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 and 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 to ) and (from to ) 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 .