Mathematical Modeling and Simulation of Logistic Growth

We propose a reproducible pipeline of work consisting of the time-driven simulation of discrete logistic growth based on the corresponding master equation, focusing on demographic variation under a carrying capacity limit. The mathematical modeling that leads to the stochastic implementation is presented in a step-by-step fashion to statistically ground the designed simulation. The main parameters of the system, whose settings include extreme values, are varied to analyze the simulation behavior and explore the empirical limits of its applicability, minimizing the distance between the theoretical and observed carrying capacity trough parameter tuning. After such tuning, a single simulation scenario is chosen and compared with the state-of-the-art Gillespie algorithm, which adopts a contrasting event-driven approach. The output analysis of these two strategies and the assessment of their statistical significance highlight the trade-off between adherence to the model and the computational effort of the proposed approach, while shedding light on multiple facets of logistic growth, including discrepancies between continuous and discrete models.