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Co-spreading dynamics of smoking behavior and awareness on social contact networks

Saicharan Ritwik Chinni, Anupama Sharma

Abstract

Smoking behavior and awareness co-spread through social interactions, giving rise to coupled contagion processes on social contact networks. In addition to initiation and cessation, awareness of the harmful effects of smoking plays an important role in shaping individual behavior and population-level outcomes. In this work, we develop a mathematical model to study the coupled dynamics of smoking behavior, quitting, and awareness in a population. A deterministic framework based on ordinary differential equations is first formulated to capture the interplay between social influence and awareness-driven behavioral change. Analysis of the model reveals the existence of smoking-free and smoking-endemic steady states, and identifies conditions under which awareness can reduce or suppress the persistence of smoking. Since social interactions are often localized rather than well mixed, the mean-field description is then extended to a network-based model that incorporates structured contact patterns. Numerical simulations performed on empirical social networks indicate that contact heterogeneity and localized awareness spreading can influence the effectiveness of interventions. Our findings underscore the importance of population structure when devising awareness-based intervention strategies for smoking cessation.

Co-spreading dynamics of smoking behavior and awareness on social contact networks

Abstract

Smoking behavior and awareness co-spread through social interactions, giving rise to coupled contagion processes on social contact networks. In addition to initiation and cessation, awareness of the harmful effects of smoking plays an important role in shaping individual behavior and population-level outcomes. In this work, we develop a mathematical model to study the coupled dynamics of smoking behavior, quitting, and awareness in a population. A deterministic framework based on ordinary differential equations is first formulated to capture the interplay between social influence and awareness-driven behavioral change. Analysis of the model reveals the existence of smoking-free and smoking-endemic steady states, and identifies conditions under which awareness can reduce or suppress the persistence of smoking. Since social interactions are often localized rather than well mixed, the mean-field description is then extended to a network-based model that incorporates structured contact patterns. Numerical simulations performed on empirical social networks indicate that contact heterogeneity and localized awareness spreading can influence the effectiveness of interventions. Our findings underscore the importance of population structure when devising awareness-based intervention strategies for smoking cessation.
Paper Structure (12 sections, 2 theorems, 28 equations, 6 figures, 1 table)

This paper contains 12 sections, 2 theorems, 28 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. The Model
  3. Model Analysis
  4. Steady states
  5. The Basic Reproduction Number
  6. Stability Analysis
  7. Numerical Simulations
  8. Network-Based Modelling
  9. Degree block approximation
  10. Numerical simulation on Theoretical Networks
  11. Numerical simulation on Empirical Networks
  12. Discussion

Key Result

Theorem 1

If $\mathcal{R}<1$, the smoking-free equilibrium $E_0$ exists and is locally asymptotically stable.

Figures (6)

  • Figure 1: Schematic diagram of the model
  • Figure 2: Global stability of the endemic equilibrium in the $(s,q,a)$ space. Trajectories starting from diverse initial conditions all converge to the same equilibrium point, providing numerical evidence of the global stability of the system.
  • Figure 3: Effects of model parameters on quitter and smoker dynamics in the ODE model.
  • Figure 4: Comparison of the temporal dynamics under the deterministic mean-field model and network-based simulations. (a) Deterministic compartmental (ODE) model. (b) Barabási--Albert Network. (c) Erdős-Rényi Network. (d) Watts-Strogatz Network. While quantitative differences are observed in the timing of peak prevalence and in the shape of the smoking trajectory across network topologies, the qualitative behavior and long-term dynamics remain consistent with the mean-field predictions.
  • Figure 5: Equilibrium population fractions as a function of mean degree $\langle k\rangle$ for Erdős–Rényi (ER), Barabási–Albert (BA), and Watts–Strogatz (WS) networks. Panels show (a) nonsmokers, (b) smokers, (c) quitters, and (d) aware individuals.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2