Dynamic modelling of covid-19 and the use of “Merah Putih” vaccination and herbal medicine treatment as optimal control strategies in Semarang city Indonesia

The Corona virus is a disease that threatens human population on earth in early 2020, the first infection began China, thought to be host mammals and then able transmits into body, this present paper will describe dynamic system of Covid-19, analyzing direction equilibrium, Disease Free Equilibrium (DFE) Endemic (EE), which can done by determining dimensionless number Basic Reproduction Number (R0). And we put vaccine treatment as control variables reduce infected population, use vaccinations treatments recommended Indonesian government. Furthermore, Pontryagin Minimum Principle find optimal solution control. Optimal method fixed time end point, means are determined duration set goal for reaching final state point. This aim minimize values (cost) measures. Numerical calculations also performed illustrate graph.