Stochastic Epidemic Models
The goal of these lectures is to describe stochastic models of epidemics. Most mathematical epidemic models are deterministic. Those models can be shown to be large-population of stochastic models which describe each event of infection and healing. The stochastic models are necessary for small populations, and also to describe the onset of an epidemic, when the number of infected individuals is not of the order of the size of the population. When an epidemic is established in a large population, and new susceptible individuals enter constantly (either by immigration, birth, or loss of immunity by individuals who have been already infected), one may face an endemic situation. In such a case, the theory of large deviations is able to predict how long it will take for the randomness propagation of the illness to halt the epidemic. We intend to devote most of the first lecture to the presentation of the typical models which we study, the second lecture to the application of the Freidlin-Wentzell theory of large deviations to this problem, and the third lecture to spatial stochastic epidemic models.
Lecture 1. Wednesday Jan 24, 09:00-11:00, Seminar Room, Ground Floor, Weeks Building (Google Map here)
Lecture 2. Thursday Jan 25, 11:00-13:00, Seminar Room, Ground Floor, Weeks Building (Google Map here)
Lecture 3. Thursday Feb 8, 14:00-16:00, Seminar Room, Ground Floor, Weeks Building (Google Map here)
*Tom Britton, Etienne Pardoux, Stochastic Epidemics in a Homogeneous Community, in preparation.
*Mark I. Freidlin and Alexander D. Wentzell. Random perturbations of dynamical systems, 3d ed. Grundlehren des Mathematischen Wissenschaften 260, Springer, New York, 2012.
*P. Kratz, E. Pardoux, Large deviations for infectious disease models, Seminaire de Probabilites, to appear.
*P. Kratz, E. Pardoux, B. Samegni-Kepgnou, Numerical methods in the context of compartmental models in epidemiology, ESAIM : Proceedings and Surveys 48, 169-189, 2014.
*E. Pardoux, B. Samegni-Kepgnou, Large deviation principle for epidemic models, Journal of Applied Probability 54, 905-920, 2017.