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<p>Banana bunchy top disease is a viral infection that threatens banana production, food, and nutritional security. Understanding the transmission dynamics of this virus is essential for developing effective control strategies. This study utilized a fractional-order framework to investigate the impact of memory and stakeholder awareness on the transmission dynamics of banana bunchy top disease, thereby providing novel theoretical insights into plant pathology. The model was formulated as a Caputo fractional differential equation system that encapsulates stakeholders awareness and memory effects which allow the present dynamics to depend on past states. The qualitative features of the model, including the existence and uniqueness of the solutions, positivity, and boundedness, were examined rigorously. The equilibria of the model were derived and analyzed for stability. Local stability was determined using Routh’s criterion, and global stability was established in the Ulam-Hyers sense. The model was subsequently solved numerically using the Adams-Bashforth-Moulton predictor-corrector method. The numerical results demonstrated that the number of latent and symptomatic infected banana plants and infected aphid vectors decreased as memory increased, underscoring the significant impact of memory on disease evolution and demonstrating the theoretical insights of incorporating memory-related dynamics into modeling Banana Bunchy Top Disease (BBTD) transmission, offering new perspectives on how past states and interventions shape epidemic outcomes. Moreover, the effects of varying levels of stakeholder awareness were examined while maintaining the fractional order of the Caputo derivative at <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2640_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha = 0.8\)</EquationSource> </InlineEquation>, which indicates a moderate memory effect within the system. The findings indicate that implementing stakeholders’ awareness programs reduces the incidence of banana bunchy top disease outbreaks. Therefore, early and sustained control strategies, such as awareness campaigns and roguing, are recommended.</p>

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Caputo fractional model of banana bunchy top virus (BBTV) transmission with memory and stakeholder awareness

  • 期刊论文

  • 发表日期：

    2025年10月14日

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  • John J. Mapinda,
  • Alfred K. Hugo,
  • Jairos K. Shinzeh,
  • Stephen Edward

摘要

Banana bunchy top disease is a viral infection that threatens banana production, food, and nutritional security. Understanding the transmission dynamics of this virus is essential for developing effective control strategies. This study utilized a fractional-order framework to investigate the impact of memory and stakeholder awareness on the transmission dynamics of banana bunchy top disease, thereby providing novel theoretical insights into plant pathology. The model was formulated as a Caputo fractional differential equation system that encapsulates stakeholders awareness and memory effects which allow the present dynamics to depend on past states. The qualitative features of the model, including the existence and uniqueness of the solutions, positivity, and boundedness, were examined rigorously. The equilibria of the model were derived and analyzed for stability. Local stability was determined using Routh’s criterion, and global stability was established in the Ulam-Hyers sense. The model was subsequently solved numerically using the Adams-Bashforth-Moulton predictor-corrector method. The numerical results demonstrated that the number of latent and symptomatic infected banana plants and infected aphid vectors decreased as memory increased, underscoring the significant impact of memory on disease evolution and demonstrating the theoretical insights of incorporating memory-related dynamics into modeling Banana Bunchy Top Disease (BBTD) transmission, offering new perspectives on how past states and interventions shape epidemic outcomes. Moreover, the effects of varying levels of stakeholder awareness were examined while maintaining the fractional order of the Caputo derivative at \(\alpha = 0.8\) , which indicates a moderate memory effect within the system. The findings indicate that implementing stakeholders’ awareness programs reduces the incidence of banana bunchy top disease outbreaks. Therefore, early and sustained control strategies, such as awareness campaigns and roguing, are recommended.