6533b82cfe1ef96bd128ff75
RESEARCH PRODUCT
Uncertainty quantification in simulations of epidemics using polynomial chaos.
Francisco-josé SantonjaBenito M. Chen-charpentiersubject
AdultMathematical optimizationArticle SubjectDifferential equationlcsh:Computer applications to medicine. Medical informaticsGeneral Biochemistry Genetics and Molecular BiologyComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONPrevalenceApplied mathematicsHumansObesityUncertainty quantificationEpidemicsRandomnessMathematicsAgedStochastic ProcessesPolynomial chaosModels StatisticalGeneral Immunology and MicrobiologyMathematical modelApplied MathematicsUncertaintyGeneral MedicineMiddle AgedModels TheoreticalNonlinear systemNonlinear DynamicsModeling and SimulationOrdinary differential equationlcsh:R858-859.7Epidemic modelAlgorithmsResearch Articledescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-05-08 | Computational and mathematical methods in medicine |