Bayesian analysis of a dynamical model for the spread of the Usutu virus |
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Authors: | Jen? Reiczigel Katharina Brugger Franz Rubel Norbert Solymosi Zsolt Lang |
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Institution: | 1. Department for Biomathematics and Informatics, Faculty of Veterinary Science, Szent István University, István u. 2, 1078, Budapest, Hungary 2. HAS-BCU Adaptation to Climate Change Research Group, Villányi út 29-43, 1118, Budapest, Hungary 3. Institute for Veterinary Public Health, University for Veterinary Medicine Vienna, Veterin?rplatz 1, 1210, Vienna, Austria
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Abstract: | The Usutu virus is an arbovirus transmitted by mosquitoes and causing disease in birds. The virus was detected in Austria
for the first time in 2001, while a major outbreak occurred in 2003. Rubel et al. (2008) developed a nine-compartment deterministic SEIR model to explain the spread of the disease. We extended this to a hierarchical
Bayes model assuming random variation in temperature data, in reproduction data of birds, and in the number of birds found
to be infected. The model was implemented in R, combined with the FORTRAN subroutine for the original deterministic model.
Analysis was made by MCMC using a random walk Metropolis scheme. Posterior means, medians, and credible intervals were calculated
for the parameters. The hierarchical Bayes approach proved to be fruitful in extending the deterministic model into a stochastic
one. It allowed for Bayesian point and interval estimation and quantification of uncertainty of predictions. The analysis
revealed that some model parameters were not identifiable; therefore we kept constant some of them and analyzed others conditional
on them. Identifiability problems are common in models aiming to mirror the mechanism of the process, since parameters with
natural interpretation are likely to exhibit interrelationships. This study illustrated that Bayesian modeling combined with
conditional analysis may help in those cases. Its application to the Usutu model improved model fit and revealed the structure
of interdependencies between model parameters: it demonstrated that determining some of them experimentally would enable estimation
of the others, except one of them, from available data. |
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