A Comparative Study for Some Mathematical Models of Epidemic Diseases with Application to Strategic Management

Abstract

A local performance of the SIR model on actual data is introduced. A good approximation of the SIR model parameters in Saudi Arabia during a period of 275 days (the first of April 2020 to the end of December 2020) is determined. The parameters are estimated from the recorded data and used to predict the values in the next subsequent period. The performance of the standard fourth order Runge–Kutta method is considered for the classical SIR models over different periods. A comparison of the recorded data and the predicted values during the considered period illustrated the effectiveness of the treatment. The mathematical properties and initial conditions are considered within the estimated parameter values. It is shown that lockdown and social distance attitudes effectively controlled the spread of the disease. The maximum number of daily active infected cases is 63,026, and occurs in July and this agrees with the calculated values. To make the graphs representable, we considered a fixed closed population, the effective sample during the considered period of size N = 400,000 only (represents only 1% of the overall population susceptible, this must be associated, with great thanks, to the authorities in KSA).

Keywords

• epidemic models
• SIR models
• SIR parameter estimation
• IVP