<p>This study explores the dynamics of smoking behavior through a mathematical model by incorporating relapse in smoking habits. The analysis ensures the system’s positivity and boundedness, confirming that solutions remain feasible over time. Sensitivity analysis is performed to evaluate how variations in key parameters affect the system’s behavior, while stability analysis is performed to assess the long-term outcomes under different conditions. Numerical simulations are used to validate the theoretical results and demonstrate the practical relevance of the model. In addition, the study extends the analysis to an optimal control problem, incorporating counseling as an effective intervention to reduce smoking rates. The optimal control approach is applied to determine the most efficient counseling strategy to minimize smoking prevalence, accounting for both short-term and long-term effects. This research provides insights into the effectiveness of behavioral interventions and highlights the potential of dynamic models in public health policy planning.</p>

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A mathematical model on smoking dynamics in society with relapse

  • I. R. Sofia,
  • Shraddha Ramdas Bandekar,
  • Mini Ghosh

摘要

This study explores the dynamics of smoking behavior through a mathematical model by incorporating relapse in smoking habits. The analysis ensures the system’s positivity and boundedness, confirming that solutions remain feasible over time. Sensitivity analysis is performed to evaluate how variations in key parameters affect the system’s behavior, while stability analysis is performed to assess the long-term outcomes under different conditions. Numerical simulations are used to validate the theoretical results and demonstrate the practical relevance of the model. In addition, the study extends the analysis to an optimal control problem, incorporating counseling as an effective intervention to reduce smoking rates. The optimal control approach is applied to determine the most efficient counseling strategy to minimize smoking prevalence, accounting for both short-term and long-term effects. This research provides insights into the effectiveness of behavioral interventions and highlights the potential of dynamic models in public health policy planning.