The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates
Open accessAbstract
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.
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Citations
Cites
A contribution to the mathematical theory of epidemics
Kermack, W. O., & McKendrick, A. G. (1927) · Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character · doi:10.1098/rspa.1927.0118 · Cited by 11,701
Mathematical Models in Population Biology and Epidemiology
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Mathematical Biology: I. An Introduction
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Analysis of a 3D chaotic system
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Cited by
Inferring change points in the spread of COVID-19 reveals the effectiveness of interventions
Dehning, J., Zierenberg, J., Spitzner, F. P., Wibral, M., Neto, J. P., Wilczek, M., & Priesemann, V. (2020) · Science · doi:10.1126/science.abb9789 · Cited by 819
Cyberspace: A Digital Ecosystem
Lippert, K. J., & Cloutier, R. (2021) · Systems · doi:10.3390/systems9030048 · Cited by 32
Schnyder, S. K., Molina, J. J., Yamamoto, R., & Turner, M. S. (2025) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2409362122 · Cited by 12
Metadata
- Authors
- Harko, T., Lobo, F. S. N., & Mak, M. K.
- Venue
- Applied Mathematics and Computation
- Publisher
- Elsevier BV
- Published
- 2014-06
- Volume
- 236
- Pages
- 184-194
- ISSN
- 0096-3003 (ISSN-L)
- OpenAlex
- W2020165868
- Cited by
- 489
- References
- 6
- FWCI
- 3.68
- Type
- journal article
- Language
- en
- Open access
- green
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- Harko, T., Lobo, F. S. N., & Mak, M. K. (2014). Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates. Applied Mathematics and Computation. https://doi.org/10.1016/j.amc.2014.03.030
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