A Compartmental Model for Chickenpox Transmission Dynamics Incorporating Control Interventions

Abstract Chickenpox remains a highly contagious viral disease that poses significant public health challenges, particularly in populations with low vaccination coverage. Understanding its transmission dynamics is essential for designing effective control strategies. This study presents a comprehensive mathematical model to analyze the spread of Chickenpox, incorporating key intervention measures such as vaccination, isolation, and treatment. The model categorizes the human population into six compartments: susceptible, exposed, infected, isolated, treated, and recovered individuals. A system of ordinary differential equations is employed to describe the interactions among these groups. The model is further examined through the determination of disease-free and endemic equilibrium states, and stability analysis is conducted to establish the conditions under which the disease can either be eliminated or persist within the population. Sensitivity analysis is performed to identified the most influential parameters affecting disease transmission, revealing that transmission rates, vaccination coverage, and recovery rates play critical roles. Numerical simulations are also carried out to evaluate the impact of various intervention strategies. The results demonstrate that increased vaccination coverage, timely isolation of infected individuals, and effective treatment significantly reduce the number of new infections and overall disease burden. The findings highlight the importance of integrated public health strategies in controlling Chickenpox transmission. This study provides valuable insights that can inform policy decisions and guide the implementation of effective disease prevention and control measures. Keywords: Chickenpox transmission, Mathematical modeling, Stability analysis, Sensitivity analysis, Numerical simulation