Uncertainty Quantification of Stochastic Epidemic SIR Models Using B-spline Polynomial Chaos

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.