Problem description

This project studies the population dynamics of a citrus agroecosystem through a system of nonlinear ordinary differential equations involving four interacting components:

• Diaphorina citri (insect pest / parasite)
• Plant shoots
• Tamarixia radiata (parasitoid)
• External stimuli

The model captures intrinsic growth, nonlinear self-limitation, and cross-species interactions through a generalized interaction matrix. Population dynamics evolve continuously in time, except for periodic augmentative releases of parasitoids, which model biological control interventions.

Periodic parasitoid releases

Parasitoid releases are implemented as impulsive events that instantaneously increase the parasitoid population by a fixed amount δ every T time units, while allowing continuous evolution between releases.

• In Wolfram Language, this mechanism is implemented using WhenEvent, directly modifying the state during numerical integration.
• In Python, the same behavior is reproduced using scipy.integrate.solve_ivp together with explicit event handling (via segmented integration or the scipy-events package).

This ensures the mathematical equivalence of the impulsive dynamics across both implementations.

Numerical methods

• The Wolfram Language version uses NDSolve with an explicit Runge–Kutta time integration scheme.
• The Python version relies on adaptive Runge–Kutta methods provided by SciPy, with configurable tolerances to balance accuracy and performance.

The resulting population trajectories are computed over a specified time horizon and visualized to analyze the impact of periodic parasitoid augmentation on ecosystem stability.

References

The modeling approach and biological motivation are inspired by:

Stucchi, L., Giménez-Benavides, L., & Galeano, J.
The role of parasitoids in a nursery–pollinator system: A population dynamics model.

Purpose of this repository

• Provide equivalent implementations of a hybrid continuous–discrete ecological model in Wolfram Language and Python.
• Demonstrate how impulsive differential equations can be faithfully translated between symbolic and numerical environments.
• Serve as a reference for researchers modeling biological control strategies using periodic interventions.