# A note on Exact solution of SIR and SIS epidemic models

@article{Shabbir2010ANO, title={A note on Exact solution of SIR and SIS epidemic models}, author={Ghalia Shabbir and Hina Khan and Muhammad Athar Sadiq}, journal={arXiv: Classical Analysis and ODEs}, year={2010} }

In this article we have successfully obtained an exact solution of a particular case of SIR and SIS epidemic models given by Kermack and Mckendrick [1] for constant population, which are described by coupled nonlinear differential equations. Our result has no limiting conditions for any parameter involved in the given models. In epidemiology many researchers believe that it is very hard to get an exact solution for such models. We hope this solution will be an opening window and good addition…

## 20 Citations

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## References

SHOWING 1-10 OF 15 REFERENCES

QUALITATIVE ANALYSIS OF AN EPIDEMIC MODEL

- Mathematics

In this paper we consider an epidemic model with a complete form of the non-monotonic incidence rate of [18]. This non-monotonic incidence rate describes the effects of psychological factor,…

The Mathematics of Infectious Diseases

- MathematicsSIAM Rev.
- 2000

Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.

A contribution to the mathematical theory of epidemics

- Medicine, Mathematics
- 1927

The present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.

On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations

- MathematicsJournal of mathematical biology
- 1990

It is shown that in certain special cases one can easily compute or estimate the expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population.

How mathematical models have helped to improve understanding the epidemiology of infection.

- MedicineEarly human development
- 2007