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

Anindya Bhadra A. Bhadra is Doctoral Student and E. L. Ionides is Associate Professor, Department of Statistics, University of Michigan, Ann Arbor, MI 48109. K. Laneri is Postdoctoral Student, Department of Ecology & Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109. M. Pascual is Rosemary Grant Collegiate Professor, Department of Ecology & Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109 and Investigator, Howard Hughes Medical Institute, 4000 Jones Bridge Road, Chevy Chase, MD 20815-6789. M. Bouma is Adjunct Faculty, Department of Infectious and Tropical Diseases, London School of Hygiene and Tropical Medicine, University of London, London, United Kingdom. R. C. Dhiman is Research Scientist, National Institute of Malaria Research, Sector 8, Dwarka, Delhi-110077, India. This work was funded in part by support from the RAPIDD program at the Science & Technology Directorate of the Department of Homeland Security and the Fogarty International Center, National Institutes of Health; the National Science Foundation (DMS-0805533); the National Oceanic and Atmospheric Administration (Oceans and Health Program NA 040 AR 460019); and the Graham Environmental Sustainability Institute of the University of Michigan. The authors thank the editor (Hal Stern), the associate editor, and two anonymous referees for their helpful comments.

Edward L. Ionides A. Bhadra is Doctoral Student and E. L. Ionides is Associate Professor, Department of Statistics, University of Michigan, Ann Arbor, MI 48109. K. Laneri is Postdoctoral Student, Department of Ecology & Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109. M. Pascual is Rosemary Grant Collegiate Professor, Department of Ecology & Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109 and Investigator, Howard Hughes Medical Institute, 4000 Jones Bridge Road, Chevy Chase, MD 20815-6789. M. Bouma is Adjunct Faculty, Department of Infectious and Tropical Diseases, London School of Hygiene and Tropical Medicine, University of London, London, United Kingdom. R. C. Dhiman is Research Scientist, National Institute of Malaria Research, Sector 8, Dwarka, Delhi-110077, India. This work was funded in part by support from the RAPIDD program at the Science & Technology Directorate of the Department of Homeland Security and the Fogarty International Center, National Institutes of Health; the National Science Foundation (DMS-0805533); the National Oceanic and Atmospheric Administration (Oceans and Health Program NA 040 AR 460019); and the Graham Environmental Sustainability Institute of the University of Michigan. The authors thank the editor (Hal Stern), the associate editor, and two anonymous referees for their helpful comments.

Karina Laneri A. Bhadra is Doctoral Student and E. L. Ionides is Associate Professor, Department of Statistics, University of Michigan, Ann Arbor, MI 48109. K. Laneri is Postdoctoral Student, Department of Ecology & Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109. M. Pascual is Rosemary Grant Collegiate Professor, Department of Ecology & Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109 and Investigator, Howard Hughes Medical Institute, 4000 Jones Bridge Road, Chevy Chase, MD 20815-6789. M. Bouma is Adjunct Faculty, Department of Infectious and Tropical Diseases, London School of Hygiene and Tropical Medicine, University of London, London, United Kingdom. R. C. Dhiman is Research Scientist, National Institute of Malaria Research, Sector 8, Dwarka, Delhi-110077, India. This work was funded in part by support from the RAPIDD program at the Science & Technology Directorate of the Department of Homeland Security and the Fogarty International Center, National Institutes of Health; the National Science Foundation (DMS-0805533); the National Oceanic and Atmospheric Administration (Oceans and Health Program NA 040 AR 460019); and the Graham Environmental Sustainability Institute of the University of Michigan. The authors thank the editor (Hal Stern), the associate editor, and two anonymous referees for their helpful comments.

Mercedes Pascual A. Bhadra is Doctoral Student and E. L. Ionides is Associate Professor, Department of Statistics, University of Michigan, Ann Arbor, MI 48109. K. Laneri is Postdoctoral Student, Department of Ecology & Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109. M. Pascual is Rosemary Grant Collegiate Professor, Department of Ecology & Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109 and Investigator, Howard Hughes Medical Institute, 4000 Jones Bridge Road, Chevy Chase, MD 20815-6789. M. Bouma is Adjunct Faculty, Department of Infectious and Tropical Diseases, London School of Hygiene and Tropical Medicine, University of London, London, United Kingdom. R. C. Dhiman is Research Scientist, National Institute of Malaria Research, Sector 8, Dwarka, Delhi-110077, India. This work was funded in part by support from the RAPIDD program at the Science & Technology Directorate of the Department of Homeland Security and the Fogarty International Center, National Institutes of Health; the National Science Foundation (DMS-0805533); the National Oceanic and Atmospheric Administration (Oceans and Health Program NA 040 AR 460019); and the Graham Environmental Sustainability Institute of the University of Michigan. The authors thank the editor (Hal Stern), the associate editor, and two anonymous referees for their helpful comments.

Menno Bouma A. Bhadra is Doctoral Student and E. L. Ionides is Associate Professor, Department of Statistics, University of Michigan, Ann Arbor, MI 48109. K. Laneri is Postdoctoral Student, Department of Ecology & Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109. M. Pascual is Rosemary Grant Collegiate Professor, Department of Ecology & Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109 and Investigator, Howard Hughes Medical Institute, 4000 Jones Bridge Road, Chevy Chase, MD 20815-6789. M. Bouma is Adjunct Faculty, Department of Infectious and Tropical Diseases, London School of Hygiene and Tropical Medicine, University of London, London, United Kingdom. R. C. Dhiman is Research Scientist, National Institute of Malaria Research, Sector 8, Dwarka, Delhi-110077, India. This work was funded in part by support from the RAPIDD program at the Science & Technology Directorate of the Department of Homeland Security and the Fogarty International Center, National Institutes of Health; the National Science Foundation (DMS-0805533); the National Oceanic and Atmospheric Administration (Oceans and Health Program NA 040 AR 460019); and the Graham Environmental Sustainability Institute of the University of Michigan. The authors thank the editor (Hal Stern), the associate editor, and two anonymous referees for their helpful comments.

Ramesh C. Dhiman A. Bhadra is Doctoral Student and E. L. Ionides is Associate Professor, Department of Statistics, University of Michigan, Ann Arbor, MI 48109. K. Laneri is Postdoctoral Student, Department of Ecology & Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109. M. Pascual is Rosemary Grant Collegiate Professor, Department of Ecology & Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109 and Investigator, Howard Hughes Medical Institute, 4000 Jones Bridge Road, Chevy Chase, MD 20815-6789. M. Bouma is Adjunct Faculty, Department of Infectious and Tropical Diseases, London School of Hygiene and Tropical Medicine, University of London, London, United Kingdom. R. C. Dhiman is Research Scientist, National Institute of Malaria Research, Sector 8, Dwarka, Delhi-110077, India. This work was funded in part by support from the RAPIDD program at the Science & Technology Directorate of the Department of Homeland Security and the Fogarty International Center, National Institutes of Health; the National Science Foundation (DMS-0805533); the National Oceanic and Atmospheric Administration (Oceans and Health Program NA 040 AR 460019); and the Graham Environmental Sustainability Institute of the University of Michigan. The authors thank the editor (Hal Stern), the associate editor, and two anonymous referees for their helpful comments.

Abstract

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 Lévy 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.

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

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

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