Dynamical Modeling of COVID-19 and Use of Optimal Control to Reduce the Infected Population and Minimize the Cost of Vaccination and Treatment

Abstract

The research described a model formulation of COVID-19 using a dynamic system of Ordinary Differential Equation (ODE) which involved four population systems (susceptible, exposed, infectious, and recovered). Then, the research analyzed the direction of the equilibrium, Disease Free Equilibrium (DFE), and Endemic Equilibrium (EE). The treatment and vaccination were the control functions applied to the dynamical system modeling of COVID-19. The research was done by determining dimensionless number R0 or Basic Reproduction Number and applying optimal control into the dynamical system using the Pontryagin Minimum Principle. Numerical calculations were also performed to illustrate and compare the graph of the dynamical system with and without a control function. From the results, there is a reduction in the number of susceptible and infected populations. It indicates that giving vaccines to susceptible populations and treating infected populations affect the number of susceptible and infected populations. It also means thatthis control can reduce the spread of the virus.