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This article is cited in 3 scientific papers (total in 3 papers)
Uncertainty Quantification of Stochastic Epidemic SIR Models
Using B-spline Polynomial Chaos
Navjot Kaur, Kavita Goyal School of Mathematics, Thapar Institute of Engineering and Technology,
Patiala, 147004 Punjab, India
Abstract:
Real-life epidemic situations are modeled using systems of differential equations
(DEs) by considering deterministic parameters. However, in reality, the transmission parameters
involved in such models experience a lot of variations and it is not possible to compute them
exactly. In this paper, we apply B-spline wavelet-based generalized polynomial chaos (gPC) to
analyze possible stochastic epidemic processes. A sensitivity analysis (SA) has been performed
to investigate the behavior of randomness in a simple epidemic model. It has been analyzed
that a linear B-spline wavelet basis shows accurate results by involving fewer polynomial chaos
expansions (PCE) in comparison to cubic B-spline wavelets. We have carried out our developed
method on two real outbreaks of diseases, firstly, influenza which affected the British boarding
school for boys in North England in 1978, and secondly, Ebola in Liberia in 2014. Real data
from the British Medical Journal (influenza) and World Health Organization (Ebola) has been
incorporated into the Susceptible-Infected-Recovered (SIR) model. It has been observed that
the numerical results obtained by the proposed method are quite satisfactory.
Keywords:
B-spline chaos, Ebola virus outbreak, Galerkin approximation, influenza, SIR model,
stochastic ordinary differential equations, uncertainty quantification.
Received: 27.06.2020 Accepted: 15.12.2020
Citation:
Navjot Kaur, Kavita Goyal, “Uncertainty Quantification of Stochastic Epidemic SIR Models
Using B-spline Polynomial Chaos”, Regul. Chaotic Dyn., 26:1 (2021), 22–38
Linking options:
https://www.mathnet.ru/eng/rcd1100 https://www.mathnet.ru/eng/rcd/v26/i1/p22
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Abstract page: | 85 | References: | 16 |
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