Information geometry and entropy in a stochastic epidemic rate process

Dodson, CTJ (2009) Information geometry and entropy in a stochastic epidemic rate process. [MIMS Preprint]

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Abstract

A commonly recurring approximation to real rate processes is of the form: dN/dt = -m N where m is some positive rate constant and N(t) measures the current value of some property relevant to the process---radioactive decay is our typical student example. The simplest stochastic version addresses the situation where N(t) is the size of the current population and the rate constant depends on the distribution of properties in the population---so different sections decay at different rates. Then the interest lies in the evolution of the distribution of properties and of the related statistical features like entropy, mean and variance, for given initial distribution. We show that there is a simple closed solution for an example of an epidemic in which the latency and infectivity are distributed properties controlled by a bivariate gamma distribution.

Item Type: MIMS Preprint
Uncontrolled Keywords: Bivariate gamma, stochastic rate process, epidemic, information geometry
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Prof CTJ Dodson
Date Deposited: 25 May 2009
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1272

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