Author: Emma Southall; Michael J. Tildesley; Louise Dyson
Title: Prospects for detecting early warning signals in discrete event sequence data: application to epidemiological incidence data Document date: 2020_4_2
ID: dp4qv77q_37
Snippet: We again use Ito's Change of variable formulae for the multivariable system (which 247 will depend on ζ 1 and ζ 2 ) to approximate ω. This leads to an SDE equation which 248 depends on the description of ζ 1 and ζ 2 (eqn. 9). In particular, we are interested in 249 statistics of the rate of incidence, such as the variance, which can be simplified in terms 250 of the original covariance matrix Θ (eqn. 12) and mean-field equations of infectio.....
Document: We again use Ito's Change of variable formulae for the multivariable system (which 247 will depend on ζ 1 and ζ 2 ) to approximate ω. This leads to an SDE equation which 248 depends on the description of ζ 1 and ζ 2 (eqn. 9). In particular, we are interested in 249 statistics of the rate of incidence, such as the variance, which can be simplified in terms 250 of the original covariance matrix Θ (eqn. 12) and mean-field equations of infectious (φ) 251 and susceptible (ψ) individuals, Following, we can describe the fluctuations about the rate of incidence (ω) using the 258 LNA. In particular,
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