Dynamic noise, chaos and parameter estimation in population biology

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 such as multi-strain dynamics to describe the virus -host interaction in dengue fever, even the most recently developed parameter estimation techniques, such as maximum likelihood iterated filtering, reach their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and the deterministic skeleton. The deterministic system on its own already displays complex dynamics up to deterministic chaos and coexistence of multiple attractors.

The Impact of the Newly Licensed Dengue Vaccine in Endemic Countries

“…Using the data given by the Sanofi-Pasteur dengue vaccine trials in the Asian-Pacific region (CYD14) as reported in [20] and the Latin American countries (CYD15) as reported in [21], we could estimate the overall vaccine efficacy for virologically confirmed dengue cases via the Bayesian approach [35–37] to obtain a probability p ( k | I v , I c ) for the vaccine efficacy k ) with infected individuals I v in the vaccine group and I c in the control group. For more detailed calculations, see [34].…”

Mathematical and theoretical ecology: linking models with ecological processes

“…Yet, often ecological data are noisy or incomplete and parameter estimates not obvious, leading to a number of issues in model parametrization [11]. By focusing on population-based epidemiology models, Stollenwerk et al [7] address issues of parameter estimates. Stollenwerk et al [7] provide a comprehensive review of this subject by first examining basic epidemiological models and then expanding their examples to cover more realistic cases focusing on models of dengue fever.…”

“…By focusing on population-based epidemiology models, Stollenwerk et al [7] address issues of parameter estimates. Stollenwerk et al [7] provide a comprehensive review of this subject by first examining basic epidemiological models and then expanding their examples to cover more realistic cases focusing on models of dengue fever. Building on this approach, Stollenwerk et al [7] then produce a master equation from which the transition probabilities can be used to compute a likelihood function; linking their theoretical models with observed data by providing the probability of observing all points from empirical time-series data describing infection dynamics, as a function of model parameters.…”

“…Building on this approach, Stollenwerk et al [7] then produce a master equation from which the transition probabilities can be used to compute a likelihood function; linking their theoretical models with observed data by providing the probability of observing all points from empirical time-series data describing infection dynamics, as a function of model parameters. Once a likelihood function is computed it can be incorporated into a Bayesian framework, and along with the maximum-likelihood estimates, Stollenwerk et al [7] then discusses the application of these methods in parameter estimation.…”

Towards the marriage of theory and data

“…That is the rationale for the excellent collection of papers that appear in this Theme Issue, and I think is emblematic of the maturation of a discipline. All of the papers in this issue in one way or another deal with the interplay of models with data, from the work by Stollenwerk et al [26] on the treatment of parameter estimation to Petrovskii & Petrovskaya's [27] review of computational challenges in ecology.…”