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.

通过考虑确定性参数，使用微分方程（DE）系统对现实生活中的流行情况进行建模。但是，实际上，此类模型中涉及的传输参数会经历很多变化，因此无法精确计算它们。在本文中，我们应用基于B样条小波的广义多项式混沌（gPC）来分析可能的随机流行过程。进行了敏感性分析（SA），以研究简单流行病模型中的随机行为。已分析，与三次B样条小波相比，线性B样条小波基通过包含较少的多项式混沌展开（PCE）来显示准确的结果。我们已经针对两种实际的疾病暴发实施了我们开发的方法，首先，流感在1978年影响了北英格兰的英国男校寄宿学校，其次是2014年在利比里亚的埃博拉疫情。《英国医学杂志》（流感）和世界卫生组织（埃博拉）的真实数据已纳入“易感人群”，恢复（SIR）模型。已经观察到，通过所提出的方法获得的数值结果是非常令人满意的。