Inference of a Susceptible-Infectious stochastic model.

IF 2.6 4区 工程技术 Q1 Mathematics
Giuseppina Albano, Virginia Giorno, Francisco Torres-Ruiz
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Abstract

We considered a time-inhomogeneous diffusion process able to describe the dynamics of infected people in a susceptible-infectious (SI) epidemic model in which the transmission intensity function was time-dependent. Such a model was well suited to describe some classes of micro-parasitic infections in which individuals never acquired lasting immunity and over the course of the epidemic everyone eventually became infected. The stochastic process related to the deterministic model was transformable into a nonhomogeneous Wiener process so the probability distribution could be obtained. Here we focused on the inference for such a process, by providing an estimation procedure for the involved parameters. We pointed out that the time dependence in the infinitesimal moments of the diffusion process made classical inference methods inapplicable. The proposed procedure were based on the generalized method of moments in order to find a suitable estimate for the infinitesimal drift and variance of the transformed process. Several simulation studies are conduced to test the procedure, these include the time homogeneous case, for which a comparison with the results obtained by applying the maximum likelihood estimation was made, and cases in which the intensity function were time dependent with particular attention to periodic cases. Finally, we applied the estimation procedure to a real dataset.

易感-传染性随机模型的推理。
在易感-感染(SI)流行病模型中,传播强度函数是随时间变化的,我们考虑了一种能够描述感染者动态的时间-均质扩散过程。这种模型非常适合描述某些类别的微寄生虫感染,在这些感染中,个体永远不会获得持久的免疫力,在流行过程中,每个人最终都会被感染。与确定性模型相关的随机过程可转化为非均质维纳过程,从而获得概率分布。在此,我们通过提供相关参数的估算程序,重点讨论了这种过程的推论。我们指出,扩散过程无穷小矩的时间依赖性使得经典推理方法无法应用。建议的程序基于广义矩法,以便为转换过程的无穷小漂移和方差找到合适的估计值。我们进行了几项模拟研究来检验该程序,其中包括时间均一的情况(与应用最大似然估计法得到的结果进行了比较),以及强度函数与时间相关的情况(特别关注周期性情况)。最后,我们将估算程序应用于真实数据集。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Mathematical Biosciences and Engineering
Mathematical Biosciences and Engineering 工程技术-数学跨学科应用
CiteScore
3.90
自引率
7.70%
发文量
586
审稿时长
>12 weeks
期刊介绍: Mathematical Biosciences and Engineering (MBE) is an interdisciplinary Open Access journal promoting cutting-edge research, technology transfer and knowledge translation about complex data and information processing. MBE publishes Research articles (long and original research); Communications (short and novel research); Expository papers; Technology Transfer and Knowledge Translation reports (description of new technologies and products); Announcements and Industrial Progress and News (announcements and even advertisement, including major conferences).
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