Optimal Control and Cost-Effective Management of COVID-19 Epidemic Model Using a Vaccination SEIAVR Framework with Bang–Bang Control

Abstract

The global spread of COVID-19 highlighted the necessity of control strategies that are not only epidemiologically effective but also economically viable. Designing such interventions requires balancing transmission reduction with associated implementation costs. Many existing mathematical models rely on continuous control mechanisms and do not explicitly connect cost-effectiveness analysis with observed epidemiological data. In this work, we first formulate a SEIAR compartmental model and subsequently extend it to a vaccination-incorporated SEIAVR framework. To capture the realistic implementation of sudden public health measures, we employ a Bang–Bang optimal control approach. The basic reproduction number is derived and the local stability of the equilibria is rigorously analyzed. The optimal control structure is characterized using the Pontryagin Maximum Principle. Model validation and policy assessment are carried out through numerical simulations calibrated with COVID-19 data from the United Kingdom. The findings indicate that the integration of vaccination with Bang–Bang interventions significantly suppresses infection peaks and reduces the duration of the overall outbreak. From an economic perspective, the combined strategy achieves improved cost-effectiveness compared to non-vaccination scenarios. Although the model assumes homogeneous mixing and simplifies certain operational aspects of intervention deployment, it offers a mathematically grounded and practically relevant framework for rapid-response policy design, contributing to the integration of epidemiological dynamics and economic optimization in infectious disease modeling. Jagannath University Journal of Science, Volume 12, Number 1, Jun. 2025, pp. 119−142