Stochastic stability and global dynamics of a mathematical model for drug use: Statistical sensitivity analysis via PRCC

Abstract

This article examines the stochastic stability and global dynamics of a mathematical model of drug use. The model divides the population into five compartments current drug users, temporarily abstinent drug users, permanently abstinent drug users, and drug users in rehabilitation. Using Brownian motion, deterministic equations are extended to incorporate stochastic perturbations, capturing real-life uncertainties in drug use within compartments. An analysis of Lyapunov functions is used to determine the global stability of the model. By introducing stochastic elements into the model, we can examine its stability under random perturbations. A global sensitivity analysis, including PRCC results, is conducted to confirm the robustness of the model. Stable drug-free and drug-present equilibria can be maintained in both deterministic and stochastic environments. Numerical simulations illustrate the impact of various parameters on population dynamics and rehabilitation program effectiveness.