Abstract
This research develops a mathematical model of the COVID-19 outbreak using actual infection data from Nakhon Sawan Province. The positivity invariant validates the model, and the next-generation method is used to compute the basic reproduction number ( \(R_{0}\) ). Parameters are estimated using a Markov Chain Monte Carlo (MCMC) technique within the Bayesian framework. The estimation results indicate the presence of virus-infected data in the environment. Additionally, the model computes the sensitivity indices of infectious individuals, revealing that reducing \(\beta_{2}\) decreases the number of infectious individuals more effectively than altering parameters \(\Pi\) and \(\omega\) . Finally, this research applies the Pontryagin Maximum Principle to the optimal control problem by the control variable \(\mathbb{T}\) representing preventive measures for COVID-19. The analysis demonstrates that these preventive measures can reduce the outbreak of each population group.
