Bacterial wilt, primarily caused by the pathogens Ralstonia solanacearum and Fusarium oxysporum, poses a major threat to global agriculture. Among the affected crops, tomatoes are particularly vulnerable due to their significant economic and nutritional value worldwide, often suffering substantial yield losses from this devastating disease. In this study, we present a comprehensive mathematical model to investigate the dynamics of soil-borne diseases in tomatoes. The model is formulated within a Two-Dimensional Spatiotemporal framework, denoted as <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2187_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="97" /> </InlineMediaObject> <EquationSource Format="TEX">$Y_{T}I_{F}I_{D}M_{T}B$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>Y</mi> <mi>T</mi> </msub> <msub> <mi>I</mi> <mi>F</mi> </msub> <msub> <mi>I</mi> <mi>D</mi> </msub> <msub> <mi>M</mi> <mi>T</mi> </msub> <mi>B</mi> </mrow> </math></EquationSource> </InlineEquation>, and utilizes fractional-order derivatives in the Caputo sense. We derive the basic reproduction number, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2187_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$R_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>, as a key threshold parameter. Our analysis shows that when <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2187_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$R_0<1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, the disease-free equilibrium is globally stable, while for <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2187_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$R_0>1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, an endemic equilibrium emerges, indicating the persistence of infection within the crop population. Extensive simulations conducted in Matlab validate the robustness of our theoretical findings and demonstrate the model’s effectiveness in predicting and managing the spread of bacterial wilt in tomatoes.

Spatiotemporal stability analysis of soil-borne disease dynamics in tomato plants

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发表日期：

2025年1月27日

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Imane Smouni,
Mohamed Baroudi,
Mohamed Alia,
Abdelbar Elmansouri,
Abderrahim Labzai,
Mohamed Belam

摘要

Bacterial wilt, primarily caused by the pathogens Ralstonia solanacearum and Fusarium oxysporum, poses a major threat to global agriculture. Among the affected crops, tomatoes are particularly vulnerable due to their significant economic and nutritional value worldwide, often suffering substantial yield losses from this devastating disease. In this study, we present a comprehensive mathematical model to investigate the dynamics of soil-borne diseases in tomatoes. The model is formulated within a Two-Dimensional Spatiotemporal framework, denoted as $Y_{T}I_{F}I_{D}M_{T}B$ $Y_{T} I_{F} I_{D} M_{T} B$ , and utilizes fractional-order derivatives in the Caputo sense. We derive the basic reproduction number, $R_0$ $R_{0}$ , as a key threshold parameter. Our analysis shows that when $R_0<1$ $R_{0} < 1$ , the disease-free equilibrium is globally stable, while for $R_0>1$ $R_{0} > 1$ , an endemic equilibrium emerges, indicating the persistence of infection within the crop population. Extensive simulations conducted in Matlab validate the robustness of our theoretical findings and demonstrate the model’s effectiveness in predicting and managing the spread of bacterial wilt in tomatoes.