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

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 $DFE{\overline{X}}_{DFE},$ and endemic $EE{\overline{X}}_{EE}$ equilibrium points, using the Jacobian matrix eigenvalues ${\lambda }_i$ of both disease-free equilibrium ${\overline{X}}_{DFE},$ and endemic equilibrium ${\overline{X}}_{EE}$ 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 ( $R_0\le 1$ ), 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 ${\overline{X}}_{DFE}$ is globally asymptotically stable, and the endemic equilibrium point ${\overline{X}}_{EE}$ , is locally unstable. The initial conditions for the decrease in transmission rates of $\beta$ and $\alpha ,$ reached the corresponding disease-free equilibrium ${\overline{X}}_{DFE}$ locally unstable, and globally asymptotically stable for endemic equilibrium ${\overline{X}}_{EE}$ . The initial conditions for the decrease in transmission rate $s\beta$ and $\alpha ,$ and increase in $\rho ,$ reached the corresponding disease-free equilibrium ${\overline{X}}_{DFE}$ globally asymptotically stable, and locally unstable in endemic equilibrium ${\overline{X}}_{EE}$ .

Keywords: COVD-19; Dynamical Behavior; Pandemic; Prediction; SEIRS model; Vaccination.