Abstract
SummaryDespite the wide application of dynamic models in infectious disease epidemiology, the particular modeling of variability in the different model components is often subjective rather than the result of a thorough model selection process. This is in part because inference for a stochastic transmission model can be difficult since the likelihood is often intractable due to partial observability. In this work, we address the question of adequate inclusion of variability by demonstrating a systematic approach for model selection and parameter inference for dynamic epidemic models. For this, we perform inference for six partially observed Markov process models, which assume the same underlying transmission dynamics, but differ with respect to the amount of variability they allow for. The inference framework for the stochastic transmission models is provided by iterated filtering methods, which are readily implemented in the R package pomp by King and others (2016, Statistical inference for partially observed Markov processes via the R package pomp. Journal of Statistical Software69, 1–43). We illustrate our approach on German rotavirus surveillance data from 2001 to 2008, discuss practical difficulties of the methods used and calculate a model based estimate for the basic reproduction number n}{}R_0 using these data.
Highlights
IntroductionInfectious disease outbreaks are often observed in the form of uni- or multivariate time series, e.g. as the number of newly reported cases aggregated over some time period
SUMMARY Despite the wide application of dynamic models in infectious disease epidemiology, the particular modeling of variability in the different model components is often subjective rather than the result of a thorough model selection process. This is in part because inference for a stochastic transmission model can be difficult since the likelihood is often intractable due to partial observability
We address the question of adequate inclusion of variability by demonstrating a systematic approach for model selection and parameter inference for dynamic epidemic models
Summary
Infectious disease outbreaks are often observed in the form of uni- or multivariate time series, e.g. as the number of newly reported cases aggregated over some time period. In order to estimate the relationship between variables, a classical statistical approach is the use of time series analysis of the incident cases, e.g. as in Finkenstädt and others (2002), Held and others (2006) These models are useful for prediction and forecasting, they teach us little about the dynamics of the disease spread, which are crucial if one wants to, e.g. assess the risk of emerging pathogens or evaluate the impact of control measures such as vaccination. Another popular approach are transmission models, i.e. dynamic models which reflect the mechanisms of disease spread between individuals explicitly (Anderson and May, 1991; Keeling and Rohani, 2008; Diekmann and others, 2013). We consider a simplified version of the SIRS-type model used in Weidemann and others (2013) who analyzed the same data in a different context, including fewer disease states and fewer age classes but accounting for seasonality, age-structure and, in particular, more variability
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