Individual impacts of memory-mediated recovery and periodic intervention on epidemic population systems: Dynamic modeling and qualitative analysis

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Abstract

This work developed a modified Gompertz-type pest-natural enemy population model that accounts for infected natural enemies and state-dependent searching behavior. The model was then extended by incorporating two further mechanisms, namely, memory-mediated disease recovery and periodic intervention. Systematic theoretical analyses were conducted on solution boundedness, the existence and local asymptotic stability of equilibria, and transcritical bifurcation behaviors. These analyses clarify the suppression mechanism of natural-enemy predation on pest proliferation and reveal the regulatory effects of the variable searching rate and memory parameters on system dynamics. Considering that natural-enemy predation alone achieves sustainable biological control but responds slowly and cannot rapidly suppress pest outbreaks, the present work adopted an integrated strategy that combines periodic natural-enemy release with pesticide spraying to enhance pest control efficacy. The global asymptotic stability of pest-free periodic solutions was established, and parametric thresholds ensuring system persistence within a specific impulsive-period range were derived. Furthermore, sufficient criteria were provided for the global asymptotic stability of the system under pest-extinction and infected-predator-extinction scenarios, together with conditions for population persistence and the coexistence of periodic solutions. All theoretical results were validated via MATLAB numerical simulations. This study extends the theoretical framework of population dynamics and provides reliable references for integrated pest prevention and ecological regulation.

Keywords

memory-mediated recovery / periodic intervention / epidemic population model / variable searching rate

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