Mathematics Model of COVID-19 with Two-Stage Vaccination, Symptomatic, Asymptomatic, and Quarantine Individuals

This research developed a model of COVID-19 based on the SEIR model which was further developed by dividing the infected subpopulation into symptomatic and asymptomatic, adding quarantine of infected individuals and vaccination in two steps. Making this model begins with making a compartment diagram of the disease and then forming a system of differential equations. After the model is formed, the disease-free equilibrium point, endemic equilibrium point, and basic reproduction number (R0) are obtained. Analysis of the stability of the disease-free equilibrium point was locally asymptotically stable if R01 and an endemic equilibrium point existed if R01. Numerical simulation for the model that has been made is in line with the analysis. Furthermore, the sensitivity analysis obtained that the parameters that have a significant effect on the spread of COVID-19 are the rate of the first dose vaccination, the rate of contact with symptomatic or asymptomatic individuals, and the rate of quarantine of symptomatic infected individuals.