Articlehybrid2012

Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos

Francisco José Santonja Gómez · Benito M. Chen‐Charpentier

21 citations0/0 files storedComputational and Mathematical Methods in Medicine

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Probabilistic and Robust Engineering Design Mathematical and Theoretical Epidemiology and Ecology Models Fuzzy Systems and Optimization

Abstract

Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equations, which is then integrated numerically to obtain the first-and the second-order moments of the output stochastic processes. A sensitivity analysis based on the polynomial chaos approach is also performed to determine which parameters have the greatest influence on the results. As an example, we will apply the approach to an obesity epidemic model.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 21 citations exist upstream.

References

2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2007Global sensitivity analysis using polynomial chaos expansions 2003Modeling uncertainty in flow simulations via generalized polynomial chaos 2008Polynomial chaos expansion for sensitivity analysis 1992Random Vibration of Mechanical and Structural Systems 2002Uncertainty analysis for fluid mechanics with applications 2008Sampling and sensitivity analyses tools (SaSAT) for computational modelling 2009Random coefficient differential equation models for bacterial growth

Cited by

2022Theory and methods for random differential equations: a survey 2018Computational uncertainty quantification for random time‐discrete epidemiological models using adaptive gPC 2016Applying the stochastic Galerkin method to epidemic models with uncertainty in the parameters 2015Influence of Physical and Geometrical Uncertainties in the Parametric Instability Load of an Axially Excited Cylindrical Shell 2018On the convergence of adaptive gPC for non-linear random difference equations: Theoretical analysis and some practical recommendations

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.