title: On the final size of epidemics in random environment.
abstract: This paper extends the final size result of the classical SIR epidemic model in constant and periodic environments to random environment. Conditionally on the basic reproduction number R0 recently defined for random environment and the initial infected population fraction, we prove a final size result of an epidemic governed by the SIR model with time-depending parameters. The parameters are driven by an ergodic inhomogeneous time-periodic Markov process with finite state space. We also analyze the classical SEIR epidemic model in random environment.
authors.affiliation: Mathematics and Population Dynamics Laboratory, Faculty of Sciences of Semlalia of Marrakech, Cadi Ayyad University (Morocco) and Sorbonne Universités, UMI209-UMMISCO IRD Paris 6 (France). Electronic address: a.l.eddarraz@gmail.com.
authors.forename: Abdelkarim
authors.initials: A
authors.lastname: Ed-Darraz
authors.affiliation: Mathematics and Population Dynamics Laboratory, Faculty of Sciences of Semlalia of Marrakech, Cadi Ayyad University (Morocco) and Sorbonne Universités, UMI209-UMMISCO IRD Paris 6 (France). Electronic address: khaladi@uca.ma.
authors.forename: Mohamed
authors.initials: M
authors.lastname: Khaladi
mesh_terms: D050936:Basic Reproduction Number; D004777:Environment; D058872:Epidemics; D008954:Models, Biological
keywords: Basic reproduction number; Final epidemic size; Random environment; SIR and SEIR model