Optimal Prevention and Treatment Control on SVEIR Type Model Spread of COVID-19

Abstract

COVID-19 pandemic has disrupted the world's health and economy and has resulted in many deaths since the first case occurred in China at the end of 2019. Moreover, The COVID-19 disease spread throughout the world, including Indonesia on March 2, 2020.  Coronavirus quickly spreads through droplets of phlegm through the throat to the lungs. Researchers in the medical field and the exact science are jointly examined the spread, prevention, and optimal control of COVID-19 disease. Due to the prevention of COVID-19, a vaccine has been found  in early 2021, which at the time, the vaccination process was carried out worldwide against COVID-19. This paper examines the spread model of SVEIR-type COVID-19 by considering the vaccination subpopulation. In this study, control of prevention efforts (  and ) and healing efforts  are given and being analyzed with the fourth-order Runge-Kutta approach. Based on numerical simulations, it can be seen that using the controls    and  can reduce the number of infected individuals in the subpopulation compared to those without control. The  control can increase the number of recovered individual subpopulations.Keywords: COVID-19; SVEIR model; optimal control; treatment; vaccination.