Asian Journal of Probability and Statistics

Background: Consumerism has become a defining feature of modern economies, significantly amplified by the expanding reach of social media platforms. Through viral content, influencer marketing, and algorithmic recommendations, consumer demand spreads rapidly among individuals and communities, accelerating market saturation while generating substantial environmental externalities. The production and disposal of consumer goods contribute significantly to greenhouse gas emissions, resource depletion, and waste generation, creating an urgent need to understand the coupled dynamics of social-media-driven consumerism and environmental accumulation.

Purpose: This paper aims to synthesize existing literature from marketing science, social network theory, mathematical epidemiology, and environmental economics to establish a unified framework for understanding the interconnected processes of social-media-driven consumerism and environmental externalities. Specifically, we develop a mathematical model that captures the feedback loops linking consumer demand, social media intensity, consumption behaviour, and environmental accumulation, hereby enabling the identification of key parameters driving system behaviour and the derivation of policy recommendations for sustainable consumption.

Methods: We develop a system of coupled nonlinear ordinary differential equations modelling the interaction among four key variables: consumer demand D(t), social media intensity S(t), consumption C(t), and environmental externality E(t). The model extends the classic Bass diffusion model to include dynamic social media influence and couples it with content generation dynamics and environmental accumulation. We perform a comprehensive sensitivity analysis by systematically varying key parameters (q, \(\mu\), \(\delta\), \(\omega\)) while holding others at baseline values. A heatmap of market saturation times and a phase diagram of dynamical regimes are constructed to identify critical thresholds and nonlinear responses.

Results: The analysis reveals explosive growth phases with rapid market saturation occurring within 8-10 days under baseline parameters, after which demand and consumption stabilise at D ≈ 98.93 and C ≈ 128.47. Environmental externalities accumulate slowly and persistently with a time constant T_E = 50 days, approaching steady-state E^* = 642.35 – nearly six times the baseline consumption level. The imitation coefficient q and content generation rate \(\mu\) are identified as critical accelerants for market saturation, while the environmental mitigation rate \(\omega\) is the most important parameter for controlling long-term environmental damage. Four distinct dynamical regimes are identified: Dormant ((p + q)/\(\delta\) ¡ 1), Slow Takeoff (1 ¡ (p + q)/\(\delta\) ¡ 2), Viral Explosion (2 ¡ (p + q)/\(\delta\) ¡ 5), and Hyper-viral ((p + q)/\(\delta\) ¿ 5), with baseline parameters (p + q)/\(\delta\) = 8.4 placing the system firmly in the hyper-viral regime. 

Conclusions: Social-media-driven consumerism exhibits hyper-viral dynamics that rapidly saturate markets and generate persistent environmental externalities. The positive feedback loop D→C→S→D drives explosive growth, and breaking any single link requires unrealistic parameter changes. Environmental mitigation investments (increasing \(\omega\)) are identified as the most effective policy intervention, reducing steady-state environmental damage by 50% when doubled. Content moderation policies (reducing \(\mu\)) may be more effective than influencer regulation (reducing q) in slowing consumerism. The rapid market saturation and persistent environmental accumulation highlight the urgency of intervention, as the dangerous lag between consumption and observable environmental damage requires immediate action to avoid irreversible consequences.

Note: The model is presented as an illustrative deterministic framework that has not yet been empirically calibrated; therefore, the numerical results should be interpreted qualitatively to identify system dynamics and key leverage points rather than as precise quantitative predictions.