Survival analysis and probability density function of switching heroin model

Area of Science:

• Epidemiology
• Mathematical Biology
• Stochastic Processes

Background:

• Heroin addiction poses a significant public health challenge.
• Opium poppy cultivation cycles influence heroin supply, creating dynamic epidemic conditions.
• Stochastic modeling is crucial for understanding complex epidemiological systems.

Purpose of the Study:

• To develop and analyze a switching heroin epidemic model incorporating Markov chains.
• To investigate the conditions for the existence and uniqueness of solutions.
• To determine the survival dynamics (extinction and persistence) of untreated drug addicts.

Main Methods:

• Formulation of a system of differential equations with Markovian switching coefficients.
• Mathematical proofs for the existence and uniqueness of global positive solutions.
• Analysis of extinction and persistence criteria for untreated drug addicts.
• Numerical simulations to explore the impact of regime switching and noise intensity.

Main Results:

• The existence and uniqueness of a global positive solution were proven.
• Conditions for the extinction and persistence of untreated drug addicts were derived.
• Numerical simulations demonstrated that higher noise intensities accelerate the extinction of untreated drug addicts.
• The model's behavior under constant conditions (non-switching) was analyzed, showing a positive equilibrium point.

Conclusions:

• Regime switching, driven by poppy cultivation, significantly impacts heroin epidemic dynamics.
• Stochastic noise plays a critical role, potentially hastening the decline of untreated drug addiction.
• The findings offer insights for developing targeted public health strategies to combat heroin epidemics.