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Dong W, Zhou J, Xu B. A stochastic delayed SIS epidemic model with Holling type II incidence rate. STOCH MODELS 2022. [DOI: 10.1080/15326349.2022.2155666] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Wenxu Dong
- College of Science, Northwest A&F University, Yangling, Shaanxi, P. R. China
| | - Jianjun Zhou
- College of Science, Northwest A&F University, Yangling, Shaanxi, P. R. China
| | - Biteng Xu
- College of Science, Northwest A&F University, Yangling, Shaanxi, P. R. China
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2
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Petros BA, Paull JS, Tomkins-Tinch CH, Loftness BC, DeRuff KC, Nair P, Gionet GL, Benz A, Brock-Fisher T, Hughes M, Yurkovetskiy L, Mulaudzi S, Leenerman E, Nyalile T, Moreno GK, Specht I, Sani K, Adams G, Babet SV, Baron E, Blank JT, Boehm C, Botti-Lodovico Y, Brown J, Buisker AR, Burcham T, Chylek L, Cronan P, Dauphin A, Desreumaux V, Doss M, Flynn B, Gladden-Young A, Glennon O, Harmon HD, Hook TV, Kary A, King C, Loreth C, Marrs L, McQuade KJ, Milton TT, Mulford JM, Oba K, Pearlman L, Schifferli M, Schmidt MJ, Tandus GM, Tyler A, Vodzak ME, Krohn Bevill K, Colubri A, MacInnis BL, Ozsoy AZ, Parrie E, Sholtes K, Siddle KJ, Fry B, Luban J, Park DJ, Marshall J, Bronson A, Schaffner SF, Sabeti PC. Multimodal surveillance of SARS-CoV-2 at a university enables development of a robust outbreak response framework. MED 2022; 3:883-900.e13. [PMID: 36198312 PMCID: PMC9482833 DOI: 10.1016/j.medj.2022.09.003] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2022] [Revised: 09/06/2022] [Accepted: 09/12/2022] [Indexed: 12/27/2022]
Abstract
BACKGROUND Universities are vulnerable to infectious disease outbreaks, making them ideal environments to study transmission dynamics and evaluate mitigation and surveillance measures. Here, we analyze multimodal COVID-19-associated data collected during the 2020-2021 academic year at Colorado Mesa University and introduce a SARS-CoV-2 surveillance and response framework. METHODS We analyzed epidemiological and sociobehavioral data (demographics, contact tracing, and WiFi-based co-location data) alongside pathogen surveillance data (wastewater and diagnostic testing, and viral genomic sequencing of wastewater and clinical specimens) to characterize outbreak dynamics and inform policy. We applied relative risk, multiple linear regression, and social network assortativity to identify attributes or behaviors associated with contracting SARS-CoV-2. To characterize SARS-CoV-2 transmission, we used viral sequencing, phylogenomic tools, and functional assays. FINDINGS Athletes, particularly those on high-contact teams, had the highest risk of testing positive. On average, individuals who tested positive had more contacts and longer interaction durations than individuals who never tested positive. The distribution of contacts per individual was overdispersed, although not as overdispersed as the distribution of phylogenomic descendants. Corroboration via technical replicates was essential for identification of wastewater mutations. CONCLUSIONS Based on our findings, we formulate a framework that combines tools into an integrated disease surveillance program that can be implemented in other congregate settings with limited resources. FUNDING This work was supported by the National Science Foundation, the Hertz Foundation, the National Institutes of Health, the Centers for Disease Control and Prevention, the Massachusetts Consortium on Pathogen Readiness, the Howard Hughes Medical Institute, the Flu Lab, and the Audacious Project.
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Affiliation(s)
- Brittany A Petros
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA; Harvard-MIT Program in Health Sciences and Technology, Cambridge, MA 02139, USA; Harvard/MIT MD-PhD Program, Boston, MA 02115, USA; Systems, Synthetic, and Quantitative Biology PhD Program, Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA
| | - Jillian S Paull
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA; Systems, Synthetic, and Quantitative Biology PhD Program, Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA.
| | - Christopher H Tomkins-Tinch
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA.
| | - Bryn C Loftness
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA; Department of Computer Science and Engineering, Colorado Mesa University, Grand Junction, CO 81501, USA; Complex Systems and Data Science PhD Program, University of Vermont, Burlington, VT 05405, USA; Vermont Complex Systems Center, University of Vermont, Burlington, VT 05405, USA.
| | | | - Parvathy Nair
- Howard Hughes Medical Institute, Chevy Chase, MD 20815, USA
| | | | - Aaron Benz
- Degree Analytics, Inc., Austin, TX 78758, USA
| | | | | | - Leonid Yurkovetskiy
- Program in Molecular Medicine, University of Massachusetts Chan Medical School, Worcester, MA 01655, USA
| | - Shandukani Mulaudzi
- Harvard Program in Bioinformatics and Integrative Genomics, Harvard Medical School, Boston, MA 02115, USA
| | | | - Thomas Nyalile
- Program in Molecular Medicine, University of Massachusetts Chan Medical School, Worcester, MA 01655, USA
| | - Gage K Moreno
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA
| | - Ivan Specht
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA
| | - Kian Sani
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA
| | - Gordon Adams
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA
| | - Simone V Babet
- Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, CO 80309, USA
| | - Emily Baron
- COVIDCheck Colorado, LLC, Denver, CO 80202, USA
| | - Jesse T Blank
- Colorado Mesa University, Grand Junction, CO 81501, USA
| | - Chloe Boehm
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA; Princeton University Molecular Biology Department, Princeton, NJ 08544, USA
| | | | - Jeremy Brown
- Colorado Mesa University, Grand Junction, CO 81501, USA
| | | | | | - Lily Chylek
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA
| | - Paul Cronan
- Fathom Information Design, Boston, MA 02114, USA
| | - Ann Dauphin
- Program in Molecular Medicine, University of Massachusetts Chan Medical School, Worcester, MA 01655, USA
| | - Valentine Desreumaux
- Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, CO 80309, USA
| | - Megan Doss
- Warrior Diagnostics, Inc., Loveland, CO 80538, USA
| | - Belinda Flynn
- Colorado Mesa University, Grand Junction, CO 81501, USA
| | | | | | | | - Thomas V Hook
- Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, CO 80309, USA
| | - Anton Kary
- Department of Biological Sciences, Colorado Mesa University, Grand Junction, CO 81501, USA
| | - Clay King
- Department of Mathematics and Statistics, Colorado Mesa University, Grand Junction, CO 81501, USA
| | | | - Libby Marrs
- Fathom Information Design, Boston, MA 02114, USA
| | - Kyle J McQuade
- Department of Biological Sciences, Colorado Mesa University, Grand Junction, CO 81501, USA
| | - Thorsen T Milton
- Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, CO 80309, USA
| | - Jada M Mulford
- Department of Biological Sciences, Colorado Mesa University, Grand Junction, CO 81501, USA
| | - Kyle Oba
- Fathom Information Design, Boston, MA 02114, USA
| | - Leah Pearlman
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA
| | | | | | - Grace M Tandus
- Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, CO 80309, USA
| | - Andy Tyler
- Colorado Mesa University, Grand Junction, CO 81501, USA
| | - Megan E Vodzak
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA
| | - Kelly Krohn Bevill
- Department of Computer Science and Engineering, Colorado Mesa University, Grand Junction, CO 81501, USA
| | - Andres Colubri
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA; University of Massachusetts Medical School, Worcester, MA 01655, USA
| | | | - A Zeynep Ozsoy
- Department of Biological Sciences, Colorado Mesa University, Grand Junction, CO 81501, USA
| | - Eric Parrie
- COVIDCheck Colorado, LLC, Denver, CO 80202, USA
| | - Kari Sholtes
- Department of Computer Science and Engineering, Colorado Mesa University, Grand Junction, CO 81501, USA; Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, CO 80309, USA
| | - Katherine J Siddle
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
| | - Ben Fry
- Fathom Information Design, Boston, MA 02114, USA
| | - Jeremy Luban
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA; Program in Molecular Medicine, University of Massachusetts Chan Medical School, Worcester, MA 01655, USA; Biochemistry and Molecular Pharmacology, University of Massachusetts Medical School, Worcester, MA 01655, USA; Massachusetts Consortium on Pathogen Readiness, Boston, MA 02115, USA
| | - Daniel J Park
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA
| | - John Marshall
- Colorado Mesa University, Grand Junction, CO 81501, USA
| | - Amy Bronson
- Physician Assistant Program, Department of Kinesiology, Colorado Mesa University, Grand Junction, CO 81501, USA
| | | | - Pardis C Sabeti
- Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA; Howard Hughes Medical Institute, Chevy Chase, MD 20815, USA; Massachusetts Consortium on Pathogen Readiness, Boston, MA 02115, USA; Department of Epidemiology, Harvard T.H. Chan School of Public Health, Boston, MA 02115, USA
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Shi L, Qi L. Dynamic analysis and optimal control of a class of SISP respiratory diseases. JOURNAL OF BIOLOGICAL DYNAMICS 2022; 16:64-97. [PMID: 35129084 DOI: 10.1080/17513758.2022.2027529] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2021] [Accepted: 01/04/2022] [Indexed: 06/14/2023]
Abstract
In this paper, the actual background of the susceptible population being directly patients after inhaling a certain amount of PM2.5 is taken into account. The concentration response function of PM2.5 is introduced, and the SISP respiratory disease model is proposed. Qualitative theoretical analysis proves that the existence, local stability and global stability of the equilibria are all related to the daily emission P0 of PM2.5 and PM2.5 pathogenic threshold K. Based on the sensitivity factor analysis and time-varying sensitivity analysis of parameters on the number of patients, it is found that the conversion rate β and the inhalation rate η has the largest positive correlation. The cure rate γ of infected persons has the greatest negative correlation on the number of patients. The control strategy formulated by the analysis results of optimal control theory is as follows: The first step is to improve the clearance rate of PM2.5 by reducing the PM2.5 emissions and increasing the intensity of dust removal. Moreover, such removal work must be maintained for a long time. The second step is to improve the cure rate of patients by being treated in time. After that, people should be reminded to wear masks and go out less so as to reduce the conversion rate of susceptible people becoming patients.
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Affiliation(s)
- Lei Shi
- School of Mathematical Sciences, Anhui University, Hefei, People's Republic of China
| | - Longxing Qi
- School of Mathematical Sciences, Anhui University, Hefei, People's Republic of China
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Song P, Xiao Y. Analysis of a diffusive epidemic system with spatial heterogeneity and lag effect of media impact. J Math Biol 2022; 85:17. [PMID: 35913603 PMCID: PMC9340761 DOI: 10.1007/s00285-022-01780-w] [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: 12/22/2021] [Revised: 04/26/2022] [Accepted: 06/24/2022] [Indexed: 12/02/2022]
Abstract
We considered an SIS functional partial differential model cooperated with spatial heterogeneity and lag effect of media impact. The wellposedness including existence and uniqueness of the solution was proved. We defined the basic reproduction number and investigated the threshold dynamics of the model, and discussed the asymptotic behavior and monotonicity of the basic reproduction number associated with the diffusion rate. The local and global Hopf bifurcation at the endemic steady state was investigated theoretically and numerically. There exists numerical cases showing that the larger the number of basic reproduction number, the smaller the final epidemic size. The meaningful conclusion generalizes the previous conclusion of ordinary differential equation.
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Affiliation(s)
- Pengfei Song
- Department of Applied Mathematics, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, PR China
| | - Yanni Xiao
- Department of Applied Mathematics, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, PR China.
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Guo Y, Li T. Modeling and dynamic analysis of novel coronavirus pneumonia (COVID-19) in China. JOURNAL OF APPLIED MATHEMATICS & COMPUTING 2022; 68:2641-2666. [PMID: 34584515 PMCID: PMC8459705 DOI: 10.1007/s12190-021-01611-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2021] [Revised: 07/17/2021] [Accepted: 07/19/2021] [Indexed: 05/04/2023]
Abstract
Although novel coronavirus pneumonia (COVID-19) was widely spread in mainland China in early 2020, it was soon controlled. To study the impact of government interventions on the spread of disease during epidemics, a differential equation system is established to simulate the process of virus propagation in this paper. We first analyze its basic properties, basic reproduction number R 0 and existence of equilibria. Then we prove that the disease-free equilibrium (DFE) is Globally Asymptotically Stable when R 0 is less than 1. Through the analysis of the daily epidemic data from January 10, 2020 to March 11, 2020, combined with the implementation of the national epidemic policy, we divide the whole process into three stages: the first stage (natural state), the second stage (isolation state), the third stage (isolation, detection and treatment). By using the weighted nonlinear least square method to fit the data of three stages, the parameters are obtained, and three basic reproduction numbers are calculated, which are: R 01 = 2.6735 , R 02 = 0.85077 , R 03 = 0.18249 . Sensitivity analysis of threshold parameters and corresponding graphical results were also performed to examine the relative importance of various model parameters to the spread and prevalence of COVID-19. Finally, we simulate the trend of three stages and verify the theory of Global Asymptotic Stability of DFE. The conclusion of this paper proves theoretically that the Chinese government's epidemic prevention measures are effective in the fight against the spread of COVID-19. This study can not only provide a reference for research methods to simulate COVID-19 transmission in other countries or regions, but also provide recommendations on COVID-19 prevention measures for them.
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Affiliation(s)
- Youming Guo
- College of Science, Guilin University of Technology, Guilin, 541004 Guangxi People’s Republic of China
| | - Tingting Li
- College of Science, Guilin University of Technology, Guilin, 541004 Guangxi People’s Republic of China
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Xue L, Jing S, Wang H. Evaluating the impacts of non-pharmaceutical interventions on the transmission dynamics of COVID-19 in Canada based on mobile network. PLoS One 2021; 16:e0261424. [PMID: 34965272 PMCID: PMC8716046 DOI: 10.1371/journal.pone.0261424] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2021] [Accepted: 12/01/2021] [Indexed: 01/08/2023] Open
Abstract
The COVID-19 outbreak has caused two waves and spread to more than 90% of Canada's provinces since it was first reported more than a year ago. During the COVID-19 epidemic, Canadian provinces have implemented many Non-Pharmaceutical Interventions (NPIs). However, the spread of the COVID-19 epidemic continues due to the complex dynamics of human mobility. We develop a meta-population network model to study the transmission dynamics of COVID-19. The model takes into account the heterogeneity of mitigation strategies in different provinces of Canada, such as the timing of implementing NPIs, the human mobility in retail and recreation, grocery and pharmacy, parks, transit stations, workplaces, and residences due to work and recreation. To determine which activity is most closely related to the dynamics of COVID-19, we use the cross-correlation analysis to find that the positive correlation is the highest between the mobility data of parks and the weekly number of confirmed COVID-19 from February 15 to December 13, 2020. The average effective reproduction numbers in nine Canadian provinces are all greater than one during the time period, and NPIs have little impact on the dynamics of COVID-19 epidemics in Ontario and Saskatchewan. After November 20, 2020, the average infection probability in Alberta became the highest since the start of the COVID-19 epidemic in Canada. We also observe that human activities around residences do not contribute much to the spread of the COVID-19 epidemic. The simulation results indicate that social distancing and constricting human mobility is effective in mitigating COVID-19 transmission in Canada. Our findings can provide guidance for public health authorities in projecting the effectiveness of future NPIs.
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Affiliation(s)
- Ling Xue
- College of Mathematical Sciences, Harbin Engineering University, Harbin, Heilongjiang, China
| | - Shuanglin Jing
- College of Mathematical Sciences, Harbin Engineering University, Harbin, Heilongjiang, China
| | - Hao Wang
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada
- * E-mail:
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7
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Determining travel fluxes in epidemic areas. PLoS Comput Biol 2021; 17:e1009473. [PMID: 34705832 PMCID: PMC8550429 DOI: 10.1371/journal.pcbi.1009473] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/26/2020] [Accepted: 09/23/2021] [Indexed: 01/08/2023] Open
Abstract
Infectious diseases attack humans from time to time and threaten the lives and survival of people all around the world. An important strategy to prevent the spatial spread of infectious diseases is to restrict population travel. With the reduction of the epidemic situation, when and where travel restrictions can be lifted, and how to organize orderly movement patterns become critical and fall within the scope of this study. We define a novel diffusion distance derived from the estimated mobility network, based on which we provide a general model to describe the spatiotemporal spread of infectious diseases with a random diffusion process and a deterministic drift process of the population. We consequently develop a multi-source data fusion method to determine the population flow in epidemic areas. In this method, we first select available subregions in epidemic areas, and then provide solutions to initiate new travel flux among these subregions. To verify our model and method, we analyze the multi-source data from mainland China and obtain a new travel flux triggering scheme in the selected 29 cities with the most active population movements in mainland China. The testable predictions in these selected cities show that reopening the borders in accordance with our proposed travel flux will not cause a second outbreak of COVID-19 in these cities. The finding provides a methodology of re-triggering travel flux during the weakening spread stage of the epidemic. Human infectious diseases spread from their origins to other places with population movements. In order to curb the spatial spread of infectious diseases, many countries and regions may introduce some travel restrictions when the epidemic is severe, and reopen the borders as the epidemic eases. This process involves some important issues such as the start and end time of travel restrictions, the geographical scope of the implementation of the exit strategy, and the allowable passenger flow on traffic lines. Here, we integrate multi-source data with a mathematical model, and consequently develop a new method to determine the travel flux in epidemic areas. As an application, we use this method to calculate when and where the travel restrictions targeting COVID-19 in China in early 2020 could be lifted, and how to optimize passenger flow along the traffic lines among the reopened cities. The testable predictions indicate that the population flow in accordance with our proposed movement pattern will not cause a resurgent outbreak of COVID-19 in the cities studied.
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Bugalia S, Tripathi JP, Wang H. Mathematical modeling of intervention and low medical resource availability with delays: Applications to COVID-19 outbreaks in Spain and Italy. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:5865-5920. [PMID: 34517515 DOI: 10.3934/mbe.2021295] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Infectious diseases have been one of the major causes of human mortality, and mathematical models have been playing significant roles in understanding the spread mechanism and controlling contagious diseases. In this paper, we propose a delayed SEIR epidemic model with intervention strategies and recovery under the low availability of resources. Non-delayed and delayed models both possess two equilibria: the disease-free equilibrium and the endemic equilibrium. When the basic reproduction number $ R_0 = 1 $, the non-delayed system undergoes a transcritical bifurcation. For the delayed system, we incorporate two important time delays: $ \tau_1 $ represents the latent period of the intervention strategies, and $ \tau_2 $ represents the period for curing the infected individuals. Time delays change the system dynamics via Hopf-bifurcation and oscillations. The direction and stability of delay induced Hopf-bifurcation are established using normal form theory and center manifold theorem. Furthermore, we rigorously prove that local Hopf bifurcation implies global Hopf bifurcation. Stability switching curves and crossing directions are analyzed on the two delay parameter plane, which allows both delays varying simultaneously. Numerical results demonstrate that by increasing the intervention strength, the infection level decays; by increasing the limitation of treatment, the infection level increases. Our quantitative observations can be useful for exploring the relative importance of intervention and medical resources. As a timing application, we parameterize the model for COVID-19 in Spain and Italy. With strict intervention policies, the infection numbers would have been greatly reduced in the early phase of COVID-19 in Spain and Italy. We also show that reducing the time delays in intervention and recovery would have decreased the total number of cases in the early phase of COVID-19 in Spain and Italy. Our work highlights the necessity to consider the time delays in intervention and recovery in an epidemic model.
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Affiliation(s)
- Sarita Bugalia
- Department of Mathematics, Central University of Rajasthan, Bandar Sindri, Kishangarh-305817, Ajmer, Rajasthan, India
| | - Jai Prakash Tripathi
- Department of Mathematics, Central University of Rajasthan, Bandar Sindri, Kishangarh-305817, Ajmer, Rajasthan, India
| | - Hao Wang
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton AB T6G 2G1, Canada
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Bandekar SR, Ghosh M. Mathematical modeling of COVID-19 in India and its states with optimal control. MODELING EARTH SYSTEMS AND ENVIRONMENT 2021; 8:2019-2034. [PMID: 34127946 PMCID: PMC8189841 DOI: 10.1007/s40808-021-01202-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/23/2021] [Accepted: 05/24/2021] [Indexed: 12/23/2022]
Abstract
A pandemic is an epidemic spread over a huge geographical area. COVID-19 is \documentclass[12pt]{minimal}
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\begin{document}$$5\hbox {th}$$\end{document}5th such pandemic documented after 1918 flu pandemic. In this work, we frame a mathematical epidemic model taking inspiration from the classic SIR model and develop a compartmental model with ten compartments to study the coronavirus dynamics in India and three of its most affected states, namely, Maharashtra, Karnataka, and Tamil Nadu, with inclusion of factors related to face mask efficacy, contact tracing, and testing along with quarantine and isolation. We fit the developed model and estimate optimum values of disease transmission rate, detection rate of undetected asymptomatic, and the same of undetected symptomatic. A sensitivity analysis is presented stressing on the importance of higher face mask usage, rapid testing, and contact tracing for curbing the disease spread. An optimal control analysis is performed with two control parameters to study the increase and decrease of the infected population with and without control. This study suggests that improved and rapid testing will help in identifying more infectives, thereby contributing in the decline of disease transmission rate. Optimal control analysis results on stressing on the importance of abiding by strict usage of face mask and social distancing for drastic decrease in number of infections. Time series behaviour of the symptomatic, asymptomatic, and hospitalized population is studied for a range of parameters, resulting in thorough understanding of significance of different parameters.
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Affiliation(s)
- Shraddha Ramdas Bandekar
- Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India
| | - Mini Ghosh
- Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India
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Zhou Y, Li L, Ghasemi Y, Kallagudde R, Goyal K, Thakur D. An agent-based model for simulating COVID-19 transmissions on university campus and its implications on mitigation interventions: a case study. INFORMATION DISCOVERY AND DELIVERY 2021. [DOI: 10.1108/idd-12-2020-0154] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Purpose
Universities across the USA are facing challenging decision-making problems amid the COVID-19 pandemic. The purpose of this study is to facilitate universities in planning disease mitigation interventions as they respond to the pandemic.
Design/methodology/approach
An agent-based model is developed to mimic the virus transmission dynamics on campus. Scenario-based experiments are conducted to evaluate the effectiveness of various interventions including course modality shift (from face-to-face to online), social distancing, mask use and vaccination. A case study is performed for a typical US university.
Findings
With 10%, 30%, 50%, 70% and 90% course modality shift, the number of total cases can be reduced to 3.9%, 20.9%, 35.6%, 60.9% and 96.8%, respectively, comparing against the baseline scenario (no interventions). More than 99.9% of the total infections can be prevented when combined social distancing and mask use are implemented even without course modality shift. If vaccination is implemented without other interventions, the reductions are 57.1%, 90.6% and 99.6% with 80%, 85% and 90% vaccine efficacies, respectively. In contrast, more than 99% reductions are found with all three vaccine efficacies if mask use is combined.
Practical implications
This study provides useful implications for supporting universities in mitigating transmissions on campus and planning operations for the upcoming semesters.
Originality/value
An agent-based model is developed to investigate COVID-19 transmissions on campus and evaluate the effectiveness of various mitigation interventions.
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Han L, Pan Q, Kang B, He M. Effects of masks on the transmission of infectious diseases. ADVANCES IN DIFFERENCE EQUATIONS 2021; 2021:169. [PMID: 33758589 PMCID: PMC7971363 DOI: 10.1186/s13662-021-03321-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Accepted: 02/23/2021] [Indexed: 06/12/2023]
Abstract
In the present paper, based on the conditions that asymptomatic virus carriers are contagious and all symptomatic infected individuals wear masks, we study the impact of wearing masks in the susceptible and the asymptomatic virus carriers on the spread of infectious diseases by developing a differential equation model. At first, we give the existence, uniqueness, boundedness, and positivity of the solution as well as the basic reproduction number R 0 for the established model. Then, for two cases of wearing masks in the susceptible and the asymptomatic virus carriers where the proportion of wearing masks is fixed and the proportion of wearing masks changes with time, the results of the numerical simulation are shown in a series of pictures, and quantitative description of effects of the proportion of the population wearing masks, the protective effect of masks, and the time when they start wearing masks on the epidemic is given. Our results show that under the situation that the proportion of wearing masks is positively related to the confirmed new cases and new deaths, though the proportion will be close to 1 during the high incidence of patients, the effect on controlling the spread of such infectious diseases is far worse than the case of always maintaining a relatively higher proportion (≥0.66) of wearing masks.
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Affiliation(s)
- Lili Han
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
| | - Qiuhui Pan
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
- School of Innovation and Entrepreneurship, Dalian University of Technology, Dalian, China
| | - Baolin Kang
- College of Mathematics and Information Science, Anshan Normal University, Anshan, China
| | - Mingfeng He
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
- School of Innovation and Entrepreneurship, Dalian University of Technology, Dalian, China
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Iorfa SK, Ottu IFA, Oguntayo R, Ayandele O, Kolawole SO, Gandi JC, Dangiwa AL, Olapegba PO. COVID-19 Knowledge, Risk Perception, and Precautionary Behavior Among Nigerians: A Moderated Mediation Approach. Front Psychol 2020; 11:566773. [PMID: 33329202 PMCID: PMC7714760 DOI: 10.3389/fpsyg.2020.566773] [Citation(s) in RCA: 83] [Impact Index Per Article: 20.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2020] [Accepted: 11/02/2020] [Indexed: 12/20/2022] Open
Abstract
The novel coronavirus has not only brought along disruptions to daily socio-economic activities, but sickness and deaths due to its high contagion. With no widely acceptable pharmaceutical cure, the best form of prevention may be precautionary measures which will guide against infections and curb the spread of the disease. This study explored the relationship between COVID-19 knowledge, risk perception, and precautionary behavior among Nigerians. The study also sought to determine whether this relationship differed for men and women. A web-based cross-sectional design approach was used to recruit 1,554 participants (mean age = 27.43, SD = 9.75; 42.7% females) from all geopolitical zones in Nigeria, through social media platforms using a snowball sampling technique. Participants responded to web-based survey forms comprising demographic questions and adapted versions of the Ebola knowledge scale, SARS risk perception scale, and precautionary behavior scale. Moderated mediation analysis of the data showed that risk perception mediated the association between COVID-19 knowledge and precautionary behavior and this indirect effect was in turn moderated by gender. Results indicate that having adequate knowledge of COVID-19 was linked to higher involvement in precautionary behavior through risk perception for females but not for males. It was also noted that awareness campaigns and psychological intervention strategies on COVID-19 related activities may be particularly important for males more than females. Drawing from the health belief model, we recommend that COVID-19 awareness campaigns should target raising more awareness of the risks associated with the infection to make individuals engage more in precautionary behaviors.
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Affiliation(s)
- Steven K Iorfa
- Department of Psychology, University of Nigeria, Nsukka, Nigeria
| | - Iboro F A Ottu
- Department of Psychology, University of Uyo, Uyo, Nigeria
| | - Rotimi Oguntayo
- Department of Psychology, University of Ilorin, Ilorin, Nigeria
| | | | | | - Joshua C Gandi
- Department of Psychology, University of Jos, Jos, Nigeria
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13
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Global dynamics for a Filippov epidemic system with imperfect vaccination. NONLINEAR ANALYSIS: HYBRID SYSTEMS 2020; 38:100932. [PMCID: PMC7339777 DOI: 10.1016/j.nahs.2020.100932] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2018] [Revised: 11/20/2019] [Accepted: 06/02/2020] [Indexed: 06/14/2023]
Abstract
Given imperfect vaccination we extend the existing non-smooth models by considering susceptible and vaccinated individuals enhance the protection and control strategies once the number of infected individuals exceeds a certain level. On the basis of global dynamics of two subsystems, for the formulated Filippov system, we examine the sliding mode dynamics, the boundary equilibrium bifurcations, and the global dynamics. Our main results show that it is possible that the pseudo-equilibrium exists and is globally stable, or the pseudo-equilibrium, the disease-free equilibrium and the real equilibrium are tri-stable, or the pseudo-equilibrium and the real equilibrium are bi-stable, or the pseudo-equilibrium and disease-free equilibrium are bi-stable, which depend on the threshold value and other parameter values. The global stability of the disease-free equilibrium or pseudo-equilibrium reveals that we may eradicate the disease or maintain the number of infected individuals at a previously given value. Further, the bi-stability and tri-stability imply that whether the number of infected individuals tends to zero or a previously given value or other positive values depends on the parameter values and the initial states of the system. This emphasizes the importance of threshold policy and challenges in the control of infectious diseases if without perfect vaccines.
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14
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Sarkar K, Khajanchi S, Nieto JJ. Modeling and forecasting the COVID-19 pandemic in India. CHAOS, SOLITONS, AND FRACTALS 2020; 139:110049. [PMID: 32834603 PMCID: PMC7321056 DOI: 10.1016/j.chaos.2020.110049] [Citation(s) in RCA: 187] [Impact Index Per Article: 46.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2020] [Revised: 06/12/2020] [Accepted: 06/22/2020] [Indexed: 05/08/2023]
Abstract
In India, 100,340 confirmed cases and 3155 confirmed deaths due to COVID-19 were reported as of May 18, 2020. Due to absence of specific vaccine or therapy, non-pharmacological interventions including social distancing, contact tracing are essential to end the worldwide COVID-19. We propose a mathematical model that predicts the dynamics of COVID-19 in 17 provinces of India and the overall India. A complete scenario is given to demonstrate the estimated pandemic life cycle along with the real data or history to date, which in turn divulges the predicted inflection point and ending phase of SARS-CoV-2. The proposed model monitors the dynamics of six compartments, namely susceptible (S), asymptomatic (A), recovered (R), infected (I), isolated infected (Iq ) and quarantined susceptible (Sq ), collectively expressed SARIIqSq . A sensitivity analysis is conducted to determine the robustness of model predictions to parameter values and the sensitive parameters are estimated from the real data on the COVID-19 pandemic in India. Our results reveal that achieving a reduction in the contact rate between uninfected and infected individuals by quarantined the susceptible individuals, can effectively reduce the basic reproduction number. Our model simulations demonstrate that the elimination of ongoing SARS-CoV-2 pandemic is possible by combining the restrictive social distancing and contact tracing. Our predictions are based on real data with reasonable assumptions, whereas the accurate course of epidemic heavily depends on how and when quarantine, isolation and precautionary measures are enforced.
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Affiliation(s)
- Kankan Sarkar
- Department of Mathematics, Malda College, Malda, West Bengal 732101, India
| | - Subhas Khajanchi
- Department of Mathematics, Presidency University, 86/1 College Street, Kolkata 700073, India
| | - Juan J Nieto
- Instituto de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Spain
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15
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Mathematical Analysis of the Ross-Macdonald Model with Quarantine. Bull Math Biol 2020; 82:47. [PMID: 32242279 PMCID: PMC7117789 DOI: 10.1007/s11538-020-00723-0] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2019] [Accepted: 03/19/2020] [Indexed: 11/23/2022]
Abstract
People infected with malaria may receive less mosquito bites when they are treated in well-equipped hospitals or follow doctors’ advice for reducing exposure to mosquitoes at home. This quarantine-like intervention measure is especially feasible in countries and areas approaching malaria elimination. Motivated by mathematical models with quarantine for directly transmitted diseases, we develop a mosquito-borne disease model where imperfect quarantine is considered to mitigate the disease transmission from infected humans to susceptible mosquitoes. The basic reproduction number \documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {R}_0$$\end{document}R0 is computed and the model equilibria and their stabilities are analyzed when the incidence rate is standard or bilinear. In particular, the model system may undergo a subcritical (backward) bifurcation at \documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {R}_0=1$$\end{document}R0=1 when standard incidence is adopted, whereas the disease-free equilibrium is globally asymptotically stable as \documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {R}_0\le 1$$\end{document}R0≤1 and the unique endemic equilibrium is locally asymptotically stable as \documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {R}_0>1$$\end{document}R0>1 when the infection incidence is bilinear. Numerical simulations suggest that the quarantine strategy can play an important role in decreasing malaria transmission. The success of quarantine mainly relies on the reduction of bites on quarantined individuals.
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Lan G, Lin Z, Wei C, Zhang S. A stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching. JOURNAL OF THE FRANKLIN INSTITUTE 2019; 356:9844-9866. [PMID: 32287361 PMCID: PMC7127215 DOI: 10.1016/j.jfranklin.2019.09.009] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/27/2019] [Revised: 06/06/2019] [Accepted: 09/07/2019] [Indexed: 06/11/2023]
Abstract
In this paper, we propose and discuss a stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching. First of all, we show that there is a unique positive solution, which is a prerequisite for analyzing the long-term behavior of the stochastic model. Then, a threshold dynamic determined by the basic reproduction number R 0 s is established: the disease can be eradicated almost surely if R 0 s < 1 and under mild extra conditions, whereas if R 0 s > 1 , the densities of the distributions of the solution can converge in L 1 to an invariant density by using the Markov semigroups theory. Finally, based on realistic parameters obtained from previous literatures, numerical simulations have been performed to verify our analytical results.
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Affiliation(s)
- Guijie Lan
- School of Science, Jimei University, Xiamen, China
| | - Ziyan Lin
- School of Science, Jimei University, Xiamen, China
| | - Chunjin Wei
- School of Science, Jimei University, Xiamen, China
| | - Shuwen Zhang
- School of Science, Jimei University, Xiamen, China
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17
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Nikbakht R, Baneshi MR, Bahrampour A, Hosseinnataj A. Comparison of methods to Estimate Basic Reproduction Number ( R 0) of influenza, Using Canada 2009 and 2017-18 A (H1N1) Data. JOURNAL OF RESEARCH IN MEDICAL SCIENCES 2019; 24:67. [PMID: 31523253 PMCID: PMC6670001 DOI: 10.4103/jrms.jrms_888_18] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/18/2018] [Revised: 03/13/2019] [Accepted: 05/17/2019] [Indexed: 12/29/2022]
Abstract
Background The basic reproduction number (R 0) has a key role in epidemics and can be utilized for preventing epidemics. In this study, different methods are used for estimating R 0's and their vaccination coverage to find the formula with the best performance. Materials and Methods We estimated R 0 for cumulative cases count data from April 18 to July 6, 2009 and 35-2017 to 34-2018 weeks in Canada: maximum likelihood (ML), exponential growth rate (EG), time-dependent reproduction numbers (TD), attack rate (AR), gamma-distributed generation time (GT), and the final size of the epidemic. Gamma distribution with mean and standard deviation 3.6 ± 1.4 is used as GT. Results The AR method obtained a R 0 (95% confidence interval [CI]) value of 1.116 (1.1163, 1.1165) and an EG (95%CI) value of 1.46 (1.41, 1.52). The R 0 (95%CI) estimate was 1.42 (1.27, 1.57) for the obtained ML, 1.71 (1.12, 2.03) for the obtained TD, 1.49 (1.0, 1.97) for the gamma-distributed GT, and 1.00 (0.91, 1.09) for the final size of the epidemic. The minimum and maximum vaccination coverage were related to AR and TD methods, respectively, where the TD method has minimum mean squared error (MSE). Finally, the R 0 (95%CI) for 2018 data was 1.52 (1.11, 1.94) by TD method, and vaccination coverage was estimated as 34.2%. Conclusion For the purposes of our study, the estimation of TD was the most useful tool for computing the R 0, because it has the minimum MSE. The estimation R 0 > 1 indicating that the epidemic has occurred. Thus, it is required to vaccinate at least 41.5% to prevent and control the next epidemic.
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Affiliation(s)
- Roya Nikbakht
- HIV/STI Surveillance Research Center, and WHO Collaborating Center for HIV Surveillance, Institute for Futures Studies in Health, Kerman University of Medical Sciences, Department of Biostatistics and Epidemiology, Faculty of Health Kerman, Iran
| | - Mohammad Reza Baneshi
- Department of Biostatistics and Epidemiology, Faculty of Health, Modeling in Health Research Center, Institute for Futures Studies in Health, Kerman University of Medical Sciences, Kerman, Iran
| | - Abbas Bahrampour
- Department of Biostatistics and Epidemiology, Faculty of Health, Modeling in Health Research Center, Institute for Futures Studies in Health, Kerman University of Medical Sciences, Kerman, Iran
| | - Abolfazl Hosseinnataj
- Department of Biostatistics and Epidemiology, Faculty of Health, Modeling in Health Research Center, Institute for Futures Studies in Health, Kerman University of Medical Sciences, Kerman, Iran
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18
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Zhou W, Xiao Y, Heffernan JM. Optimal media reporting intensity on mitigating spread of an emerging infectious disease. PLoS One 2019; 14:e0213898. [PMID: 30897141 PMCID: PMC6428274 DOI: 10.1371/journal.pone.0213898] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2018] [Accepted: 03/04/2019] [Indexed: 11/18/2022] Open
Abstract
Mass media reports can induce individual behaviour change during a disease outbreak, which has been found to be useful as it reduces the force of infection. We propose a compartmental model by including a new compartment of the intensity of the media reports, which extends existing models by considering a novel media function, which is dependent both on the number of infected individuals and on the intensity of mass media. The existence and stability of the equilibria are analyzed and an optimal control problem of minimizing the total number of cases and total cost is considered, using reduction or enhancement in the media reporting rate as the control. With the help of Pontryagin's Maximum Principle, we obtain the optimal media reporting intensity. Through parameterization of the model with the 2009 A/H1N1 influenza outbreak data in the 8th Hospital of Xi'an in Shaanxi Province of China, we obtain the basic reproduction number for the formulated model with two particular media functions. The optimal media reporting intensity obtained here indicates that during the early stage of an epidemic we should quickly enhance media reporting intensity, and keep it at a maximum level until it can finally weaken when epidemic cases have decreased significantly. Numerical simulations show that media impact reduces the number of cases during an epidemic, but that the number of cases is further mitigated under the optimal reporting intensity. Sensitivity analysis implies that the outbreak severity is more sensitive to the weight α1 (weight of media effect sensitive to infected individuals) than weight α2 (weight of media effect sensitive to media items).
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Affiliation(s)
- Weike Zhou
- Department of Applied Mathematics, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, PR China
| | - Yanni Xiao
- Department of Applied Mathematics, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, PR China
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19
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Campeau L, Degroote S, Ridde V, Carabali M, Zinszer K. Containment measures for emerging and re-emerging vector-borne and other infectious diseases of poverty in urban settings: a scoping review. Infect Dis Poverty 2018; 7:95. [PMID: 30173673 PMCID: PMC6120079 DOI: 10.1186/s40249-018-0478-4] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2018] [Accepted: 08/06/2018] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND The emergence and re-emergence of vector-borne and other infectious diseases of poverty pose a threat to the health of populations living in urban and low-income settings. A detailed understanding of intervention strategies, including effectiveness of past outbreak containment, is necessary to improve future practices. The objective was to determine what is known about the effectiveness of containment measures for emerging and re-emerging vector-borne and other infectious diseases of poverty in urban settings and identify research gaps and implications for public health practice. MAIN BODY We conducted a scoping review and systematically searched peer-reviewed and grey literature published between 2000 and 2016. Different data extraction tools were used for data coding and extraction, and data on implementation process and transferability were extracted from all studies. A quality assessment was conducted for each included study. We screened 205 full-text articles and reports for a total of 31 articles included in the review. The quality of the studies was generally low to moderate. The largest body of evidence concerned control activities for Ebola virus and dengue fever. The majority of interventions (87%) relied on multiple types of measures, which were grouped into four categories: 1) healthcare provision; 2) epidemiological investigation and/or surveillance; 3) environmental or sanitary interventions; and 4) community-based interventions. The quality of the majority of studies (90%) was poor or moderate, and one-third of the studies did not provide a clear description of the outcomes and of the procedures and/or tools used for the intervention. CONCLUSIONS Our results highlight the difficulty of establishing causation when assessing the effect of containment measures. Studies that extend beyond solely reporting on effectiveness and take into account the complexity of real-world settings are urgently needed. We recommend the allocation of research efforts to the evaluation of the implementation processes of interventions as well as their comprehensive and systematic description using validated checklists.
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Affiliation(s)
- Laurence Campeau
- University of Montreal Public Health Research Institute (IRSPUM), Montreal, Quebec, Canada
| | - Stéphanie Degroote
- University of Montreal Public Health Research Institute (IRSPUM), Montreal, Quebec, Canada.
| | - Valery Ridde
- University of Montreal Public Health Research Institute (IRSPUM), Montreal, Quebec, Canada
- French Institute For Research on sustainable Development (IRD), IRD-Paris Descartes University (CEPED), Paris Sorbonne Cités University, Erl Inserm Sagesud, Paris, France
| | | | - Kate Zinszer
- University of Montreal Public Health Research Institute (IRSPUM), Montreal, Quebec, Canada
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20
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Kang Y, Wang W, Cai Y. Global stability of the steady states of an epidemic model incorporating intervention strategies. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2018; 14:1071-1089. [PMID: 29161851 DOI: 10.3934/mbe.2017056] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In this paper, we investigate the global stability of the steady states of a general reaction-diffusion epidemiological model with infection force under intervention strategies in a spatially heterogeneous environment. We prove that the reproductoin number R0 can be played an essential role in determining whether the disease will extinct or persist: if R0< 1, there is a unique disease-free equilibrium which is globally asymptotically stable; and if R0 >1, there exists a unique endemic equilibrium which is globally asymptotically stable. Furthermore, we study the relation between R0 with the diffusion and spatial heterogeneity and find that, it seems very necessary to create a low-risk habitat for the population to effectively control the spread of the epidemic disease. This may provide some potential applications in disease control.
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Affiliation(s)
- Yun Kang
- Science and Mathematics Faculty, School of Letters and Sciences, Arizona State University, Mesa, AZ 85212, United States
| | - Weiming Wang
- School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China
| | - Yongli Cai
- School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China
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21
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Tang S, Yan Q, Shi W, Wang X, Sun X, Yu P, Wu J, Xiao Y. Measuring the impact of air pollution on respiratory infection risk in China. ENVIRONMENTAL POLLUTION (BARKING, ESSEX : 1987) 2018; 232:477-486. [PMID: 28966029 DOI: 10.1016/j.envpol.2017.09.071] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2017] [Revised: 09/17/2017] [Accepted: 09/20/2017] [Indexed: 06/07/2023]
Abstract
China is now experiencing major public health challenges caused by air pollution. Few studies have quantified the dynamics of air pollution and its impact on the risk of respiratory infection. We conducted an integrated data analysis to quantify the association among air quality index (AQI), meteorological variables and respiratory infection risk in Shaanxi province of China in the period of November 15th, 2010 to November 14th, 2016. Our analysis illustrated a statistically significantly positive correlation between the number of influenza-like illness (ILI) cases and AQI, and the respiratory infection risk has increased progressively with increased AQI with a time lag of 0-3 days. We also developed mathematical models for the AQI trend and respiratory infection dynamics, incorporating AQI-dependent incidence and AQI-based behaviour change interventions. Our combined data and modelling analysis estimated the basic reproduction number for the respiratory infection during the studying period to be 2.4076, higher than the basic reproduction number of the 2009 pandemic influenza in the same province. Our modelling-based simulations concluded that, in terms of respiratory infection risk reduction, the persistent control of emission in the China's blue-sky programme is much more effective than substantial social-economic interventions implemented only during the smog days.
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Affiliation(s)
- Sanyi Tang
- School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, PR China
| | - Qinling Yan
- School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, PR China
| | - Wei Shi
- Shaanxi Center for Disease Control and Prevention, Xi'an, 710054, PR China
| | - Xia Wang
- School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, PR China
| | - Xiaodan Sun
- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, PR China
| | - Pengbo Yu
- Shaanxi Center for Disease Control and Prevention, Xi'an, 710054, PR China.
| | - Jianhong Wu
- Centre for Disease Modelling, York University, Toronto, Ontario M3J 1P3, Canada.
| | - Yanni Xiao
- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, PR China.
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22
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Yan QL, Tang SY, Xiao YN. Impact of individual behaviour change on the spread of emerging infectious diseases. Stat Med 2017; 37:948-969. [PMID: 29193194 DOI: 10.1002/sim.7548] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2017] [Revised: 09/06/2017] [Accepted: 10/06/2017] [Indexed: 11/11/2022]
Abstract
Human behaviour plays an important role in the spread of emerging infectious diseases, and understanding the influence of behaviour changes on epidemics can be key to improving control efforts. However, how the dynamics of individual behaviour changes affects the development of emerging infectious disease is a key public health issue. To develop different formula for individual behaviour change and introduce how to embed it into a dynamic model of infectious diseases, we choose A/H1N1 and Ebola as typical examples, combined with the epidemic reported cases and media related news reports. Thus, the logistic model with the health belief model is used to determine behaviour decisions through the health belief model constructs. Furthermore, we propose 4 candidate infectious disease models without and with individual behaviour change and use approximate Bayesian computation based on sequential Monte Carlo method for model selection. The main results indicate that the classical compartment model without behaviour change and the model with average rate of behaviour change depicted by an exponential function could fit the observed data best. The results provide a new way on how to choose an infectious disease model to predict the disease prevalence trend or to evaluate the influence of intervention measures on disease control. However, sensitivity analyses indicate that the accumulated number of hospital notifications and deaths could be largely reduced as the rate of behaviour change increases. Therefore, in terms of mitigating emerging infectious diseases, both media publicity focused on how to guide people's behaviour change and positive responses of individuals are critical.
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Affiliation(s)
- Q L Yan
- School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, P.R. China
| | - S Y Tang
- School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, P.R. China
| | - Y N Xiao
- Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, P.R. China
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23
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Li GH, Zhang YX. Dynamic behaviors of a modified SIR model in epidemic diseases using nonlinear incidence and recovery rates. PLoS One 2017; 12:e0175789. [PMID: 28426775 PMCID: PMC5398581 DOI: 10.1371/journal.pone.0175789] [Citation(s) in RCA: 45] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2017] [Accepted: 03/31/2017] [Indexed: 12/02/2022] Open
Abstract
The transmission of infectious diseases has been studied by mathematical methods since 1760s, among which SIR model shows its advantage in its epidemiological description of spread mechanisms. Here we established a modified SIR model with nonlinear incidence and recovery rates, to understand the influence by any government intervention and hospitalization condition variation in the spread of diseases. By analyzing the existence and stability of the equilibria, we found that the basic reproduction number [Formula: see text] is not a threshold parameter, and our model undergoes backward bifurcation when there is limited number of hospital beds. When the saturated coefficient a is set to zero, it is discovered that the model undergoes the Saddle-Node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation of codimension 2. The bifurcation diagram can further be drawn near the cusp type of the Bogdanov-Takens bifurcation of codimension 3 by numerical simulation. We also found a critical value of the hospital beds bc at [Formula: see text] and sufficiently small a, which suggests that the disease can be eliminated at the hospitals where the number of beds is larger than bc. The same dynamic behaviors exist even when a ≠ 0. Therefore, it can be concluded that a sufficient number of the beds is critical to control the epidemic.
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Affiliation(s)
- Gui-Hua Li
- Department of Mathematics, North University of China, Taiyuan, Shan'xi 030051, P. R. China
| | - Yong-Xin Zhang
- Department of Mathematics, North University of China, Taiyuan, Shan'xi 030051, P. R. China
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24
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Tang B, Xiao Y, Tang S, Wu J. Modelling weekly vector control against Dengue in the Guangdong Province of China. J Theor Biol 2016; 410:65-76. [PMID: 27650706 DOI: 10.1016/j.jtbi.2016.09.012] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2016] [Revised: 09/13/2016] [Accepted: 09/15/2016] [Indexed: 11/19/2022]
Abstract
We develop a mathematical model to closely mimic the integrated program of impulsive vector control (every Friday afternoon since the initiation of the program) and continuous patient treatment and isolation implemented in the Guangdong Province of China during its 2014 dengue outbreak. We fitted the data of accumulated infections and used the parameterized model to carry out a retrospective analysis to estimate the basic reproduction number 1.7425 (95% CI 1.4443-2.0408), the control reproduction number 0.1709, and the mosquito-killing ratios 0.1978, 0.2987, 0.6158 and 0.5571 on October 3, 10, 17 and 24, respectively. This suggests that integrated intervention is highly effective in controlling the dengue outbreak. We also simulated outbreak outcomes under different variations of the implemented interventions. We showed that skipping one Friday for vector control would not result in raising the control reproduction number to the threshold value 1 but would lead to significant increase in the accumulated infections at the end of the outbreak. The findings indicate that quick and persistent impulsive implementation of vector control result in an effective reduction in the control reproduction number and hence lead to significant decline of new infections.
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Affiliation(s)
- Biao Tang
- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, PR China; Centre for Disease Modelling, York Institute for Health Research, York University, Toronto, ON, Canada M3J 1P3
| | - Yanni Xiao
- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, PR China.
| | - Sanyi Tang
- College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, PR China
| | - Jianhong Wu
- Centre for Disease Modelling, York Institute for Health Research, York University, Toronto, ON, Canada M3J 1P3
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25
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Yan Q, Tang S, Gabriele S, Wu J. Media coverage and hospital notifications: Correlation analysis and optimal media impact duration to manage a pandemic. J Theor Biol 2015; 390:1-13. [PMID: 26582723 DOI: 10.1016/j.jtbi.2015.11.002] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2015] [Revised: 11/03/2015] [Accepted: 11/04/2015] [Indexed: 10/22/2022]
Abstract
News reporting has the potential to modify a community's knowledge of emerging infectious diseases and affect peoples' attitudes and behavior. Here we developed a quantitative approach to evaluate the effects of media on such behavior. Statistically significant correlations between the number of new hospital notifications, during the 2009 A/H1N1 influenza epidemic in the Shaanxi province of China, and the number of daily news items added to eight major websites were found from Pearson correlation and cross-correlation analyses. We also proposed a novel model to examine the implication for transmission dynamics of these correlations. The model incorporated the media impact function into the intensity of infection, and enhanced the traditional epidemic SEIR model with the addition of media dynamics. We used a nonlinear least squares estimation to identify the best-fit parameter values in the model from the observed data. We also carried out the uncertainty and sensitivity analyses to determine key parameters during early phase of the disease outbreak for the final outcome of the outbreak with media impact. The findings confirm the importance of responses by individuals to the media reports, with behavior changes having important consequence for the emerging infectious disease control. Therefore, for mitigating emerging infectious diseases, media reports should be focused on how to guide people's behavioral changes, which are critical for limiting the spread of disease.
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Affiliation(s)
- Qinling Yan
- College of Mathematics and Information Science, Shaanxi Normal University, Xi׳an 710062, PR China
| | - Sanyi Tang
- College of Mathematics and Information Science, Shaanxi Normal University, Xi׳an 710062, PR China.
| | - Sandra Gabriele
- Department of Design, School of the Arts, Media, Performance & Design, York University, Toronto, Ontario, Canada M3J 1P3
| | - Jianhong Wu
- Centre for Disease Modelling, York University, Toronto, Ontario, Canada M3J 1P3
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Model Selection and Evaluation Based on Emerging Infectious Disease Data Sets including A/H1N1 and Ebola. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2015; 2015:207105. [PMID: 26451161 PMCID: PMC4586906 DOI: 10.1155/2015/207105] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/26/2015] [Revised: 08/19/2015] [Accepted: 08/27/2015] [Indexed: 11/25/2022]
Abstract
The aim of the present study is to apply simple ODE models in the area of modeling the spread of emerging infectious diseases and show the importance of model selection in estimating parameters, the basic reproduction number, turning point, and final size. To quantify the plausibility of each model, given the data and the set of four models including Logistic, Gompertz, Rosenzweg, and Richards models, the Bayes factors are calculated and the precise estimates of the best fitted model parameters and key epidemic characteristics have been obtained. In particular, for Ebola the basic reproduction numbers are 1.3522 (95% CI (1.3506, 1.3537)), 1.2101 (95% CI (1.2084, 1.2119)), 3.0234 (95% CI (2.6063, 3.4881)), and 1.9018 (95% CI (1.8565, 1.9478)), the turning points are November 7,November 17, October 2, and November 3, 2014, and the final sizes until December 2015 are 25794 (95% CI (25630, 25958)), 3916 (95% CI (3865, 3967)), 9886 (95% CI (9740, 10031)), and 12633 (95% CI (12515, 12750)) for West Africa, Guinea, Liberia, and Sierra Leone, respectively. The main results confirm that model selection is crucial in evaluating and predicting the important quantities describing the emerging infectious diseases, and arbitrarily picking a model without any consideration of alternatives is problematic.
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Wang X, Liu S, Wang L, Zhang W. An Epidemic Patchy Model with Entry-Exit Screening. Bull Math Biol 2015; 77:1237-55. [PMID: 25976693 PMCID: PMC7088875 DOI: 10.1007/s11538-015-0084-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2014] [Accepted: 04/30/2015] [Indexed: 10/25/2022]
Abstract
A multi-patch SEIQR epidemic model is formulated to investigate the long-term impact of entry-exit screening measures on the spread and control of infectious diseases. A threshold dynamics determined by the basic reproduction number R₀ is established: The disease can be eradicated if R₀ < 1, while the disease persists if R₀ > 1. As an application, six different screening strategies are explored to examine the impacts of screening on the control of the 2009 influenza A (H1N1) pandemic. We find that it is crucial to screen travelers from and to high-risk patches, and it is not necessary to implement screening in all connected patches, and both the dispersal rates and the successful detection rate of screening play an important role on determining an effective and practical screening strategy.
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Affiliation(s)
- Xinxin Wang
- Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, 3041#, 2 Yi-Kuang Street, Nan-Gang District, Harbin, 150080, China
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Xiao Y, Tang S, Wu J. Media impact switching surface during an infectious disease outbreak. Sci Rep 2015; 5:7838. [PMID: 25592757 PMCID: PMC4296304 DOI: 10.1038/srep07838] [Citation(s) in RCA: 79] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2014] [Accepted: 12/15/2014] [Indexed: 11/18/2022] Open
Abstract
There are many challenges to quantifying and evaluating the media impact on the control of emerging infectious diseases. We modeled such media impacts using a piecewise smooth function depending on both the case number and its rate of change. The proposed model was then converted into a switching system, with the switching surface determined by a functional relationship between susceptible populations and different subgroups of infectives. By parameterizing the proposed model with the 2009 A/H1N1 influenza outbreak data in the Shaanxi province of China, we observed that media impact switched off almost as the epidemic peaked. Our analysis implies that media coverage significantly delayed the epidemic's peak and decreased the severity of the outbreak. Moreover, media impacts are not always effective in lowering the disease transmission during the entire outbreak, but switch on and off in a highly nonlinear fashion with the greatest effect during the early stage of the outbreak. The finding draws the attention to the important role of informing the public about 'the rate of change of case numbers' rather than 'the absolute number of cases' to alter behavioral changes, through a self-adaptive media impact switching on and off, for better control of disease transmission.
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Affiliation(s)
- Yanni Xiao
- Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, P. R. China
| | - Sanyi Tang
- School of Mathematics and Information Science Shaanxi Normal University, Xi'an, 710062, P. R. China
| | - Jianhong Wu
- Centre for Disease Modelling, York Institute for Health Research, York University, Toronto, ON, M3J 1P3, Canada
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Biggerstaff M, Cauchemez S, Reed C, Gambhir M, Finelli L. Estimates of the reproduction number for seasonal, pandemic, and zoonotic influenza: a systematic review of the literature. BMC Infect Dis 2014; 14:480. [PMID: 25186370 PMCID: PMC4169819 DOI: 10.1186/1471-2334-14-480] [Citation(s) in RCA: 311] [Impact Index Per Article: 31.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2014] [Accepted: 08/28/2014] [Indexed: 12/19/2022] Open
Abstract
BACKGROUND The potential impact of an influenza pandemic can be assessed by calculating a set of transmissibility parameters, the most important being the reproduction number (R), which is defined as the average number of secondary cases generated per typical infectious case. METHODS We conducted a systematic review to summarize published estimates of R for pandemic or seasonal influenza and for novel influenza viruses (e.g. H5N1). We retained and summarized papers that estimated R for pandemic or seasonal influenza or for human infections with novel influenza viruses. RESULTS The search yielded 567 papers. Ninety-one papers were retained, and an additional twenty papers were identified from the references of the retained papers. Twenty-four studies reported 51 R values for the 1918 pandemic. The median R value for 1918 was 1.80 (interquartile range [IQR]: 1.47-2.27). Six studies reported seven 1957 pandemic R values. The median R value for 1957 was 1.65 (IQR: 1.53-1.70). Four studies reported seven 1968 pandemic R values. The median R value for 1968 was 1.80 (IQR: 1.56-1.85). Fifty-seven studies reported 78 2009 pandemic R values. The median R value for 2009 was 1.46 (IQR: 1.30-1.70) and was similar across the two waves of illness: 1.46 for the first wave and 1.48 for the second wave. Twenty-four studies reported 47 seasonal epidemic R values. The median R value for seasonal influenza was 1.28 (IQR: 1.19-1.37). Four studies reported six novel influenza R values. Four out of six R values were <1. CONCLUSIONS These R values represent the difference between epidemics that are controllable and cause moderate illness and those causing a significant number of illnesses and requiring intensive mitigation strategies to control. Continued monitoring of R during seasonal and novel influenza outbreaks is needed to document its variation before the next pandemic.
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Affiliation(s)
- Matthew Biggerstaff
- />Epidemiology and Prevention Branch, Influenza Division, National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, 1600 Clifton Road NE, MS A-32, Atlanta, 30333 Georgia
| | - Simon Cauchemez
- />Mathematical Modelling of Infectious Diseases Unit, Institut Pasteur, Paris, France
| | - Carrie Reed
- />Epidemiology and Prevention Branch, Influenza Division, National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, 1600 Clifton Road NE, MS A-32, Atlanta, 30333 Georgia
| | - Manoj Gambhir
- />National Center for Immunization and Respiratory Diseases, CDC, Atlanta, Georgia
| | - Lyn Finelli
- />Epidemiology and Prevention Branch, Influenza Division, National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, 1600 Clifton Road NE, MS A-32, Atlanta, 30333 Georgia
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30
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Transmission characteristics of different students during a school outbreak of (H1N1) pdm09 influenza in China, 2009. Sci Rep 2014; 4:5982. [PMID: 25102240 PMCID: PMC4124738 DOI: 10.1038/srep05982] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2014] [Accepted: 07/17/2014] [Indexed: 11/25/2022] Open
Abstract
Many outbreaks of A(H1N1)pdm09 influenza have occurred in schools with a high population density. Containment of school outbreaks is predicted to help mitigate pandemic influenza. Understanding disease transmission characteristics within the school setting is critical to implementing effective control measures. Based on a school outbreak survey, we found almost all (93.7%) disease transmission occurred within a single grade, only 6.3% crossed grades. Transmissions originating from freshmen exhibited a star-shaped network; other grades exhibited branch- or line-shaped networks, indicating freshmen have higher activity and are more likely to cause infection. R0 for freshmen, calculated as 2.04, estimated as 2.76, was greater than for other grades (P < 0.01). Without intervention, the estimated number of cases was much greater when the outbreak was initiated by freshmen than by other grades. Furthermore, the estimated number of cases required to be under quarantine and isolation for freshmen was less than that of equivalent other grades. So we concluded that different grades have different transmission mode. Freshmen were the main facilitators of the spread of A(H1N1)pdm09 influenza during this school outbreak, so control measures (e.g. close contact isolation) priority used for freshmen would likely have effectively reduced spread of influenza in school settings.
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31
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Li X, Geng W, Tian H, Lai D. Was mandatory quarantine necessary in China for controlling the 2009 H1N1 pandemic? INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2013; 10:4690-700. [PMID: 24084677 PMCID: PMC3823329 DOI: 10.3390/ijerph10104690] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/10/2013] [Revised: 09/17/2013] [Accepted: 09/20/2013] [Indexed: 11/16/2022]
Abstract
The Chinese government enforced mandatory quarantine for 60 days (from 10 May to 8 July 2009) as a preventative strategy to control the spread of the 2009 H1N1 pandemic. Such a prevention strategy was stricter than other non-pharmaceutical interventions that were carried out in many other countries. We evaluated the effectiveness of the mandatory quarantine and provide suggestions for interventions against possible future influenza pandemics. We selected one city, Beijing, as the analysis target. We reviewed the epidemiologic dynamics of the 2009 H1N1 pandemic and the implementation of quarantine measures in Beijing. The infectious population was simulated under two scenarios (quarantined and not quarantined) using a deterministic Susceptible-Exposed-Infectious-Recovered (SEIR) model. The basic reproduction number R0 was adjusted to match the epidemic wave in Beijing. We found that mandatory quarantine served to postpone the spread of the 2009 H1N1 pandemic in Beijing by one and a half months. If mandatory quarantine was not enforced in Beijing, the infectious population could have reached 1,553 by 21 October, i.e., 5.6 times higher than the observed number. When the cost of quarantine is taken into account, mandatory quarantine was not an economically effective intervention approach against the 2009 H1N1 pandemic. We suggest adopting mitigation methods for an influenza pandemic with low mortality and morbidity.
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Affiliation(s)
- Xinhai Li
- Key Laboratory of the Zoological Systematics and Evolution, Institute of Zoology, Chinese Academy of Sciences, 1-5 Beichen West Road, Chaoyang District, Beijing 100101, China; E-Mail:
| | - Wenjun Geng
- Chia Tai Tianqing Pharmaceutical Group Co., Ltd., 9 Huiou Road, Nanjing Economic Development Zone, Nanjing 210038, China; E-Mail:
| | - Huidong Tian
- Key Laboratory of the Zoological Systematics and Evolution, Institute of Zoology, Chinese Academy of Sciences, 1-5 Beichen West Road, Chaoyang District, Beijing 100101, China; E-Mail:
| | - Dejian Lai
- School of Public Health, University of Texas, 1200 Herman Pressler Street, Suite 1006 Houston, TX 77030, USA; E-Mail:
- Faculty of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China
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32
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Chowell G, Nishiura H, Viboud C. Modeling rapidly disseminating infectious disease during mass gatherings. BMC Med 2012; 10:159. [PMID: 23217051 PMCID: PMC3532170 DOI: 10.1186/1741-7015-10-159] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/04/2012] [Accepted: 12/07/2012] [Indexed: 11/25/2022] Open
Abstract
We discuss models for rapidly disseminating infectious diseases during mass gatherings (MGs), using influenza as a case study. Recent innovations in modeling and forecasting influenza transmission dynamics at local, regional, and global scales have made influenza a particularly attractive model scenario for MG. We discuss the behavioral, medical, and population factors for modeling MG disease transmission, review existing model formulations, and highlight key data and modeling gaps related to modeling MG disease transmission. We argue that the proposed improvements will help integrate infectious-disease models in MG health contingency plans in the near future, echoing modeling efforts that have helped shape influenza pandemic preparedness plans in recent years.
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Affiliation(s)
- Gerardo Chowell
- School of Human Evolution and Social Change, Arizona State University, 900 S. Cady Mall, Tempe, AZ 85287-2402, USA.
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33
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Xiao Y, Xu X, Tang S. Sliding mode control of outbreaks of emerging infectious diseases. Bull Math Biol 2012; 74:2403-22. [PMID: 22836868 DOI: 10.1007/s11538-012-9758-5] [Citation(s) in RCA: 79] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2011] [Accepted: 07/12/2012] [Indexed: 01/19/2023]
Abstract
This paper proposes and analyzes a mathematical model of an infectious disease system with a piecewise control function concerning threshold policy for disease management strategy. The proposed models extend the classic models by including a piecewise incidence rate to represent control or precautionary measures being triggered once the number of infected individuals exceeds a threshold level. The long-term behaviour of the proposed non-smooth system under this strategy consists of the so-called sliding motion-a very rapid switching between application and interruption of the control action. Model solutions ultimately approach either one of two endemic states for two structures or the sliding equilibrium on the switching surface, depending on the threshold level. Our findings suggest that proper combinations of threshold densities and control intensities based on threshold policy can either preclude outbreaks or lead the number of infected to a previously chosen level.
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Affiliation(s)
- Yanni Xiao
- Department of Applied Mathematics, Xi'an Jiaotong University, PR China
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