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Hayes BH, Vergne T, Andraud M, Rose N. Mathematical modeling at the livestock-wildlife interface: scoping review of drivers of disease transmission between species. Front Vet Sci 2023; 10:1225446. [PMID: 37745209 PMCID: PMC10511766 DOI: 10.3389/fvets.2023.1225446] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2023] [Accepted: 08/17/2023] [Indexed: 09/26/2023] Open
Abstract
Modeling of infectious diseases at the livestock-wildlife interface is a unique subset of mathematical modeling with many innate challenges. To ascertain the characteristics of the models used in these scenarios, a scoping review of the scientific literature was conducted. Fifty-six studies qualified for inclusion. Only 14 diseases at this interface have benefited from the utility of mathematical modeling, despite a far greater number of shared diseases. The most represented species combinations were cattle and badgers (for bovine tuberculosis, 14), and pigs and wild boar [for African (8) and classical (3) swine fever, and foot-and-mouth and disease (1)]. Assessing control strategies was the overwhelming primary research objective (27), with most studies examining control strategies applied to wildlife hosts and the effect on domestic hosts (10) or both wild and domestic hosts (5). In spatially-explicit models, while livestock species can often be represented through explicit and identifiable location data (such as farm, herd, or pasture locations), wildlife locations are often inferred using habitat suitability as a proxy. Though there are innate assumptions that may not be fully accurate when using habitat suitability to represent wildlife presence, especially for wildlife the parsimony principle plays a large role in modeling diseases at this interface, where parameters are difficult to document or require a high level of data for inference. Explaining observed transmission dynamics was another common model objective, though the relative contribution of involved species to epizootic propagation was only ascertained in a few models. More direct evidence of disease spill-over, as can be obtained through genomic approaches based on pathogen sequences, could be a useful complement to further inform such modeling. As computational and programmatic capabilities advance, the resolution of the models and data used in these models will likely be able to increase as well, with a potential goal being the linking of modern complex ecological models with the depth of dynamics responsible for pathogen transmission. Controlling diseases at this interface is a critical step toward improving both livestock and wildlife health, and mechanistic models are becoming increasingly used to explore the strategies needed to confront these diseases.
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Affiliation(s)
- Brandon H. Hayes
- IHAP, Université de Toulouse, INRAE, ENVT, Toulouse, France
- Ploufragan-Plouzané-Niort Laboratory, The French Agency for Food, Agriculture and the Environment (ANSES), Ploufragan, France
| | | | - Mathieu Andraud
- Ploufragan-Plouzané-Niort Laboratory, The French Agency for Food, Agriculture and the Environment (ANSES), Ploufragan, France
| | - Nicolas Rose
- Ploufragan-Plouzané-Niort Laboratory, The French Agency for Food, Agriculture and the Environment (ANSES), Ploufragan, France
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2
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Calatayud J, Jornet M, Mateu J. Spatio-temporal stochastic differential equations for crime incidence modeling. STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT : RESEARCH JOURNAL 2023; 37:1839-1854. [PMID: 36619700 PMCID: PMC9810525 DOI: 10.1007/s00477-022-02369-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 12/15/2022] [Indexed: 06/17/2023]
Abstract
We propose a methodology for the quantitative fitting and forecasting of real spatio-temporal crime data, based on stochastic differential equations. The analysis is focused on the city of Valencia, Spain, for which 90247 robberies and thefts with their latitude-longitude positions are available for a span of eleven years (2010-2020) from records of the 112-emergency phone. The incidents are placed in the 26 zip codes of the city (46001-46026), and monthly time series of crime are built for each of the zip codes. Their annual-trend components are modeled by Itô diffusion, with jointly correlated noises to account for district-level relations. In practice, this study may help simulate spatio-temporal situations and identify risky areas and periods from present and past data.
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Affiliation(s)
- Julia Calatayud
- Departament de Matemàtiques, Universitat Jaume I, 12071 Castellón, Spain
| | - Marc Jornet
- Departament de Matemàtiques, Universitat de València, 46100 Burjassot, Spain
| | - Jorge Mateu
- Departament de Matemàtiques, Universitat Jaume I, 12071 Castellón, Spain
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3
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Fintzi J, Wakefield J, Minin VN. A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts. Biometrics 2022; 78:1530-1541. [PMID: 34374071 DOI: 10.1111/biom.13538] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2020] [Revised: 06/10/2021] [Accepted: 06/17/2021] [Indexed: 12/30/2022]
Abstract
Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJPs), but are computationally challenging as imperfect surveillance, lack of subject-level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulation-based computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that approximates the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large-population settings, but requires modification for analyzing incidence counts without assuming that the data are normally distributed. We demonstrate how to reparameterize SEMs to appropriately analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation-based methods, computationally. Our framework is computationally robust when the model dynamics are complex and applies to a broad class of SEMs. We evaluate our method in simulations that reflect Ebola, influenza, and SARS-CoV-2 dynamics, and apply our method to national surveillance counts from the 2013-2015 West Africa Ebola outbreak.
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Affiliation(s)
- Jonathan Fintzi
- Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, Rockville, Maryland, USA
| | - Jon Wakefield
- Departments of Biostatistics and Statistics, University of Washington, Seattle, Washington, USA
| | - Vladimir N Minin
- Department of Statistics, University of California, Irvine, California, USA
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Jorge DCP, Oliveira JF, Miranda JGV, Andrade RFS, Pinho STR. Estimating the effective reproduction number for heterogeneous models using incidence data. ROYAL SOCIETY OPEN SCIENCE 2022; 9:220005. [PMID: 36133147 DOI: 10.6084/m9.figshare.c.6167795] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 08/16/2022] [Indexed: 05/25/2023]
Abstract
The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.
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Affiliation(s)
- D C P Jorge
- Instituto de Física Teórica, Universidade Estadual Paulista-UNESP, R. Dr. Teobaldo Ferraz 271, São Paulo 01140-070, Brazil
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - J F Oliveira
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
| | - J G V Miranda
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - R F S Andrade
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - S T R Pinho
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
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Jorge DCP, Oliveira JF, Miranda JGV, Andrade RFS, Pinho STR. Estimating the effective reproduction number for heterogeneous models using incidence data. ROYAL SOCIETY OPEN SCIENCE 2022; 9:220005. [PMID: 36133147 DOI: 10.5281/zenodo.5822669] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 08/16/2022] [Indexed: 05/25/2023]
Abstract
The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.
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Affiliation(s)
- D C P Jorge
- Instituto de Física Teórica, Universidade Estadual Paulista-UNESP, R. Dr. Teobaldo Ferraz 271, São Paulo 01140-070, Brazil
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - J F Oliveira
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
| | - J G V Miranda
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - R F S Andrade
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - S T R Pinho
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
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Jorge DCP, Oliveira JF, Miranda JGV, Andrade RFS, Pinho STR. Estimating the effective reproduction number for heterogeneous models using incidence data. ROYAL SOCIETY OPEN SCIENCE 2022; 9:220005. [PMID: 36133147 PMCID: PMC9449464 DOI: 10.1098/rsos.220005] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 08/16/2022] [Indexed: 05/10/2023]
Abstract
The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.
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Affiliation(s)
- D. C. P. Jorge
- Instituto de Física Teórica, Universidade Estadual Paulista—UNESP, R. Dr. Teobaldo Ferraz 271, São Paulo 01140-070, Brazil
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - J. F. Oliveira
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
| | - J. G. V. Miranda
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - R. F. S. Andrade
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - S. T. R. Pinho
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
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Telionis PA, Corbett P, Venkatramanan S, Lewis B. Methods for Rapid Mobility Estimation to Support Outbreak Response. Health Secur 2020; 18:1-15. [PMID: 32078419 DOI: 10.1089/hs.2019.0101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
When pressed for time, outbreak investigators often use homogeneous mixing models to model infectious diseases in data-poor regions. But recent outbreaks such as the 2014 Ebola outbreak in West Africa have shown the limitations of this approach in an era of increasing urbanization and connectivity. Both outbreak detection and predictive modeling depend on realistic estimates of human and disease mobility, but these data are difficult to acquire in a timely manner. This is especially true when dealing with an emerging outbreak in an under-resourced nation. Weighted travel networks with realistic estimates for population flows are often proprietary, expensive, or nonexistent. Here we propose a method for rapidly generating a mobility model from open-source data. As an example, we use road and river network data, along with population estimates, to construct a realistic model of human movement between health zones in the Democratic Republic of the Congo (DRC). Using these mobility data, we then fit an epidemic model to real-world surveillance data from the recent Ebola outbreak in the Nord Kivu region of the DRC to illustrate a potential use of the generated mobility estimation. In addition to providing a way for rapid risk estimation, this approach brings together novel techniques to merge diverse GIS datasets that can then be used to address issues that pertain to public health and global health security.
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Affiliation(s)
- Pyrros A Telionis
- Pyrros A. Telionis, PhD, is a postdoctoral research assistant, Biocomplexity Institute & Initiative, University of Virginia, Charlottesville, VA, and Population Health Sciences, Virginia-Maryland College of Veterinary Medicine, Virginia Tech, Blacksburg, VA. Patrick Corbett is an undergraduate research assistant; Srinivasan Venkatramanan, PhD, is a Research Scientist; and Bryan Lewis, PhD, is a Research Associate Professor; all in Population Health Sciences, Virginia-Maryland College of Veterinary Medicine, Virginia Tech, Blacksburg, VA
| | - Patrick Corbett
- Pyrros A. Telionis, PhD, is a postdoctoral research assistant, Biocomplexity Institute & Initiative, University of Virginia, Charlottesville, VA, and Population Health Sciences, Virginia-Maryland College of Veterinary Medicine, Virginia Tech, Blacksburg, VA. Patrick Corbett is an undergraduate research assistant; Srinivasan Venkatramanan, PhD, is a Research Scientist; and Bryan Lewis, PhD, is a Research Associate Professor; all in Population Health Sciences, Virginia-Maryland College of Veterinary Medicine, Virginia Tech, Blacksburg, VA
| | - Srinivasan Venkatramanan
- Pyrros A. Telionis, PhD, is a postdoctoral research assistant, Biocomplexity Institute & Initiative, University of Virginia, Charlottesville, VA, and Population Health Sciences, Virginia-Maryland College of Veterinary Medicine, Virginia Tech, Blacksburg, VA. Patrick Corbett is an undergraduate research assistant; Srinivasan Venkatramanan, PhD, is a Research Scientist; and Bryan Lewis, PhD, is a Research Associate Professor; all in Population Health Sciences, Virginia-Maryland College of Veterinary Medicine, Virginia Tech, Blacksburg, VA
| | - Bryan Lewis
- Pyrros A. Telionis, PhD, is a postdoctoral research assistant, Biocomplexity Institute & Initiative, University of Virginia, Charlottesville, VA, and Population Health Sciences, Virginia-Maryland College of Veterinary Medicine, Virginia Tech, Blacksburg, VA. Patrick Corbett is an undergraduate research assistant; Srinivasan Venkatramanan, PhD, is a Research Scientist; and Bryan Lewis, PhD, is a Research Associate Professor; all in Population Health Sciences, Virginia-Maryland College of Veterinary Medicine, Virginia Tech, Blacksburg, VA
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8
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Simon CM. The SIR dynamic model of infectious disease transmission and its analogy with chemical kinetics. PEERJ PHYSICAL CHEMISTRY 2020. [DOI: 10.7717/peerj-pchem.14] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
Mathematical models of the dynamics of infectious disease transmission are used to forecast epidemics and assess mitigation strategies. In this article, we highlight the analogy between the dynamics of disease transmission and chemical reaction kinetics while providing an exposition on the classic Susceptible–Infectious–Removed (SIR) epidemic model. Particularly, the SIR model resembles a dynamic model of a batch reactor carrying out an autocatalytic reaction with catalyst deactivation. This analogy between disease transmission and chemical reaction enables the exchange of ideas between epidemic and chemical kinetic modeling communities.
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9
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FITZGIBBON WE, MORGAN JJ, WEBB GF, WU Y. ANALYSIS OF A REACTION–DIFFUSION EPIDEMIC MODEL WITH ASYMPTOMATIC TRANSMISSION. J BIOL SYST 2020. [DOI: 10.1142/s0218339020500126] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
We develop a dynamic model of an evolving epidemic in a spatially inhomogeneous environment. We analyze the model, as a system of reaction–diffusion partial differential equations, to predict the outbreak and spatio-temporal spread of the disease. The model features both an asymptomatic infectious stage and symptomatic infectious stage, with both the asymptomatic and the symptomatic infected populations dispersing through the susceptible population. We prove the existence and uniform boundedness of solutions, and investigate their long-time behavior. We apply the spatially homogeneous version of the model to the current COVID-19 epidemic in Brazil.
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Affiliation(s)
- W. E. FITZGIBBON
- Mathematics Department, University of Houston, Houston, Texas 77204, US
| | - J. J. MORGAN
- Mathematics Department, University of Houston, Houston, Texas 77204, US
| | - G. F. WEBB
- Mathematics Department, Vanderbilt University, Nashville, Tennessee 37240, US
| | - Y. WU
- Mathematics Sciences Department, Middle Tennessee State University, Murfreesboro, Tennessee 37132, US
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10
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Khan T, Zaman G, Chohan MI. The transmission dynamic of different hepatitis B-infected individuals with the effect of hospitalization. JOURNAL OF BIOLOGICAL DYNAMICS 2018; 12:611-631. [PMID: 30047315 DOI: 10.1080/17513758.2018.1500649] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2018] [Accepted: 07/09/2018] [Indexed: 06/08/2023]
Abstract
We propose an epidemic model for the transmission of hepatitis B virus along with the classification of different infection phases and hospitalized class. We formulate the model and discuss its basic mathematical properties, e.g. existence, positivity, and biological feasibility. Exploiting the next generation matrix approach, we find the basic reproductive number of the model. We perform sensitivity analysis to illustrate the effect of various parameters on the transmission of the disease. We investigate stability of the equilibria of the model in terms of the basic reproduction number. Conditions for the stability of the proposed model are obtained using various approaches. Finally, we perform the numerical simulations to discuss sensitivity analysis and to support our analytical work.
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Affiliation(s)
- Tahir Khan
- a Department of Mathematics , University of Malakand , Chakdara , Khyber Pakhtunkhwa , Pakistan
| | - Gul Zaman
- a Department of Mathematics , University of Malakand , Chakdara , Khyber Pakhtunkhwa , Pakistan
| | - Muhammad Ikhlaq Chohan
- b Department of Business Administration and Accounting , Buraimi University College , Al-Buraimi , Oman
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11
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Mourant JR, Fenimore PW, Manore CA, McMahon BH. Decision Support for Mitigation of Livestock Disease: Rinderpest as a Case Study. Front Vet Sci 2018; 5:182. [PMID: 30234131 PMCID: PMC6129599 DOI: 10.3389/fvets.2018.00182] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2017] [Accepted: 07/17/2018] [Indexed: 12/25/2022] Open
Abstract
A versatile, interactive model to predict geographically resolved epidemic progression after pathogen introduction into a population is presented. Deterministic simulations incorporating a compartmental disease model run rapidly, facilitating the analysis of mitigations such as vaccination and transmission reduction on epidemic spread and progression. We demonstrate the simulation model using rinderpest infection of cattle, a devastating livestock disease. Rinderpest has been extinguished in the wild, but it is still a threat due to stored virus in some laboratories. Comparison of simulations to historical outbreaks provides some validation of the model. Simulations of potential outbreaks demonstrate potential consequences of rinderpest virus release for a variety of possible disease parameters and mitigations. Our results indicate that a rinderpest outbreak could result in severe social and economic consequences.
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Affiliation(s)
- Judith R. Mourant
- Bioscience Division, Los Alamos National Laboratory (DOE), Los Alamos, NM, United States
| | - Paul W. Fenimore
- Theoretical Division, Los Alamos National Laboratory (DOE), Los Alamos, NM, United States
| | - Carrie A. Manore
- Theoretical Division, Los Alamos National Laboratory (DOE), Los Alamos, NM, United States
| | - Benjamin H. McMahon
- Theoretical Division, Los Alamos National Laboratory (DOE), Los Alamos, NM, United States
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12
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Bürger R, Chowell G, Gavilán E, Mulet P, Villada LM. Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2018; 15:95-123. [PMID: 29161828 DOI: 10.3934/mbe.2018004] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In this article we describe the transmission dynamics of hantavirus in rodents using a spatio-temporal susceptible-exposed-infective-recovered (SEIR) compartmental model that distinguishes between male and female subpopulations [L.J.S. Allen, R.K. McCormack and C.B. Jonsson, Bull. Math. Biol. 68 (2006), 511--524]. Both subpopulations are assumed to differ in their movement with respect to local variations in the densities of their own and the opposite gender group. Three alternative models for the movement of the male individuals are examined. In some cases the movement is not only directed by the gradient of a density (as in the standard diffusive case), but also by a non-local convolution of density values as proposed, in another context, in [R.M. Colombo and E. Rossi, Commun. Math. Sci., 13 (2015), 369--400]. An efficient numerical method for the resulting convection-diffusion-reaction system of partial differential equations is proposed. This method involves techniques of weighted essentially non-oscillatory (WENO) reconstructions in combination with implicit-explicit Runge-Kutta (IMEX-RK) methods for time stepping. The numerical results demonstrate significant differences in the spatio-temporal behavior predicted by the different models, which suggest future research directions.
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Affiliation(s)
- Raimund Bürger
- CI²MA and Departamento de Ingeniería Matemática , Universidad de Concepción, Casilla 160-C, Concepción , Chile
| | - Gerardo Chowell
- Mathematical, Computational and Modeling Sciences Center, School of Human Evolution and Social Change, Arizona State University, Box 872402, Tempe, AZ 85287, United States
| | - Elvis Gavilán
- CI2MA and Departamento de Ingeniería Matemática , Universidad de Concepción, Casilla 160-C, Concepción, Chile
| | - Pep Mulet
- Departament de Matemàtica Aplicada, Universitat de València, Av. Dr. Moliner 50, E-46100 Burjassot, Spain
| | - Luis M Villada
- GIMNAP-Departamento de Matemáticas, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile
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Spatial Representations and Analysis Techniques. FORMAL METHODS FOR THE QUANTITATIVE EVALUATION OF COLLECTIVE ADAPTIVE SYSTEMS 2016. [DOI: 10.1007/978-3-319-34096-8_5] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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