# Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates

@article{Harko2014ExactAS, title={Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates}, author={Tiberiu Harko and Francisco S. N. Lobo and M. K. Mak}, journal={Appl. Math. Comput.}, year={2014}, volume={236}, pages={184-194} }

## 317 Citations

A simple computational approach to the Susceptible-Infected-Recovered (SIR) epidemic model via the Laplace-Adomian Decomposition Method

- Mathematics
- 2020

A series representation of the solution of the SIR model is obtained by using the Laplace-Adomian Decomposition Method to solve the basic evolution equation of the model.

Series solution of the Susceptible-Infected-Recovered (SIR) epidemic model with vital dynamics via the Adomian and Laplace-Adomian Decomposition Methods

- Mathematics
- 2020

The series representations of the time evolution of the SIR model with vital dynamics are compared with the exact numerical solutions of the model, and it is found that, at least for a specific range of parameters, there is a good agreement between the Adomian and Laplace-Adomian semianalytical solutions, and the numerical results.

Analytical solution of the SIR-model for the temporal evolution of epidemics. Part A: time-independent reproduction factor

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020

We revisit the susceptible-infectious-recovered/removed (SIR) model which is one of the simplest compartmental models. Many epidemological models are derivatives of this basic form. While an analytic…

Exact closed-form solution of a modified SIR model.

- Mathematics
- 2020

The exact analytical solution in closed form of a modified SIR system is presented. This is, to the best of our knowledge, the first closed-form solution for a three-dimensional deterministic…

Analytical solutions and parameter estimation of the SIR epidemic model

- MathematicsMathematical Analysis of Infectious Diseases
- 2022

Analytical solution for post-death transmission model of Ebola epidemics

- MathematicsAppl. Math. Comput.
- 2020

Analytical Parameter Estimation of the SIR Epidemic Model. Applications to the COVID-19 Pandemic

- MathematicsEntropy
- 2021

Novel analytical results and numerical algorithms suitable for parametric estimation of the SIR model are reported and it is proven that the explicit solution of the model requires the introduction of a new transcendental special function, describing the incidence.

Discrete SIR model on a homogeneous tree and its continuous limit

- Mathematics
- 2020

This paper concerns a stochastic Susceptible-Infected-Recovered (SIR) model for the spread of infectious disease on a homogeneous tree. Under general assumptions on infection rates and recovery times…

The approximately universal shapes of epidemic curves in the Susceptible-Exposed-Infectious-Recovered (SEIR) model

- MathematicsScientific reports
- 2020

The approach of Harko et al. is generalised to obtain an approximate semi-analytical solution of the Susceptible-Exposed-Infectious-Recovered (SEIR) model, implying an approximate characteristic timescale that is universal to all SEIR models, which only depends on the basic reproduction number and initial fraction of the population that is infectious.

Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2021

The earlier analytical analysis (part A) of the susceptible–infectious–recovered (SIR) epidemics model for a constant ratio k of infection to recovery rates is extended here to the semi-time case…

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