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Ngwira A, Manda S, Karimuribo ED, Kimera SI. Identification of common spatial and temporal trends in the epidemiology of cattle bovine tuberculosis and human extrapulmonary and drug-resistant tuberculosis in Malawi. One Health 2024; 19:100905. [PMID: 39483753 PMCID: PMC11525156 DOI: 10.1016/j.onehlt.2024.100905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2024] [Accepted: 09/26/2024] [Indexed: 11/03/2024] Open
Abstract
Background Identification of common spatial disease trends between cattle bovine tuberculosis (BTB) and human extrapulmonary tuberculosis (EPTB) and drug-resistant tuberculosis (DRTB) can support integrated disease control and monitoring programmes. We employed the recently developed multivariate disease mapping methods to examine whether the diseases exhibited any spatial correlation. Methods A retrospective study of cattle BTB and human EPTB and DRTB cases from 2018 to 2022 was conducted. Bivariate shared spatiotemporal components models were fitted to a) cattle BTB and human EPTB and b) cattle BTB and human DRTB at the district level in Malawi, with cattle density, human density and climatic variables as independent variables. Results Disease specific spatial effects were higher in the southern half of the country, while the shared spatial effects were more dominant in both the south and western parts of the country. The shared temporal effects showed constant trends, while disease specific temporal effects showed an increasing pattern for cattle BTB and a constant pattern for human EPTB and DRTB. The predicted disease incidence pattern for all forms of TB in the period without data showed a constant pattern over the years. Cattle density was positively associated with cattle BTB ( β : 0.022; 95% Credible Interval (CI): 0.004, 0.042). Human density was positively associated with human EPTB ( β : 0.005; 95% CI: 0.001, 0.009). Conclusion Cattle BTB and human EPTB and DRTB have a common spatial pattern in the west and southern parts of Malawi. Integrated interventions targeting high-density areas for cattle and human may have positive impacts on cattle BTB and human EPTB and DRTB.
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Affiliation(s)
- Alfred Ngwira
- Department of Veterinary Medicine and Public Health, Sokoine University of Agriculture, Morogoro, Tanzania
- Department of Basic Sciences, Lilongwe University of Agriculture and Natural Resources, Lilongwe, Malawi
- SACIDS Africa Centre of Excellence for Infectious Diseases, SACIDS Foundation for One Health, Sokoine University of Agriculture, Morogoro, Tanzania
| | - Samuel Manda
- Department of Statistics, University of Pretoria, Pretoria 0002, South Africa
| | - Esron Daniel Karimuribo
- Department of Veterinary Medicine and Public Health, Sokoine University of Agriculture, Morogoro, Tanzania
- SACIDS Africa Centre of Excellence for Infectious Diseases, SACIDS Foundation for One Health, Sokoine University of Agriculture, Morogoro, Tanzania
| | - Sharadhuli Iddi Kimera
- Department of Veterinary Medicine and Public Health, Sokoine University of Agriculture, Morogoro, Tanzania
- SACIDS Africa Centre of Excellence for Infectious Diseases, SACIDS Foundation for One Health, Sokoine University of Agriculture, Morogoro, Tanzania
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2
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Tesema GA, Tessema ZT, Heritier S, Stirling RG, Earnest A. A Systematic Review of Joint Spatial and Spatiotemporal Models in Health Research. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2023; 20:5295. [PMID: 37047911 PMCID: PMC10094468 DOI: 10.3390/ijerph20075295] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Revised: 03/13/2023] [Accepted: 03/24/2023] [Indexed: 06/19/2023]
Abstract
With the advancement of spatial analysis approaches, methodological research addressing the technical and statistical issues related to joint spatial and spatiotemporal models has increased. Despite the benefits of spatial modelling of several interrelated outcomes simultaneously, there has been no published systematic review on this topic, specifically when such models would be useful. This systematic review therefore aimed at reviewing health research published using joint spatial and spatiotemporal models. A systematic search of published studies that applied joint spatial and spatiotemporal models was performed using six electronic databases without geographic restriction. A search with the developed search terms yielded 4077 studies, from which 43 studies were included for the systematic review, including 15 studies focused on infectious diseases and 11 on cancer. Most of the studies (81.40%) were performed based on the Bayesian framework. Different joint spatial and spatiotemporal models were applied based on the nature of the data, population size, the incidence of outcomes, and assumptions. This review found that when the outcome is rare or the population is small, joint spatial and spatiotemporal models provide better performance by borrowing strength from related health outcomes which have a higher prevalence. A framework for the design, analysis, and reporting of such studies is also needed.
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Affiliation(s)
- Getayeneh Antehunegn Tesema
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC 3004, Australia
- Department of Epidemiology and Biostatistics, Institute of Public Health, College of Medicine and Health Sciences, University of Gondar, Gondar 196, Ethiopia
| | - Zemenu Tadesse Tessema
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC 3004, Australia
- Department of Epidemiology and Biostatistics, Institute of Public Health, College of Medicine and Health Sciences, University of Gondar, Gondar 196, Ethiopia
| | - Stephane Heritier
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC 3004, Australia
| | - Rob G. Stirling
- Department of Respiratory Medicine, Alfred Health, Melbourne, VIC 3004, Australia
- Faculty of Medicine, Nursing and Health Sciences, Central Clinical School, Monash University, Melbourne, VIC 3004, Australia
| | - Arul Earnest
- School of Public Health and Preventive Medicine, Monash University, Melbourne, VIC 3004, Australia
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3
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Lawson AB, Kim J. Issues in Bayesian prospective surveillance of spatial health data. Spat Spatiotemporal Epidemiol 2022; 41:100431. [PMID: 35691635 DOI: 10.1016/j.sste.2021.100431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/01/2020] [Revised: 04/30/2021] [Accepted: 04/30/2021] [Indexed: 10/21/2022]
Abstract
In this paper I review some of the major issues that arise when geo-referenced health data are to be the subject of prospective surveillance. The review focusses on modelbased approaches to this activity, and proposes the Bayesian paradigm as a convenient vehicle for modeling. Various posterior functional measures are discussed including the SCPO and SKL and a number of extensions to these are considered. Overall the value of Bayesian Hierarchical Modeling (BHM) with surveillance functionals is stressed in its relevance to early warning of adverse risk scenarios.
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Affiliation(s)
- Andrew B Lawson
- Department of Public Health Sciences, Medical University of South Carolina, Charleston, SC 29466, USA.
| | - Joanne Kim
- Department of Public Health Sciences, Medical University of South Carolina, Charleston, SC 29466, USA.
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4
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Rotejanaprasert C, Lee D, Ekapirat N, Sudathip P, Maude RJ. Spatiotemporal distributed lag modelling of multiple Plasmodium species in a malaria elimination setting. Stat Methods Med Res 2021; 30:22-34. [PMID: 33595402 DOI: 10.1177/0962280220938977] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In much of the Greater Mekong Sub-region, malaria is now confined to patches and small foci of transmission. Malaria transmission is seasonal with the spatiotemporal patterns being associated with variation in environmental and climatic factors. However, the possible effect at different lag periods between meteorological variables and clinical malaria has not been well studied in the region. Thus, in this study we developed distributed lagged modelling accounting for spatiotemporal excessive zero cases in a malaria elimination setting. A multivariate framework was also extended to incorporate multiple data streams and investigate the spatiotemporal patterns from multiple parasite species via their lagged association with climatic variables. A simulation study was conducted to examine robustness of the methodology and a case study is provided of weekly data of clinical malaria cases at sub-district level in Thailand.
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Affiliation(s)
- Chawarat Rotejanaprasert
- Department of Tropical Hygiene, Faculty of Tropical Medicine, Mahidol University, Bangkok, Thailand.,Mahidol-Oxford Tropical Medicine Research Unit, Faculty of Tropical Medicine, Mahidol University, Bangkok, Thailand
| | - Duncan Lee
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - Nattwut Ekapirat
- Mahidol-Oxford Tropical Medicine Research Unit, Faculty of Tropical Medicine, Mahidol University, Bangkok, Thailand
| | - Prayuth Sudathip
- Division of Vector Borne Diseases, Department of Disease Control, Ministry of Public Health, Nonthaburi, Thailand
| | - Richard J Maude
- Mahidol-Oxford Tropical Medicine Research Unit, Faculty of Tropical Medicine, Mahidol University, Bangkok, Thailand.,Harvard T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA.,Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, Oxford, UK
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Multichart Schemes for Detecting Changes in Disease Incidence. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2020; 2020:7267801. [PMID: 32508978 PMCID: PMC7245694 DOI: 10.1155/2020/7267801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/06/2019] [Revised: 03/06/2020] [Accepted: 03/27/2020] [Indexed: 11/17/2022]
Abstract
Several methods have been proposed in open literatures for detecting changes in disease outbreak or incidence. Most of these methods are likelihood-based as well as the direct application of Shewhart, CUSUM and EWMA schemes. We use CUSUM, EWMA and EWMA-CUSUM multi-chart schemes to detect changes in disease incidence. Multi-chart is a combination of several single charts that detects changes in a process and have been shown to have elegant properties in the sense that they are fast in detecting changes in a process as well as being computationally less expensive. Simulation results show that the multi-CUSUM chart is faster than EWMA and EWMA-CUSUM multi-charts in detecting shifts in the rate parameter. A real illustration with health data is used to demonstrate the efficiency of the schemes.
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NIMBLE for Bayesian Disease Mapping. Spat Spatiotemporal Epidemiol 2020; 33:100323. [PMID: 32370936 DOI: 10.1016/j.sste.2020.100323] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 12/11/2019] [Revised: 01/23/2020] [Accepted: 01/23/2020] [Indexed: 11/23/2022]
Abstract
This tutorial describes the basic implementation of Bayesian hierarchical models for spatial health data using the R package nimble. To quote the nimble R description: A system for writing hierarchical statistical models largely compatible with 'BUGS' and 'JAGS', writing nimbleFunctions to operate models and do basic R-style math, and compiling both models and nimbleFunctions via custom-generated C++. 'NIMBLE' includes default methods for MCMC, particle filtering, Monte Carlo Expectation Maximization, and some other tools. The nimbleFunction system makes it easy to do things like implement new MCMC samplers from R, customize the assignment of samplers to different parts of a model from R, and compile the new samplers automatically via C++ alongside the samplers 'NIMBLE' provides. Examples of the use of the package for a small range of Bayesian Disease Mapping (BDM) models is explored and focus on different approaches to model fitting and analysis are discussed. Examples of publicly available small area health data is used throughout.
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7
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Santitissadeekorn N, Lloyd DJ, Short MB, Delahaies S. Approximate filtering of conditional intensity process for Poisson count data: Application to urban crime. Comput Stat Data Anal 2020. [DOI: 10.1016/j.csda.2019.106850] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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8
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Gonsalves GS, Copple JT, Johnson T, Paltiel AD, Warren JL. Bayesian adaptive algorithms for locating HIV mobile testing services. BMC Med 2018; 16:155. [PMID: 30173667 PMCID: PMC6120098 DOI: 10.1186/s12916-018-1129-0] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/30/2018] [Accepted: 07/13/2018] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND We have previously conducted computer-based tournaments to compare the yield of alternative approaches to deploying mobile HIV testing services in settings where the prevalence of undetected infection may be characterized by 'hotspots'. We report here on three refinements to our prior assessments and their implications for decision-making. Specifically, (1) enlarging the number of geographic zones; (2) including spatial correlation in the prevalence of undetected infection; and (3) evaluating a prospective search algorithm that accounts for such correlation. METHODS Building on our prior work, we used a simulation model to create a hypothetical city consisting of up to 100 contiguous geographic zones. Each zone was randomly assigned a prevalence of undetected HIV infection. We employed a user-defined weighting scheme to correlate infection levels between adjacent zones. Over 180 days, search algorithms selected a zone in which to conduct a fixed number of HIV tests. Algorithms were permitted to observe the results of their own prior testing activities and to use that information in choosing where to test in subsequent rounds. The algorithms were (1) Thompson sampling (TS), an adaptive Bayesian search strategy; (2) Besag York Mollié (BYM), a Bayesian hierarchical model; and (3) Clairvoyance, a benchmarking strategy with access to perfect information. RESULTS Over 250 tournament runs, BYM detected 65.3% (compared to 55.1% for TS) of the cases identified by Clairvoyance. BYM outperformed TS in all sensitivity analyses, except when there was a small number of zones (i.e., 16 zones in a 4 × 4 grid), wherein there was no significant difference in the yield of the two strategies. Though settings of no, low, medium, and high spatial correlation in the data were examined, differences in these levels did not have a significant effect on the relative performance of BYM versus TS. CONCLUSIONS BYM narrowly outperformed TS in our simulation, suggesting that small improvements in yield can be achieved by accounting for spatial correlation. However, the comparative simplicity with which TS can be implemented makes a field evaluation critical to understanding the practical value of either of these algorithms as an alternative to existing approaches for deploying HIV testing resources.
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Affiliation(s)
- Gregg S. Gonsalves
- Department of Epidemiology of Microbial Diseases, Yale School of Public Health, 60 College Street, New Haven, CT USA
| | - J. Tyler Copple
- Department of Epidemiology of Microbial Diseases, Yale School of Public Health, 60 College Street, New Haven, CT USA
- Independent Consultant, Yale School of Public Health, 60 College Street, New Haven, CT USA
| | - Tyler Johnson
- Department of Epidemiology of Microbial Diseases, Yale School of Public Health, 60 College Street, New Haven, CT USA
| | - A. David Paltiel
- Department of Health Policy and Management, Yale School of Public Health, 60 College Street, New Haven, CT USA
| | - Joshua L. Warren
- Department of Biostatistics, Yale School of Public Health, 60 College Street, New Haven, CT USA
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9
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Lawson AB, Carroll R, Faes C, Kirby RS, Aregay M, Watjou K. Spatiotemporal multivariate mixture models for Bayesian model selection in disease mapping. ENVIRONMETRICS 2017; 28:e2465. [PMID: 29230091 PMCID: PMC5722237 DOI: 10.1002/env.2465] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
It is often the case that researchers wish to simultaneously explore the behavior of and estimate overall risk for multiple, related diseases with varying rarity while accounting for potential spatial and/or temporal correlation. In this paper, we propose a flexible class of multivariate spatio-temporal mixture models to fill this role. Further, these models offer flexibility with the potential for model selection as well as the ability to accommodate lifestyle, socio-economic, and physical environmental variables with spatial, temporal, or both structures. Here, we explore the capability of this approach via a large scale simulation study and examine a motivating data example involving three cancers in South Carolina. The results which are focused on four model variants suggest that all models possess the ability to recover simulation ground truth and display improved model fit over two baseline Knorr-Held spatio-temporal interaction model variants in a real data application.
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Affiliation(s)
- AB Lawson
- Department of Public Health Sciences, Medical University of South Carolina
| | - R Carroll
- Department of Public Health Sciences, Medical University of South Carolina
| | - C Faes
- Interuniversity Institute for Statistics and Statistical Bioinformatics, Hasselt University
| | - RS Kirby
- Department of Community and Family Health, University of South Florida
| | - M Aregay
- Department of Public Health Sciences, Medical University of South Carolina
| | - K Watjou
- Interuniversity Institute for Statistics and Statistical Bioinformatics, Hasselt University
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10
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Hopkins RS, Tong CC, Burkom HS, Akkina JE, Berezowski J, Shigematsu M, Finley PD, Painter I, Gamache R, Vilas VJDR, Streichert LC. A Practitioner-Driven Research Agenda for Syndromic Surveillance. Public Health Rep 2017; 132:116S-126S. [PMID: 28692395 DOI: 10.1177/0033354917709784] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Syndromic surveillance has expanded since 2001 in both scope and geographic reach and has benefited from research studies adapted from numerous disciplines. The practice of syndromic surveillance continues to evolve rapidly. The International Society for Disease Surveillance solicited input from its global surveillance network on key research questions, with the goal of improving syndromic surveillance practice. A workgroup of syndromic surveillance subject matter experts was convened from February to June 2016 to review and categorize the proposed topics. The workgroup identified 12 topic areas in 4 syndromic surveillance categories: informatics, analytics, systems research, and communications. This article details the context of each topic and its implications for public health. This research agenda can help catalyze the research that public health practitioners identified as most important.
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Affiliation(s)
- Richard S Hopkins
- 1 Department of Epidemiology, College of Public Health and Health Professions and College of Medicine, University of Florida, Gainesville, FL, USA
| | - Catherine C Tong
- 2 International Society for Disease Surveillance, Braintree, MA, USA
| | - Howard S Burkom
- 3 Applied Physics Laboratory, Johns Hopkins University, Laurel, MD, USA
| | - Judy E Akkina
- 4 Center for Epidemiology and Animal Health, Veterinary Services, Animal and Plant Health Inspection Service, US Department of Agriculture, Fort Collins, CO, USA
| | - John Berezowski
- 5 Veterinary Public Health Institute, University of Bern, Bern, Switzerland
| | - Mika Shigematsu
- 6 International Biological and Chemical Threat Reduction Program, Sandia National Laboratories, Albuquerque, NM, USA.,7 National Institute of Infectious Diseases, Tokyo, Japan
| | - Patrick D Finley
- 8 Department of Operations Research and Computational Analysis, Sandia National Laboratories, Albuquerque, NM, USA
| | - Ian Painter
- 9 Department of Health Services, School of Public Health, University of Washington, Seattle, WA, USA.,10 Gamache Consulting, Rockville, MD, USA
| | - Roland Gamache
- 11 School of Veterinary Medicine, University of Surrey, Kent, UK.,12 Center for Population Health Information Technology, Department of Health Policy and Management, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA
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11
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A simulation study on the statistical monitoring of condemnation rates from slaughterhouses for syndromic surveillance: an evaluation based on Swiss data. Epidemiol Infect 2015; 143:3423-33. [PMID: 26018224 DOI: 10.1017/s0950268815000989] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Abstract
Syndromic surveillance (SyS) systems currently exploit various sources of health-related data, most of which are collected for purposes other than surveillance (e.g. economic). Several European SyS systems use data collected during meat inspection for syndromic surveillance of animal health, as some diseases may be more easily detected post-mortem than at their point of origin or during the ante-mortem inspection upon arrival at the slaughterhouse. In this paper we use simulation to evaluate the performance of a quasi-Poisson regression (also known as an improved Farrington) algorithm for the detection of disease outbreaks during post-mortem inspection of slaughtered animals. When parameterizing the algorithm based on the retrospective analyses of 6 years of historic data, the probability of detection was satisfactory for large (range 83-445 cases) outbreaks but poor for small (range 20-177 cases) outbreaks. Varying the amount of historical data used to fit the algorithm can help increasing the probability of detection for small outbreaks. However, while the use of a 0·975 quantile generated a low false-positive rate, in most cases, more than 50% of outbreak cases had already occurred at the time of detection. High variance observed in the whole carcass condemnations time-series, and lack of flexibility in terms of the temporal distribution of simulated outbreaks resulting from low reporting frequency (monthly), constitute major challenges for early detection of outbreaks in the livestock population based on meat inspection data. Reporting frequency should be increased in the future to improve timeliness of the SyS system while increased sensitivity may be achieved by integrating meat inspection data into a multivariate system simultaneously evaluating multiple sources of data on livestock health.
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12
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Zamiri A, Yazdi HS, Goli SA. Temporal and spatial monitoring and prediction of epidemic outbreaks. IEEE J Biomed Health Inform 2014; 19:735-44. [PMID: 25122846 PMCID: PMC7186040 DOI: 10.1109/jbhi.2014.2338213] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
This paper introduces a nonlinear dynamic model to study spatial and temporal dynamics of epidemics of susceptible-infected-removed type. It involves modeling the respective collections of epidemic states and syndromic observations as random finite sets. Each epidemic state consists of the number of infected individuals in an isolated population system and the corresponding partially known parameters of the epidemic model. The infectious disease could spread between population systems with known probabilities based on prior knowledge of ecological and biological features of the environment. The problem is then formulated in the context of Bayesian framework and estimated via a probability hypothesis density filter. Each population system under surveillance is assumed to be homogenous and fixed, with daily reports on the number of infected people available for monitoring and prediction. When model parameters are partially known, results of numerical studies indicate that the proposed approach can help early prediction of the epidemic in terms of peak and duration.
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13
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Corberán-Vallet A, Lawson AB. Prospective analysis of infectious disease surveillance data using syndromic information. Stat Methods Med Res 2014; 23:572-90. [PMID: 24659490 DOI: 10.1177/0962280214527385] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In this paper, we describe a Bayesian hierarchical Poisson model for the prospective analysis of data for infectious diseases. The proposed model consists of two components. The first component describes the behavior of disease during nonepidemic periods and the second component represents the increase in disease counts due to the presence of an epidemic. A novelty of our model formulation is that the parameters describing the spread of epidemics are allowed to vary in both space and time. We also show how syndromic information can be incorporated into the model to provide a better description of the data and more accurate one-step-ahead forecasts. These real-time forecasts can be used to identify high-risk areas for outbreaks and, consequently, to develop efficient targeted surveillance. We apply the methodology to weekly emergency room discharges for acute bronchitis in South Carolina.
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Affiliation(s)
- Ana Corberán-Vallet
- Department of Statistics and Operations Research, University of Valencia, Burjassot, Spain
| | - Andrew B Lawson
- Department of Public Health Sciences, Medical University of South Carolina, Charleston, U.S.A
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