A Stochastic Edge-Based SEIR Dynamics by Cherrylyn P. Alota and Carlene P. Arceo
Poster presented during the 2019 Mathematics Society of the Philippines ANNUAL CONVENTION, Greenleaf Hotel, General Santos City 27–29 May 2019
Abstract
Stochastic epidemic models naturally describe the spread of disease, defining the probability of disease transmission between individuals. In this study, we formulate a stochastic model describing the dynamics of the spread of a disease in an SEIR population of finite size through a network model. The population of each class is associated with a finite counting of point measure which keeps track of the number of nodes in each class. These finite measures of N define the degree of distributions used in the model, and these are measured Markov processes. The evolution of each degree distribution process is described by a measured-valued stochastic differential system is also a Markov process with an infinitesimal generator. We prove the solution by showing the boundedness of finiteness of the moments of each population size. These conditions are very useful in proving the convergence of the stochastic model to deterministic model as population size becomes large.