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Computational uncertainty quantification for random time‐discrete epidemiological models using adaptive gPC
Author(s) -
Calatayud Julia,
Cortés Juan Carlos,
Jornet Marc,
Villanueva Rafael Jacinto
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5315
Subject(s) - discrete time stochastic process , discrete time and continuous time , mathematics , stochastic process , polynomial chaos , uncertainty quantification , population , nonlinear system , process (computing) , mathematical optimization , stochastic simulation , stochastic modelling , computer science , continuous time stochastic process , statistics , monte carlo method , physics , demography , quantum mechanics , sociology , operating system
Population dynamics models consisting of nonlinear difference equations allow us to get a better understanding of the processes involved in epidemiology. Usually, these mathematical models are studied under a deterministic approach. However, in order to take into account the uncertainties associated with the measurements of the model input parameters, a more realistic approach would be to consider these inputs as random variables. In this paper, we study the random time‐discrete epidemiological models SIS, SIR, SIRS, and SEIR using a powerful unified approach based upon the so‐called adaptive generalized polynomial chaos (gPC) technique. The solution to these random difference equations is a stochastic process in discrete time, which represents the number of susceptible, infected, recovered, etc individuals at each time step. We show, via numerical experiments, how adaptive gPC permits quantifying the uncertainty for the solution stochastic process of the aforementioned random time‐discrete epidemiological model and obtaining accurate results at a cheap computational expense. We also highlight how adaptive gPC can be applied in practice, by means of an example using real data.