Abstract
We revisit the parameter estimation framework for population biological dynamical systems, and apply it to calibrate various models in epidemiology with empirical time series, namely influenza and dengue fever. When it comes to more complex models like multi‐strain dynamics to describe the virus‐host interaction in dengue fever, even most recently developed parameter estimation techniques, like maximum likelihood iterated filtering, come to their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and deterministic skeleton. The deterministic system on its own already displays complex dynamics up to deterministic chaos and coexistence of multiple attractors.
Highlights
A major contribution to stochasticicty in empirical epidemiological data is population noise which is modelled by time continuous Markov processes or master equations [1, 2, 3]
We start with an example of a linear infection model which can be solved analytically in all aspects and generalize to more complex epidemiological models which are relevant for the description of e.g. influenza or dengue fever [5], on the cost of having to perform more and more steps by simulation to obtain the likelihood function by complete enumeration [6] or even just to search for the maximum in extreme cases
Recent applications to a multi-strain model applied to empirical data sets of dengue fever in Thailand, where the model displays such complex dynamics as deterministic chaos in wide parameter regions [5, 7], stretch the presently available methods of parameter estimation well to its limits
Summary
A major contribution to stochasticicty in empirical epidemiological data is population noise which is modelled by time continuous Markov processes or master equations [1, 2, 3]. We start with an example of a linear infection model which can be solved analytically in all aspects and generalize to more complex epidemiological models which are relevant for the description of e.g. influenza or dengue fever [5], on the cost of having to perform more and more steps by simulation to obtain the likelihood function by complete enumeration [6] or even just to search for the maximum in extreme cases. Recent applications to a multi-strain model applied to empirical data sets of dengue fever in Thailand, where the model displays such complex dynamics as deterministic chaos in wide parameter regions [5, 7], stretch the presently available methods of parameter estimation well to its limits. The analysis of scaling of solely population noise indicates that very large world regions have to be considered in data analysis in order to be able to compare the fluctuations of the stochastic system with the much easier to analyze deterministic skeleton, which can already show deterministic chaos [8, 9], here via torus bifurcations [10]
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