Optimal Control Analysis and Cost‐Effectiveness Calculations of Chickenpox Transmission Dynamics

ABSTRACT This study develops and analyses a mathematical model for chickenpox transmission dynamics. The model's basic properties, including positivity, boundedness, and stability of disease‐free and endemic equilibria, are rigorously established. The basic reproduction number is derived, and sensitivity analysis identifies the most sensitive parameters. An optimal control problem is formulated with four time‐dependent controls (preventive measures, vaccination, pharmaceutical interventions, and non‐pharmaceutical treatments). Numerical simulations using a forward‐backward sweep method (FBSM) are conducted. Several control scenarios that resulted from the intersection of the recommended controls to clarify the impact of these controls and explore the most effective way to halt the disease's progress are presented. Moreover, the cost‐effectiveness analysis is presented to offer a quantitative comparison between the suggested five control scenarios. We conclude that while all proposed controls contribute to disease mitigation, the optimal strategy depends on resource availability: Scenario I (all controls) is recommended for maximum infection reduction, whereas Scenario II (excluding preventive measures) is preferred under budget constraints.