basic reproduction number <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_10938_Article_IEq4.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$\widetilde{{\mathcal {R}}}_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mover accent="true"> <mi mathvariant="script">R</mi> <mo stretchy="true">~</mo> </mover> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> of model with spatially homogeneous is obtained, which determines the existence and stability of the disease-free steady state, phage-free endemic steady state and phage-present endemic steady state. Finally, numerical simulations are presented to explain the main theoretical results and to discuss the effects of the latency delay and diffusion on the spatio-temporal distribution of the disease.</p>

Global dynamics of a nonlocal delayed reaction-diffusion Cholera model with phage-bacteria interaction

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发表日期：

2025年2月7日

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Zhenxiang Hu,
Jiao Li,
Lin Hu,
Linfei Nie

摘要

A nonlocal delay reaction-diffusion Cholera model is developed to consider the effects of the latency delay of infected host and the phage-bacteria interaction. We prove, firstly, the well-posedness of solutions for this model, which includes the existence, uniqueness, boundedness and the existence of global attractor. And then, by using the next generation operator, the basic reproduction number ${\mathcal {R}}_{0}$ $R_{0}$ is defined. Further, the disease-free steady state is globally asymptotically stable if ${\mathcal {R}}_{0}$ $R_{0}$ is less than one. And, the uniform persistence of model without phage is studied for ${\mathcal {R}}_0>1$ $R_{0} > 1$ . Besides, the exact expression of the basic reproduction number $\widetilde{{\mathcal {R}}}_0$ ${\tilde{R}}_{0}$ of model with spatially homogeneous is obtained, which determines the existence and stability of the disease-free steady state, phage-free endemic steady state and phage-present endemic steady state. Finally, numerical simulations are presented to explain the main theoretical results and to discuss the effects of the latency delay and diffusion on the spatio-temporal distribution of the disease.