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Computing the density function of complex models with randomness by using polynomial expansions and the RVT technique. Application to the SIR epidemic model

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  • Calatayud, Julia
  • Carlos Cortés, Juan
  • Jornet, Marc

Abstract

This paper concerns the computation of the probability density function of the stochastic solution to general complex systems with uncertainties formulated via random differential equations. In the existing literature, the uncertainty quantification for random differential equations is based on the approximation of statistical moments by simulation or spectral methods, or on the computation of the exact density function via the random variable transformation (RVT) method when a closed-form solution is available. However, the problem of approximating the density function in a general setting has not been published yet. In this paper, we propose a hybrid method based on stochastic polynomial expansions, the RVT technique, and multidimensional integration schemes, to obtain accurate approximations to the solution density function. A problem-independent algorithm is proposed. The algorithm is tested on the SIR (susceptible-infected-recovered) epidemiological model, showing significant improvements compared to the previous literature.

Suggested Citation

  • Calatayud, Julia & Carlos Cortés, Juan & Jornet, Marc, 2020. "Computing the density function of complex models with randomness by using polynomial expansions and the RVT technique. Application to the SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:chsofr:v:133:y:2020:i:c:s0960077920300382
    DOI: 10.1016/j.chaos.2020.109639
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    References listed on IDEAS

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    1. Slama, Howida & Hussein, A. & El-Bedwhey, Nabila A. & Selim, Mustafa M., 2019. "An approximate probabilistic solution of a random SIR-type epidemiological model using RVT technique," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 144-156.
    2. Chen-Charpentier, B.-M. & Cortés, J.-C. & Licea, J.-A. & Romero, J.-V. & Roselló, M.-D. & Santonja, Francisco-J. & Villanueva, Rafael-J., 2015. "Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 113-129.
    3. Dorini, F.A. & Cunha, M.C.C., 2011. "On the linear advection equation subject to random velocity fields," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 679-690.
    4. Calatayud, J. & Cortés, J.-C. & Jornet, M., 2018. "The damped pendulum random differential equation: A comprehensive stochastic analysis via the computation of the probability density function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 261-279.
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