Semendyaeva NL, Orlov MV, Rui T, Enping Y. Analytical and Numerical Investigation of the SIR Mathematical Model.
COMPUTATIONAL MATHEMATICS AND MODELING 2023. [PMCID:
PMC10074335 DOI:
10.1007/s10598-023-09572-7]
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Abstract
This is a theoretical study of the SIR model — a popular mathematical model of the propagation of infectious diseases. We construct a solution of the Cauchy problem for a system of two ordinary differential equations describing in integral form the concentration dynamics of infected and recovered individuals in an immune population. A qualitative analysis is carried out of the stationary system states using the Lyapunov function. An expression is obtained for the coordinates of the equilibrium points in terms of the Lambert W-function for arbitrary initial values. The application of the SIR model for the description of COVID-19 propagation dynamic is demonstrated.
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