Malaria in Northwest India: Data Analysis via Partially Observed Stochastic Differential Equation Models Driven by Levy Noise

• 成果类型: Article
• 署名作者: Bhadra, Anindya; Ionides, Edward L.; Laneri, Karina; Pascual, Mercedes; Bouma, Menno; Dhiman, Ramesh C.
• 署名单位: University of Michigan System; University of Michigan; University of Michigan System; University of Michigan; Howard Hughes Medical Institute; University of London; London School of Hygiene & Tropical Medicine; Indian Council of Medical Research (ICMR); ICMR - National Institute of Malaria Research (NIMR)
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2011.ap10323
• 发表日期: 2011
• 页码: 440-451
• 关键词: epidemic models; euler scheme; monte-carlo; inference; transmission; DYNAMICS; measles; burden; infections; parameter

摘要

Many biological systems are appropriately described by partially observed Markov process (POMP) models, also known as state space models. Such models also arise throughout the physical and social sciences, in engineering, and in finance. Statistical challenges arise in carrying out inference on nonlinear, nonstationary, vector-valued POMP models. Methodologies that depend on the Markov process model only through numerical solution of sample paths are said to have the plug-and-play property. This property enables consideration of models for which the evaluation of transition densities is problematic. Our case study employs plug-and-play methodology to investigate malaria transmission in Northwest India. We address the scientific question of the respective roles of environmental factors, immunity, and nonlinear disease transmission dynamics in epidemic malaria. Previous debates on this question have been hindered by the lack of a statistical investigation that gives simultaneous consideration to the roles of human immunity and the fluctations in mosquito abundance associated with environmental or ecological covariates. We present the first time series analysis integrating these various components into a single vector-valued dynamic model. We are led to investigate a POMP involving a system of stochastic differential equations driven by Levy noise. We find a clear role for rainfall and evidence to support models featuring the possibility of clinical immunity. An online supplement presents details of the methodology implemented and two additional figures.