Analysis of optimum control on the implementation of vaccination and quarantine on the spread of covid-19

This study constructs an SVIR-type COVID-19 spread model into a model with control variables or optimum control problems. In the formulation of the model with controls, we set four control variables, namely vaccination strategy, quarantine, reduction of vaccine shrinkage, and treatment. Pontryagin 's maximum principle is applied in the model as a sufficient condition to achieve optimum conditions for minimizing the objective function . This study uses a numerical solution to describe the theoretical results. The results showed that the control model could accelerate the decrease in the number of individuals in the infected population class. We found that vaccination is a top priority that needs to be done to reduce the number of cases of COVID-19 infection. In addition, the implementation of quarantine can also be considered to accelerate the decrease in the number of individuals infected with COVID-19.