Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates
By Tiberiu Harko, Francisco S. N. Lobo, Man Kwong Mak. Applied Mathematics and Computation, 2014
491 citations recorded by the source corpus.
Abstract In this paper, the exact analytical solution of the Susceptible-Infected-Recovered (SIR) epidemic model is obtained in a parametric form. By using the exact solution we investigate some explicit models corresponding to fixed values of the parameters, and show that the numerical solution reproduces exactly the analytical solution. We also show that the generalization of the SIR model, including births and deaths, described by a nonlinear system of differential equations, can be reduced to an Abel type equation. The reduction of the complex SIR model with vital dynamics to an Abel type equation can greatly simplify the analysis of its properties. The general solution of the Abel equation is obtained by using a perturbative approach, in a power series form, and it is shown that the general solution of the SIR model with vital dynamics can be represented in an exact parametric form.
Subfields: Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/930161e0a54a68e09f59a12a10fca480bbaa5f8b
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In Public Health, Environmental and Occupational Health
Citations in the corpus
- Inter-Series Attention Model for COVID-19 Forecasting (2020, background): “Examples includes [2, 20, 32] that are built upon classic SIR or SEIR models [10].”