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.