Selected article for: "analytical solution and Î Poisson process rate"
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_31
    Snippet: Rate of Incidence Theory 214 We consider the rate of incidence (or the rate of the Poisson process) λ(t) = T (I + 1|I), 215 which can be described dynamically with an SDE. Our analyses shows that the critical 216 transition of the rate of the Poisson process corresponds to prevalence models (e.g. at 217 R 0 = 1) and importantly exhibits behaviours predicted by CSD. 218 We investigate here calculating statistics on the rate of incidence (RoI) and.....
    Document: Rate of Incidence Theory 214 We consider the rate of incidence (or the rate of the Poisson process) λ(t) = T (I + 1|I), 215 which can be described dynamically with an SDE. Our analyses shows that the critical 216 transition of the rate of the Poisson process corresponds to prevalence models (e.g. at 217 R 0 = 1) and importantly exhibits behaviours predicted by CSD. 218 We investigate here calculating statistics on the rate of incidence (RoI) and its 219 potential to be used as an EWS for disease transitions. In particular, by considering the time 227 derivative of λ t we can conclude that the fixed points of the rate of incidence can be 228 described by the transcritical bifurcation at R 0 = 1. We find that the stability of the 229 fixed points of λ t also correspond to those of I, as expected. 230 We describe the fluctuations, ω, about the steady state of λ t = β(N −I)I N using the 231 linear noise approximation (LNA). We are interested in statistics calculated on the 232 fluctuations about the rate of incidence, to develop new indicators of disease elimination. 233 We derive the resulting analytical solution for ω using Ito's Change of variable formulae 234 (details in supporting text: S1 Appendix) to approximate ω with the following Gaussian 235 process:

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