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

Abstract

The Corona virus is a disease that threatens human population on earth in early 2020, the first infection began in China, is thought to be a virus that host in mammals and then able transmits into human body, this present paper will describe dynamic system of Covid-19, analyzing direction of the equilibrium, Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE), which can be done by determining dimensionless number of Basic Reproduction Number (R 0). And then we put vaccine and treatment as control variables to reduce the infected population, we use the vaccinations and treatments recommended by the Indonesian government. Furthermore, we use Pontryagin Minimum Principle to find optimal solution of the control. Optimal control method in this paper is fixed time and fixed end point, means that we are determined the duration of the control and set goal for reaching the final state point. This optimal control will aim to minimize the number of infected population and values (cost) of control measures. Numerical calculations also performed to illustrate the graph.