Modelling the effects of delayed mortality and saturated incidence on the population dynamics of infected ash trees

Zhenjie Zhang; Yueyang Ding; Nan Jiang; Ruizhi Yang; Zhenjie Zhang; Yueyang Ding; Nan Jiang; Ruizhi Yang

doi:10.3934/era.2026017

Electronic Research Archive

2026, Volume 34, Issue 1: 351-375. doi: 10.3934/era.2026017

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Research article

Modelling the effects of delayed mortality and saturated incidence on the population dynamics of infected ash trees

Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Received: 04 November 2025 Revised: 16 December 2025 Accepted: 04 January 2026 Published: 13 January 2026

This study centers on infectious disease models that feature a delayed mortality rate and the Holling II type functional response function. Through a theoretical analysis, it is confirmed that the solutions of the model possess positivity and boundedness, and the equilibrium points are obtained with their local and global stability conditions ascertained. The research indicates that, in the absence of time delay, transcritical and Hopf bifurcations emerge in the model under specific parameter conditions, thus furnishing a foundation to understand the dynamics of disease transmission. Subsequently, a time delay is incorporated into the system, and its impact on the Hopf bifurcation is analyzed. Numerical simulations depict the dynamic behaviors of the model at different delay times. For instance, the system can swiftly reach a stable state without delay, and periodic oscillations occur when the delay surpasses the critical value, thus validating the theory and suggesting that the delayed death factor has a significant influence. By comparing with actual data, the model effectively depicts the spread and lethality of the disease in infected ash trees across different regions, and uncovers the population differences and dynamic change patterns. Thus, it offers targeted strategies for disease prevention and control, as well as the ecological management of ash trees, which is relevant to the study on the impacts of delayed mortality and the Holling-II functional response function on the population dynamics of infected ash trees.
- bifurcation,
- delayed mortality,
- Holling type II,
- stability
Citation: Zhenjie Zhang, Yueyang Ding, Nan Jiang, Ruizhi Yang. Modelling the effects of delayed mortality and saturated incidence on the population dynamics of infected ash trees[J]. Electronic Research Archive, 2026, 34(1): 351-375. doi: 10.3934/era.2026017

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Abstract

This study centers on infectious disease models that feature a delayed mortality rate and the Holling II type functional response function. Through a theoretical analysis, it is confirmed that the solutions of the model possess positivity and boundedness, and the equilibrium points are obtained with their local and global stability conditions ascertained. The research indicates that, in the absence of time delay, transcritical and Hopf bifurcations emerge in the model under specific parameter conditions, thus furnishing a foundation to understand the dynamics of disease transmission. Subsequently, a time delay is incorporated into the system, and its impact on the Hopf bifurcation is analyzed. Numerical simulations depict the dynamic behaviors of the model at different delay times. For instance, the system can swiftly reach a stable state without delay, and periodic oscillations occur when the delay surpasses the critical value, thus validating the theory and suggesting that the delayed death factor has a significant influence. By comparing with actual data, the model effectively depicts the spread and lethality of the disease in infected ash trees across different regions, and uncovers the population differences and dynamic change patterns. Thus, it offers targeted strategies for disease prevention and control, as well as the ecological management of ash trees, which is relevant to the study on the impacts of delayed mortality and the Holling-II functional response function on the population dynamics of infected ash trees.

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