Predicting the dynamical behavior of COVID-19 epidemic and the effect of control strategies

This paper uses transformed subsystem of ordinary differential equation $$ model, with vital dynamics of birth and death rates, and temporary immunity (of infectious individuals or vaccinated susceptible) to evaluate the disease-free $$ and endemic $$ equilibrium points, using the Jacobian matrix eigenvalues $$ of both disease-free equilibrium $$ and endemic equilibrium $$ 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 ( $$ ), the effect of control strategies has been added to the model (in order to decrease transmission rate $$ and reinforce susceptible to recovered flow), to determine how much they are effective, in a mass immunization program. The effect of transmission rates $$ (from S to E) and $$ (from R to S) varies, and when vaccination effect $$ , is added to the model, disease-free equilibrium $$ is globally asymptotically stable, and the endemic equilibrium point $$ , is locally unstable. The initial conditions for the decrease in transmission rates of $$ and $$ reached the corresponding disease-free equilibrium $$ locally unstable, and globally asymptotically stable for endemic equilibrium $$ . The initial conditions for the decrease in transmission rate $$ and $$ and increase in $$ reached the corresponding disease-free equilibrium $$ globally asymptotically stable, and locally unstable in endemic equilibrium $$ .