Mathematical Modelling on Chickenpox Using the Basic Reproduction Number

Abstract

Chickenpox (varicella) is still a major public health issue especially among young children. This study develops an enhanced SIR-based compartmental model to investigate the transmission dynamics of chickenpox, incorporating vaccination as a critical control mechanism. The model includes a vaccination rate parameter that directly reduces the susceptible population, thereby lowering the force of infection and altering the disease progression. Numerical simulations are performed under various vaccination scenarios, with results showing a marked decline in infection levels as vaccination coverage increases. The disease-free equilibrium becomes globally asymptotically stable when the fundamental reproduction number R0 is smaller than one,the disease free equilibrium is globally asymptotically stable indicating effective containment of outbreaks.The model emphasizes the need of ongoing immunization campaigns in stopping major spread and lowering the healthcare load. Furthermore underlined is the part mathematical modeling plays in public health policies since it offers a quantitative framework to assess and maximize vaccination campaigns. Future directions of research call for including age structure, spatial heterogeneity, seasonal effects, declining immunity, and behavioral dynamics in addition to real-time surveillance data. These improvements would increase the prediction capacity of the model and enable more responsive, data-driven decision-making in the control of epidemic. The overall results highlight the critical importance of vaccination and show mathematical modeling as a necessary instrument in public health planning and epidemic readiness.