Diffusion Models in Life Sciences

Christiane Fuchs
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Christiane Fuchs: Helmholtz Zentrum München, Institute for Bioinformatics and Systems Biology

Chapter Chapter 5 in Inference for Diffusion Processes, 2013, pp 101-129 from Springer

Abstract: Abstract This chapter investigates models for the spread of infectious diseases as a representative application field which involves large populations. In particular, it covers the standard susceptible–infected–removed (SIR) model and proposes an extension in order to allow for host heterogeneity. The considered dynamics is described in terms of jump processes, deterministic processes and diffusion processes. The latter enables convenient simulation of the random course of an epidemic even for large populations. The purpose of this chapter is on the one hand to illustrate the methods from Chap. 4 for the approximation of Markov jump processes by diffusions. On the other hand, the presented models and their diffusion approximations are the basis for Chap. 8 , where Bayesian inference is performed on them.

Keywords: Master Equation; Diffusion Approximation; Jump Process; Infinitesimal Generator; Diffusion Matrix (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-25969-2_5

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DOI: 10.1007/978-3-642-25969-2_5

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