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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.

Large Deviations for Infectious Diseases Models