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

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 DFE (X) over bar (DFE), and endemic EE (X) over bar (EE) equilibrium points, using the Jacobian matrix eigenvalues lambda(i) of both disease-free equilibrium (X) over bar (DFE), and endemic equilibrium (X) over bar (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 (R-0 <= 1), the effect of control strategies has been added to the model (in order to decrease transmission rate beta, and reinforce susceptible to recovered flow), to determine how much they are effective, in a mass immunization program. The effect of transmission rates beta (from S to E ) and alpha (from R to S ) varies, and when vaccination effect rho, is added to the model, disease-free equilibrium (X) over bar (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 beta and alpha, reached the cor-responding disease-free equilibrium (X) over bar (DFE) locally unstable, and globally asymptotically stable for endemic equilibrium (X) over bar (EE). The initial conditions for the decrease in transmission rates beta and alpha, and increase in rho, reached the corresponding disease-free equilibrium (X) over bar (DFE) globally asymptotically stable, and locally unsta-ble in endemic equilibrium (X) over bar (EE). (C) 2021 Elsevier Ltd. All rights reserved.