Predicting the Dynamical Behavior of COVID-19 Epidemic and the Effect of Control Strategies

Shakhany, Mohammad Qaleh; Salimifard, Khodakaram

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