A discrete-time mathematical model for mosaic disease dynamics in cassava: Neimark-Sacker bifurcation and sensitivity analysis

Selim Reja; Fahad Al Basir; Khalid Aldawsari; Selim Reja; Fahad Al Basir; Khalid Aldawsari

doi:10.3934/math.2025817

AIMS Mathematics

2025, Volume 10, Issue 8: 18295-18320. doi: 10.3934/math.2025817

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Research article

A discrete-time mathematical model for mosaic disease dynamics in cassava: Neimark-Sacker bifurcation and sensitivity analysis

1.
Agricultural and Ecological Research Unit, Indian Statistical Institute, Kolkata 700108, West Bengal, India
2.
Department of Mathematics, Asansol Girls' College, Asansol 713304, West Bengal, India
3.
Department of Mathematics, College of Science and Humanities, Prince Sattam Bin Abdulaziz University, Al Kharj 11942, Saudi Arabia

Received: 04 June 2025 Revised: 28 July 2025 Accepted: 06 August 2025 Published: 13 August 2025
MSC : 39A22, 39A28, 39A30

Cassava mosaic disease remains a significant threat to cassava production, leading to severe yield losses and food insecurity. While several continuous-time models have been proposed to understand cassava mosaic disease transmission, there is limited understanding of cassava mosaic disease behavior in discrete-time settings. Discrete-time models are often easier to apply in agricultural settings, as they align more naturally with seasonal planting schedules and data collection intervals. To address this, we developed and analyzed a novel discrete-time mathematical model that captured the complex dynamics of cassava mosaic disease transmission via whitefly vectors. We introduced a density-dependent modification theorem for the nonnegativity and discussed the boundedness of solutions. The basic reproduction number was derived, and the stability of the disease-free equilibrium was examined. Additionally, we investigated the existence and stability of endemic fixed points. We conducted an analytical study of the Neimark-Sacker bifurcation using a novel approach without eigenvalues. Furthermore, we performed a comprehensive sensitivity analysis of our discrete model using Sobol indices. Numerical simulations validated our analytical findings and illustrated the impact of various parameters on the stability of fixed points. We also presented stability regions in different parameter planes. Our findings emphasized that elevated infection rates contributed to seasonal outbreaks of cassava mosaic disease. Furthermore, effective management of both plant infection rates and vector abundance was essential for controlling the disease. Finally, our results were consistent with those obtained from continuous models.
- discrete model setup,
- boundedness and convergence of solutions,
- Jury criteria,
- Sobol indices and sensitivity analysis,
- Neimark-Sacker bifurcation,
- numerical verifications
Citation: Selim Reja, Fahad Al Basir, Khalid Aldawsari. A discrete-time mathematical model for mosaic disease dynamics in cassava: Neimark-Sacker bifurcation and sensitivity analysis[J]. AIMS Mathematics, 2025, 10(8): 18295-18320. doi: 10.3934/math.2025817

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Abstract

Cassava mosaic disease remains a significant threat to cassava production, leading to severe yield losses and food insecurity. While several continuous-time models have been proposed to understand cassava mosaic disease transmission, there is limited understanding of cassava mosaic disease behavior in discrete-time settings. Discrete-time models are often easier to apply in agricultural settings, as they align more naturally with seasonal planting schedules and data collection intervals. To address this, we developed and analyzed a novel discrete-time mathematical model that captured the complex dynamics of cassava mosaic disease transmission via whitefly vectors. We introduced a density-dependent modification theorem for the nonnegativity and discussed the boundedness of solutions. The basic reproduction number was derived, and the stability of the disease-free equilibrium was examined. Additionally, we investigated the existence and stability of endemic fixed points. We conducted an analytical study of the Neimark-Sacker bifurcation using a novel approach without eigenvalues. Furthermore, we performed a comprehensive sensitivity analysis of our discrete model using Sobol indices. Numerical simulations validated our analytical findings and illustrated the impact of various parameters on the stability of fixed points. We also presented stability regions in different parameter planes. Our findings emphasized that elevated infection rates contributed to seasonal outbreaks of cassava mosaic disease. Furthermore, effective management of both plant infection rates and vector abundance was essential for controlling the disease. Finally, our results were consistent with those obtained from continuous models.

References

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