Interpreting time-series analyses for continuous-time biological models--measles as a case study.
An increasing number of recent studies involve the fitting of mechanistic models to ecological time-series. In some cases, it is necessary for these models to be discrete-time approximations of continuous-time processes. We test the validity of discretization in the case of measles, where time-series models have recently been developed to estimate ecological parameters directly from data. We find that a non-homogeneous contact function is necessary to capture the host-parasite interaction in a discrete-time model, even in the absence of heterogeneities due to spatial or age structure. We derive a mathematical relationship describing the expected departure from mass-action transmission in terms of the epidemiological parameters in the model, and identify conditions under which the discretization process may fail.
Glass
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K
Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK. katie@zoo.cam.ac.uk
Xia
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Grenfell
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D001723:Birth Rate; D018562:Disease Transmission, Infectious; D006790:Host-Parasite Interactions; D006801:Humans; D008457:Measles / Q000453:epidemiology* / Q000517:prevention & control / Q000635:transmission; D008954:Models, Biological; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D014611:Vaccination