Séminaire de Probabilités XLIX pp 221-327 | Cite as

# Large Deviations for Infectious Diseases Models

## Abstract

We study large deviations of a Poisson driven system of stochastic differential equations modeling the propagation of an infectious disease in a large population, considered as a small random perturbation of its law of large numbers ODE limit. Since some of the rates vanish on the boundary of the domain where the solution takes its values, thus making the action functional possibly explode, our system does not obey assumptions which are usually made in the literature. We present the whole theory of large deviations for systems which include the infectious disease models, and apply our results to the study of the time taken for an endemic equilibrium to cease, due to random effects.

## Keywords

Poisson process driven SDE Lareg deviations Freidlin-Wentzell theory Epidemic models## Notes

### Acknowledgements

The authors thank an anonymous Referee, whose careful reading and detailed remarks allowed us to improve an earlier version of this paper.

This research was supported by the ANR project MANEGE, the DAAD, and the Labex Archimède.

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