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Diffusion Models in Life Sciences

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Inference for Diffusion Processes

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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.

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Notes

  1. 1.

    More precisely, the number is α ⋅S ∕ (N − 1) as self-infections are excluded. However, this difference is compensated by adequate choice of α and marginal for large N anyway. Division by N instead of N − 1 is the standard notation.

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Authors and Affiliations

  1. Institute for Bioinformatics and Systems Biology, Helmholtz Zentrum München, Neuherberg, Germany

    Christiane Fuchs

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  1. Christiane Fuchs
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Fuchs, C. (2013). Diffusion Models in Life Sciences. In: Inference for Diffusion Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25969-2_5

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