Abstract
This paper uses transformed subsystem of ordinary differential equation seirs model, with vital dynamics of birth and death rates, and temporary immunity (of infectious individuals or vaccinated susceptible) to evaluate the disease-free DFEX¯DFE, and endemic EEX¯EE equilibrium points, using the Jacobian matrix eigenvalues λi of both disease-free equilibrium X¯DFE, and endemic equilibrium X¯EE for COVID-19 infectious disease to show S, E, I, and R ratios to the population in time-series. In order to obtain the disease-free equilibrium point, globally asymptotically stable ( R0 ≤ 1 ), the effect of control strategies has been added to the model (in order to decrease transmission rate β, and reinforce susceptible to recovered flow), to determine how much they are effective, in a mass immunization program. The effect of transmission rates β (from S to E) and α (from R to S) varies, and when vaccination effect ρ , is added to the model, disease-free equilibrium X¯DFE is globally asymptotically stable, and the endemic equilibrium point X¯EE , is locally unstable. The initial conditions for the decrease in transmission rates of β and α, reached the corresponding disease-free equilibrium X¯DFE locally unstable, and globally asymptotically stable for endemic equilibrium X¯EE . The initial conditions for the decrease in transmission rate s β and α, and increase in ρ, reached the corresponding disease-free equilibrium X¯DFE globally asymptotically stable, and locally unstable in endemic equilibrium X¯EE .