Modeling and optimal control of COVID-19 with comorbidity and three-dose vaccination in Indonesia

This paper presents and examines a COVID-19 model that takes comorbidities and up to three vaccine doses into account. We analyze the stability of the equilibria, examine herd immunity, and conduct a sensitivity analysis validated by data on COVID-19 in Indonesia. The disease-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number is less than one, while an endemic equilibrium exists and is globally asymptotically stable when the number is greater than one. Subsequently, the model incorporates two effective measures, namely public education and enhanced medical care, to determine the most advantageous approach for mitigating the transmission of the disease. The optimal control model is then determined using Pontryagin's maximum principle. The integrated control strategy is the best method for reliably safeguarding the general population against COVID-19 infection. Cost evaluations and numerical simulations corroborate this conclusion.