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Dynamics analysis of a Filippov ash infectious diseases model with a saturated incidence rate and delayed mortality

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  • Zhang, Zhenjie
  • Yang, Ruizhi

Abstract

The prevention and control of ash tree infectious diseases is a significant challenge in forestry ecological protection. Aiming at the saturated incidence rate and delayed mortality in its disease transmission process, this paper constructs a Filippov model with a susceptible population threshold strategy, aiming to explore the regulatory mechanisms of such threshold control strategies and time delay and other factors on the dynamic behavior of the system. By analyzing the equilibrium points of subsystems and the characteristics of sliding mode dynamics, the study finds that changes in the value of the threshold can trigger complex behaviors such as system bifurcation, while changes in the time delay parameter significantly affect the stability of the system. Numerical simulations verify the interaction between these two parameters in disease transmission. In conclusion, precise regulation of the threshold and attention to the time delay effect are crucial for the effective prevention and control of ash tree infectious diseases. This study provides a theoretical basis for forestry disease management and highlights the value of a comprehensive prevention and control strategy that combines population density regulation and time delay effects.

Suggested Citation

  • Zhang, Zhenjie & Yang, Ruizhi, 2026. "Dynamics analysis of a Filippov ash infectious diseases model with a saturated incidence rate and delayed mortality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 513-527.
    • Handle: RePEc:eee:matcom:v:241:y:2026:i:pa:p:513-527
    DOI: 10.1016/j.matcom.2025.09.014
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    References listed on IDEAS

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    1. Zhou, Weike & Zhao, Tingting & Wang, Aili & Tang, Sanyi, 2024. "Bifurcations and dynamics of a Filippov epidemic model with nonlinear threshold control policy and medical-resource constraints," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    2. Dong, Cunjuan & Xiang, Changcheng & Xiang, Zhongyi & Yang, Yi, 2022. "Global dynamics of a Filippov epidemic system with nonlinear thresholds," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    3. Jiao, Xubin & Liu, Li & Yu, Xiao, 2025. "Rich dynamics of a reaction–diffusion Filippov Leslie–Gower predator–prey model with time delay and discontinuous harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 339-361.
    4. Jiao, Xubin & Li, Xiaodi & Yang, Youping, 2022. "Dynamics and bifurcations of a Filippov Leslie-Gower predator-prey model with group defense and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Li, Wenxiu & Chen, Yuming & Huang, Lihong & Wang, Jiafu, 2022. "Global dynamics of a filippov predator-prey model with two thresholds for integrated pest management," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    6. Zhou, Hao & Zhang, Qianqian & Tang, Sanyi, 2025. "Qualitative analysis of the sliding vector field in a Filippov food chain model with integrated pest management strategy," Applied Mathematics and Computation, Elsevier, vol. 490(C).
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