<p>In this research article, a theta logistic model is proposed and analyzed for the dynamics of vector borne plant disease in Cassava. The model contains two populations namely the plant and the vector population. The vector population follows theta logistic growth as theta logistic growth curve is a more natural choice in comparison with the classical logistic growth curve model. We have also include the effects of roguing and pesticide spraying on dynamics of the mosaic disease. We examine how different values of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2419_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\theta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> might impact crop survival during vector invasion by utilizing control measures which enhances the biological realism of the model. For the analytical analysis of the theta-logistic model system, we derive the discreet-time version of the continuous model. The analytical results are validated by numerical simulations. The results show that the system is stable when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2419_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\theta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> lies below a threshold value and unstable via limit cycle oscillation when <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2419_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\theta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> crosses the critical value that lasts until <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2419_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">$\theta = 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>θ</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. The critical value of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2419_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\theta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> is 0.485 and this value depends on other parameters such as the infection rate, roguing and insecticides spraying. This study shows that the results obtained from theta-logistic model are more applicable for proper management of mosaic disease in Cassava.</p>

A theta logistic model for the dynamics of whitefly borne mosaic disease in Cassava: impact of roguing and insecticide spraying

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发表日期：

2025年2月20日

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Jahangir Chowdhury,
Fahad Al Basir,
Anirban Mukherjee,
Priti Kumar Roy

摘要

In this research article, a theta logistic model is proposed and analyzed for the dynamics of vector borne plant disease in Cassava. The model contains two populations namely the plant and the vector population. The vector population follows theta logistic growth as theta logistic growth curve is a more natural choice in comparison with the classical logistic growth curve model. We have also include the effects of roguing and pesticide spraying on dynamics of the mosaic disease. We examine how different values of $\theta $ $θ$ might impact crop survival during vector invasion by utilizing control measures which enhances the biological realism of the model. For the analytical analysis of the theta-logistic model system, we derive the discreet-time version of the continuous model. The analytical results are validated by numerical simulations. The results show that the system is stable when $\theta $ $θ$ lies below a threshold value and unstable via limit cycle oscillation when $\theta $ $θ$ crosses the critical value that lasts until $\theta = 1$ $θ = 1$ . The critical value of $\theta $ $θ$ is 0.485 and this value depends on other parameters such as the infection rate, roguing and insecticides spraying. This study shows that the results obtained from theta-logistic model are more applicable for proper management of mosaic disease in Cassava.