In this talk we extend the classical susceptible-infected-susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation (SDE) for the number of infectious individuals I(t). We then prove that this SDE has a unique global positive solution I(t) and establish conditions for extinction and persistence of I(t). We discuss perturbation by stochastic noise. In the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance. The results are illustrated by computer simulations, including two examples based on real-life diseases.
Texto informado pelo autor.
* Os participantes dos seminários não poderão acessar às dependências da FGV usando bermuda, chinelos, blusa modelo top ou cropped, minissaia ou camiseta regata. O uso da máscara é facultativo, porém é obrigatória a apresentação do comprovante de vacinação (físico ou digital).
Apoiadores / Parceiros / Patrocinadores
David Greenhalgh - gained a PhD from the University of Cambridge in 1984 and worked at Imperial College, London from 1984 to 1986. He also has a first class Honours degree in Mathematics and a distinction in Part III Mathematics. He is am currently a member of the Population Modelling and Epidemiology Research Group at Strathclyde and has been a member of staff at Strathclyde in the Departments of Mathematics, Statistics and Modelling Science and Mathematics and Statistics since 1986. He is currently Postgraduate Director (Mathematics and Statistics) at Strathclyde and also Associate Editor of Journal of Biological Systems. In 2015 he awarded a two year (2015-2017) Leverhulme Trust Research Fellowship grant (50K RF-2015-88) as PI to study mathematical modelling of vaccination against dengue. He has also been involved in collaboration with Malaysia to mathematically model a mosquito trap to control dengue and won a 187K grant from the Newton Fund to do this in 2016. He is currently a Visitor Researcher at EMAp FGV.
a) Opção presencial *
Praia de Botafogo, 190
5o andar, Auditório 537
b) Opção remota (via Zoom)
Meeting ID: 981 5075 6795
Tel: 55 21 3799-5917