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Yang L, Fan M, Wang Y, Sun X, Zhu H. Effect of avian influenza scare on transmission of zoonotic avian influenza: A case study of influenza A (H7N9). Math Biosci 2024; 367:109125. [PMID: 38072124 DOI: 10.1016/j.mbs.2023.109125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Revised: 11/15/2023] [Accepted: 12/06/2023] [Indexed: 01/09/2024]
Abstract
Avian influenza scare is a human psychological factor that asserts both positive and negative effects on the transmission of zoonotic avian influenza. In order to study the dichotomous effect of avian influenza scare on disease transmission, taking H7N9 avian influenza as a typical case, a two-patch epidemic model is proposed. The global dynamics and the threshold criteria are established by LaSalle invariant principle and the theory of asymptotic autonomous system. To mitigate the negative effects and curb illegal poultry trade, a game-theoretic model is adopted to explore the optimal policy of culling subsidies to reasonably compensate stakeholders for their economic losses resulting from the scare. The optimal policy of culling subsidy is found to heavily depend on the penalty of illegal poultry trade, the stakeholders' income, the intensity of control measures, and the prevalence level of the disease. The negative effect of avian influenza scare on disease transmission is considerably more significant than the positive effect. In order to avoid a widespread outbreak of zoonotic avian influenza across the region, a comprehensive national global control strategy is essential and effective, even in the presence of the negative effect of the avian influenza scare.
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Affiliation(s)
- Liu Yang
- School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, PR China; China Animal Health and Epidemiology Center, Qingdao, Shandong, 266032, PR China
| | - Meng Fan
- School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, PR China.
| | - Youming Wang
- China Animal Health and Epidemiology Center, Qingdao, Shandong, 266032, PR China
| | - Xiangdong Sun
- China Animal Health and Epidemiology Center, Qingdao, Shandong, 266032, PR China
| | - Huaiping Zhu
- LAMPS, Department of Mathematics and Statistics, York university, 4700 Keele Street, Toronto, ON M3J 1P3, Canada
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2
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Yang L, Song D, Fan M, Gao L. Transmission dynamics and optimal control of H7N9 in China. INT J BIOMATH 2021. [DOI: 10.1142/s1793524522500073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
H7N9 avian influenza is a highly pathogenic zoonotic disease. In order to control the disease, many strategies have been adopted in China such as poultry culling, the closure of live poultry markets (LPMs), the vaccination of poultry, and the treatment for humans. Due to the limited resource, it is of paramount significance to achieve the optimal control. In this paper, an epidemic model incorporating the selective culling rate is formulated to investigate the transmission mechanism of H7N9. The threshold dynamics and bifurcation analyses of the model are well investigated. Furthermore, the problem of optimal control is explored in line with Pontryagin’s Maximum Principle, with consideration given to the comprehensive measures. The numerical simulations suggest that the vaccination of poultry and the closure of LPMs are the two most economical and effective measures.
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Affiliation(s)
- Liu Yang
- School of Mathematics and Statistics, Northeast Normal University 5268 Renmin Street, Changchun, Jilin 130024, P. R. China
| | - Da Song
- School of Mathematics Science, Fudan University, 220 Handan Road, Shanghai 200433, P. R. China
| | - Meng Fan
- School of Mathematics and Statistics, Northeast Normal University 5268 Renmin Street, Changchun, Jilin 130024, P. R. China
| | - Lu Gao
- China Animal Health and Epidemiology Center, Qingdao 266032, P. R. China
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3
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Son H, Denu D. Vector-host epidemic model with direct transmission in random environment. CHAOS (WOODBURY, N.Y.) 2021; 31:113117. [PMID: 34881607 DOI: 10.1063/5.0059031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2021] [Accepted: 10/25/2021] [Indexed: 06/13/2023]
Abstract
This paper studies a stochastic vector-host epidemic model with direct transmission in random environment, governed by a system of stochastic differential equations with regime-switching diffusion. We first examine the existence and uniqueness of a positive global solution. Then, we investigate stability properties of the solution, including almost sure and pth moment exponential stability and stochastic asymptotic stability. Moreover, we study conditions for the existence and uniqueness of a stationary distribution. Numerical simulations are presented to illustrate the theoretical results.
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Affiliation(s)
- Hyunjin Son
- Mathematics, Division of Science, Southern Wesleyan University, 907 Wesleyan Drive, Central, South Carolina 29630, USA
| | - Dawit Denu
- Department of Mathematics, Georgia Southern University, 11935 Abercorn Street, Savannah, Georgia 31419, USA
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4
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Shi Z, Zhang X. Modeling a stochastic avian influenza model under regime switching and with human-to-human transmission. INT J BIOMATH 2020. [DOI: 10.1142/s1793524520500643] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, we investigate the stochastic avian influenza model with human-to-human transmission, which is disturbed by both white and telegraph noises. First, we show that the solution of the stochastic system is positive and global. Furthermore, by using stochastic Lyapunov functions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution. Then we obtain the conditions for extinction. Finally, numerical simulations are employed to demonstrate the analytical results.
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Affiliation(s)
- Zhenfeng Shi
- College of Science, China University of Petroleum (East China), Qingdao 266580, P. R. China
| | - Xinhong Zhang
- College of Science, China University of Petroleum (East China), Qingdao 266580, P. R. China
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Royce K, Fu F. Mathematically modeling spillovers of an emerging infectious zoonosis with an intermediate host. PLoS One 2020; 15:e0237780. [PMID: 32845922 PMCID: PMC7449412 DOI: 10.1371/journal.pone.0237780] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2019] [Accepted: 08/03/2020] [Indexed: 01/01/2023] Open
Abstract
Modeling the behavior of zoonotic pandemic threats is a key component of their control. Many emerging zoonoses, such as SARS, Nipah, and Hendra, mutated from their wild type while circulating in an intermediate host population, usually a domestic species, to become more transmissible among humans, and this transmission route will only become more likely as agriculture and trade intensifies around the world. Passage through an intermediate host enables many otherwise rare diseases to become better adapted to humans, and so understanding this process with accurate mathematical models is necessary to prevent epidemics of emerging zoonoses, guide policy interventions in public health, and predict the behavior of an epidemic. In this paper, we account for a zoonotic disease mutating in an intermediate host by introducing a new mathematical model for disease transmission among three species. We present a model of these disease dynamics, including the equilibria of the system and the basic reproductive number of the pathogen, finding that in the presence of biologically realistic interspecies transmission parameters, a zoonotic disease with the capacity to mutate in an intermediate host population can establish itself in humans even if its R0 in humans is less than 1. This result and model can be used to predict the behavior of any zoonosis with an intermediate host and assist efforts to protect public health.
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Affiliation(s)
- Katherine Royce
- Dartmouth College Mathematics Department, Hanover, NH, United States of America
- * E-mail:
| | - Feng Fu
- Dartmouth College Mathematics Department, Hanover, NH, United States of America
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Chen C, Wang P, Zhang L. A two-thresholds policy for a Filippov model in combating influenza. J Math Biol 2020; 81:435-461. [PMID: 32588119 DOI: 10.1007/s00285-020-01514-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2020] [Revised: 06/13/2020] [Indexed: 11/29/2022]
Abstract
This work designs a two-thresholds policy for a Filippov model in combating influenza, so as to estimate when and whether to take control strategies, including the media coverage, antiviral treatment of infected individuals and vaccination of susceptible population. By introducing two tolerance thresholds [Formula: see text] and [Formula: see text] of susceptible and infected individuals, the two-thresholds policy is designed as: a vaccination program is implemented when the number of susceptible individuals is above [Formula: see text]; an antiviral treatment strategy is taken and the mass media begins to report information about influenza when the infection number is larger than [Formula: see text]; no control strategies are required in other cases. Furthermore, the global dynamics of the model are analyzed by varying these two thresholds, including the existence and dynamics of sliding mode, and the existence and global stability of equilibrium. It is shown that the model solutions ultimately converge to a pseudoequilibrium or a pseudoattractor on the switching surface, or a real equilibrium. The obtained results indicate that, by choosing susceptible and infected thresholds properly, the infection number can be remained below or at an acceptable level.
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Affiliation(s)
- Can Chen
- School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou, 450046, China.
| | - Pengde Wang
- College of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, 450046, China
| | - Litao Zhang
- School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou, 450046, China
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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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8
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Wang WH, Erazo EM, Ishcol MRC, Lin CY, Assavalapsakul W, Thitithanyanont A, Wang SF. Virus-induced pathogenesis, vaccine development, and diagnosis of novel H7N9 avian influenza A virus in humans: a systemic literature review. J Int Med Res 2019; 48:300060519845488. [PMID: 31068040 PMCID: PMC7140199 DOI: 10.1177/0300060519845488] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
H7N9 avian influenza virus (AIV) caused human infections in 2013 in China.
Phylogenetic analyses indicate that H7N9 AIV is a novel reassortant strain with
pandemic potential. We conducted a systemic review regarding virus-induced
pathogenesis, vaccine development, and diagnosis of H7N9 AIV infection in
humans. We followed PRISMA guidelines and searched PubMed, Web of Science, and
Google Scholar to identify relevant articles published between January 2013 and
December 2018. Pathogenesis data indicated that H7N9 AIV belongs to low
pathogenic avian influenza, which is mostly asymptomatic in avian species;
however, H7N9 induces high mortality in humans. Sporadic human infections have
recently been reported, caused by highly pathogenic avian influenza viruses
detected in poultry. H7N9 AIVs resistant to adamantine and oseltamivir cause
severe human infection by rapidly inducing progressive acute community-acquired
pneumonia, multiorgan dysfunction, and cytokine dysregulation; however,
mechanisms via which the virus induces severe syndromes remain unclear. An H7N9
AIV vaccine is lacking; designs under evaluation include synthesized peptide,
baculovirus-insect system, and virus-like particle vaccines. Molecular diagnosis
of H7N9 AIVs is suggested over conventional assays, for biosafety reasons.
Several advanced or modified diagnostic assays are under investigation and
development. We summarized virus-induced pathogenesis, vaccine development, and
current diagnostic assays in H7N9 AIVs.
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Affiliation(s)
- Wen-Hung Wang
- Division of Infectious Disease, Department of Internal Medicine, Kaohsiung Medical University Hospital, Kaohsiung Medical University, Kaohsiung.,Center for Infectious Disease and Cancer Research, Kaohsiung Medical University, Kaohsiung
| | - Esmeralda Merari Erazo
- Department of Medical Laboratory Science and Biotechnology, Kaohsiung Medical University, Kaohsiung
| | - Max R Chang Ishcol
- Program in Tropical Medicine, College of Medicine, Kaohsiung Medical University, Kaohsiung
| | - Chih-Yen Lin
- Center for Infectious Disease and Cancer Research, Kaohsiung Medical University, Kaohsiung.,Department of Medical Laboratory Science and Biotechnology, Kaohsiung Medical University, Kaohsiung
| | - Wanchai Assavalapsakul
- Department of Microbiology, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
| | | | - Sheng-Fan Wang
- Center for Infectious Disease and Cancer Research, Kaohsiung Medical University, Kaohsiung.,Department of Medical Laboratory Science and Biotechnology, Kaohsiung Medical University, Kaohsiung.,Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung
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9
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Yan Q, Tang S, Jin Z, Xiao Y. Identifying Risk Factors Of A(H7N9) Outbreak by Wavelet Analysis and Generalized Estimating Equation. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2019; 16:ijerph16081311. [PMID: 31013684 PMCID: PMC6518036 DOI: 10.3390/ijerph16081311] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/09/2019] [Revised: 03/29/2019] [Accepted: 04/07/2019] [Indexed: 11/16/2022]
Abstract
Five epidemic waves of A(H7N9) occurred between March 2013 and May 2017 in China. However, the potential risk factors associated with disease transmission remain unclear. To address the spatial–temporal distribution of the reported A(H7N9) human cases (hereafter referred to as “cases”), statistical description and geographic information systems were employed. Based on long-term observation data, we found that males predominated the majority of A(H7N9)-infected individuals and that most males were middle-aged or elderly. Further, wavelet analysis was used to detect the variation in time-frequency between A(H7N9) cases and meteorological factors. Moreover, we formulated a Poisson regression model to explore the relationship among A(H7N9) cases and meteorological factors, the number of live poultry markets (LPMs), population density and media coverage. The main results revealed that the impact factors of A(H7N9) prevalence are manifold, and the number of LPMs has a significantly positive effect on reported A(H7N9) cases, while the effect of weekly average temperature is significantly negative. This confirms that the interaction of multiple factors could result in a serious A(H7N9) outbreak. Therefore, public health departments adopting the corresponding management measures based on both the number of LPMs and the forecast of meteorological conditions are crucial for mitigating A(H7N9) prevalence.
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Affiliation(s)
- Qinling Yan
- School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, China.
| | - Sanyi Tang
- School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, China.
| | - Zhen Jin
- Complex System Research center, Shanxi University, Taiyuan 030006, China.
| | - Yanni Xiao
- Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China.
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10
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Global Dynamics of an Avian Influenza A(H7N9) Epidemic Model with Latent Period and Nonlinear Recovery Rate. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2018; 2018:7321694. [PMID: 29681998 PMCID: PMC5842725 DOI: 10.1155/2018/7321694] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/18/2017] [Accepted: 01/22/2018] [Indexed: 11/17/2022]
Abstract
An SEIR type of compartmental model with nonlinear incidence and recovery rates was formulated to study the combined impacts of psychological effect and available resources of public health system especially the number of hospital beds on the transmission and control of A(H7N9) virus. Global stability of the disease-free and endemic equilibria is determined by the basic reproduction number as a threshold parameter and is obtained by constructing Lyapunov function and second additive compound matrix. The results obtained reveal that psychological effect and available resources do not change the stability of the steady states but can indeed diminish the peak and the final sizes of the infected. Our studies have practical implications for the transmission and control of A(H7N9) virus.
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11
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Contact reductions from live poultry market closures limit the epidemic of human infections with H7N9 influenza. J Infect 2018; 76:295-304. [PMID: 29406153 DOI: 10.1016/j.jinf.2017.12.015] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2017] [Revised: 10/27/2017] [Accepted: 12/08/2017] [Indexed: 11/20/2022]
Abstract
An early steep increase in the number of humans infected with avian influenza A(H7N9) virus was observed in China, raising great public concern domestically and internationally. Little is known about the dynamics of the transmission contacts between poultry and human populations, although such understanding is essential for developing effective strategies to control this zoonosis. In this study, we evaluated the effects of contact reductions from live poultry markets (LPMs) closures on the transmission of H7N9 virus during epidemics in Guangdong Province, China. A mathematical model of the poultry-to-person transmission dynamics of H7N9 virus was constructed. The parameters in the model were estimated from publicly available data on confirmed cases of human infection and information on LPMs closure during 2013-2017. By fitting the model, we measured the time-dependent contact quantity of the susceptible population to LPMs. The results showed that periodic intervention strategies can greatly reduce the magnitude of outbreaks, and the earlier interventions for policy are implemented, the smaller is the outbreak. The control efforts for LPMs to decrease the contact quantity are critical in preventing epidemics in the long term. This model should provide important insights for the development of a national intervention strategy for the long-term control of avian influenza virus epidemics.
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ZHANG XINAN, ZOU LAN, CHEN JING, FANG YILE, HUANG JICAI, ZHANG JINHUI, LIU SANHONG, FENG GUANGTING, YANG CUIHONG, RUAN SHIGUI. AVIAN INFLUENZA A H7N9 VIRUS HAS BEEN ESTABLISHED IN CHINA. J BIOL SYST 2017. [DOI: 10.1142/s0218339017400095] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In March 2013, a novel avian-origin influenza A H7N9 virus was identified among human patients in China and a total of 124 human cases with 24 related deaths were confirmed by May 2013. From November 2013 to July 2017, H7N9 broke out four more times in China. A deterministic model is proposed to study the transmission dynamics of the avian influenza A H7N9 virus between wild and domestic birds and from birds to humans, and is applied to simulate the open data on numbers of the infected human cases and related deaths reported from March to May 2013 and from November 2013 to June 2014 by the Chinese Center for Disease Control and Prevention. The basic reproduction number [Formula: see text] is estimated and sensitivity analysis of [Formula: see text] in terms of model parameters is performed. Taking into account the fact that it broke out again from November 2014 to June 2015, from November 2015 to July 2016, and from October 2016 to July 2017, we believe that H7N9 virus has been well established in birds and will likely cause regular outbreaks in humans again in the future. Control measures for the future spread of H7N9 include (i) reducing the transmission opportunities between wild birds and domestic birds, (ii) closing or monitoring the retail live-poultry markets in the infected areas, and (iii) culling the infected domestic birds in the epidemic regions.
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Affiliation(s)
- XINAN ZHANG
- School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China
| | - LAN ZOU
- Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China
| | - JING CHEN
- Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA
| | - YILE FANG
- Department of Electrical and Electronic Education, Huazhong University of Science and Technology, Wuchang Branch, Wuhan 430064, P. R. China
| | - JICAI HUANG
- School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China
| | - JINHUI ZHANG
- Department of Applied Mathematics, Zhongyuan University of Technology, Zhengzhou 451191, P. R. China
| | - SANHONG LIU
- School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, P. R. China
| | - GUANGTING FENG
- School of Mathematics and Quantitative Economics, Hubei University of Education, Wuhan 432025, P. R. China
| | - CUIHONG YANG
- School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China
| | - SHIGUI RUAN
- School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China
- Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA
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13
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A Filippov model describing the effects of media coverage and quarantine on the spread of human influenza. Math Biosci 2017; 296:98-112. [PMID: 29273381 DOI: 10.1016/j.mbs.2017.12.002] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2017] [Revised: 12/02/2017] [Accepted: 12/08/2017] [Indexed: 12/11/2022]
Abstract
Mass-media reports on an epidemic or pandemic have the potential to modify human behaviour and affect social attitudes. Here we construct a Filippov model to evaluate the effects of media coverage and quarantine on the transmission dynamics of influenza. We first choose a piecewise smooth incidence rate to represent media reports being triggered once the number of infected individuals exceeds a certain critical level [Formula: see text] . Further, if the number of infected cases increases and exceeds another larger threshold value [Formula: see text] ( [Formula: see text] ), we consider that the incidence rate tends to a saturation level due to the protection measures taken by individuals; meanwhile, we begin to quarantine susceptible individuals when the number of susceptible individuals is larger than a threshold value Sc. Then, for each susceptible threshold value Sc, the global properties of the Filippov model with regard to the existence and stability of all possible equilibria and sliding-mode dynamics are examined, as we vary the infected threshold values [Formula: see text] and [Formula: see text] . We show generically that the Filippov system stabilizes at either the endemic equilibrium of the subsystem or the pseudoequilibrium on the switching surface or the endemic equilibrium [Formula: see text] depending on the choice of the threshold values. The findings suggest that proper combinations of infected and susceptible threshold values can maintain the number of infected individuals either below a certain threshold level or at a previously given level.
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GUO SHUMIN, WANG JUAN, GHOSH MINI, LI XUEZHI. ANALYSIS OF AVIAN INFLUENZA A (H7N9) MODEL BASED ON THE LOW PATHOGENICITY IN POULTRY. J BIOL SYST 2017. [DOI: 10.1142/s0218339017500140] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The avian influenza A (H7N9) virus is one subtype of influenza viruses, which has previously been isolated only in birds. Recently, an outbreak of a new avian influenza (H7N9) in China has resulted in numerous infections and high mortality in the humans. The H7N9 virus is low pathogenic in poultry and high pathogenic in human and that is critically different from other avian influenza viruses. An increasing number of the new H7N9 cases and the high mortality have caused a serious global concern. Here, based on the reported data, we propose and analyze an SE-SEIS avian–human influenza model. We prove the global stability results for both the disease-free equilibrium point and the endemic equilibrium point by using a general Bendixson–Dulac theorem. Our reported theoretical results of this paper are expected to help in exploring the development of efficient methods to controlling the spread of avian influenza A(H7N9).
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Affiliation(s)
- SHU-MIN GUO
- Department of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, P. R. China
| | - JUAN WANG
- Department of Mathematics, Xinyang Normal University, Xinyang 464000, P. R. China
| | - MINI GHOSH
- School of Advanced Sciences, VIT University, Chennai Campus, Chennai 600127, India
| | - XUE-ZHI LI
- College of Mathematics and Physics, Anyang Institute of Technology, Anyang 455000, P. R. China
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15
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Lin Q, Lin Z, Chiu APY, He D. Seasonality of Influenza A(H7N9) Virus in China-Fitting Simple Epidemic Models to Human Cases. PLoS One 2016; 11:e0151333. [PMID: 26963937 PMCID: PMC4786326 DOI: 10.1371/journal.pone.0151333] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2015] [Accepted: 02/26/2016] [Indexed: 11/18/2022] Open
Abstract
Background Three epidemic waves of influenza A(H7N9) (hereafter ‘H7N9’) human cases have occurred between March 2013 and July 2015 in China. However, the underlying transmission mechanism remains unclear. Our main objective is to use mathematical models to study how seasonality, secular changes and environmental transmission play a role in the spread of H7N9 in China. Methods Data on human cases and chicken cases of H7N9 infection were downloaded from the EMPRES-i Global Animal Disease Information System. We modelled on chicken-to-chicken transmission, assuming a constant ratio of 10−6 human case per chicken case, and compared the model fit with the observed human cases. We developed three different modified Susceptible-Exposed-Infectious-Recovered-Susceptible models: (i) a non-periodic transmission rate model with an environmental class, (ii) a non-periodic transmission rate model without an environmental class, and (iii) a periodic transmission rate model with an environmental class. We then estimated the key epidemiological parameters and compared the model fit using Akaike Information Criterion and Bayesian Information Criterion. Results Our results showed that a non-periodic transmission rate model with an environmental class provided the best model fit to the observed human cases in China during the study period. The estimated parameter values were within biologically plausible ranges. Conclusions This study highlighted the importance of considering secular changes and environmental transmission in the modelling of human H7N9 cases. Secular changes were most likely due to control measures such as Live Poultry Markets closures that were implemented during the initial phase of the outbreaks in China. Our results suggested that environmental transmission via viral shedding of infected chickens had contributed to the spread of H7N9 human cases in China.
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Affiliation(s)
- Qianying Lin
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong (SAR) China
| | - Zhigui Lin
- School of Mathematical Science, Yangzhou University, Yangzhou, 225002, People Republic of China
| | - Alice P. Y. Chiu
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong (SAR) China
- * E-mail:
| | - Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong (SAR) China
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Interpreting the transmissibility of the avian influenza A(H7N9) infection from 2013 to 2015 in Zhejiang Province, China. Epidemiol Infect 2015; 144:1584-91. [PMID: 26645357 PMCID: PMC4855998 DOI: 10.1017/s0950268815002812] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Three epidemic waves of human influenza A(H7N9) were documented in several different provinces in China between 2013 and 2015. With limited understanding of the potential for human-to-human transmission, it was difficult to implement control measures efficiently or to inform the public adequately about the application of interventions. In this study, the human-to-human transmission rate for the epidemics that occurred between 2013 and 2015 in Zhejiang Province, China, was analysed. The reproduction number (R), a key indicator of transmission intensity, was estimated by fitting the number of infections from poultry to humans and from humans to humans into a mathematical model. The posterior mean R for human-to-human transmission was estimated to be 0·27, with a 95% credible interval of 0·14–0·44 for the first wave, whereas the posterior mean Rs decreased to 0·15 in the second and third waves. Overall, these estimates indicate that a human H7N9 pandemic is unlikely to occur in Zhejiang. The reductions in the viral transmissibility and the number of poultry-transmitted infections after the first epidemic may be attributable to the various intervention measures taken, including changes in the extent of closures of live poultry markets.
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Liu Z, Fang CT. A modeling study of human infections with avian influenza A H7N9 virus in mainland China. Int J Infect Dis 2015; 41:73-8. [PMID: 26585941 DOI: 10.1016/j.ijid.2015.11.003] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2015] [Revised: 11/02/2015] [Accepted: 11/06/2015] [Indexed: 11/24/2022] Open
Abstract
OBJECTIVES Since February 2013, more than 400 laboratory-confirmed human cases of avian influenza A H7N9 infection have been reported in mainland China. Little is known of the dynamics of this novel virus in poultry and human populations, which is essential for developing effective long-term control strategies for this zoonosis. The aim of this study was to evaluate the impact of screening and culling of infected poultry on the evolution of the H7N9 epidemic. METHODS A mathematical model for transmission dynamics of avian influenza A H7N9 virus in human and poultry populations was constructed. Parameters in the model were estimated using publicly available nationwide surveillance data on animal and human infections. RESULTS By fitting a two-host model, it was shown that screening for H7N9 in poultry and culling could effectively decrease the number of new human H7N9 cases. Furthermore, the elimination of circulating H7N9 virus is possible if an intensive, but technically feasible, poultry screening and culling policy is adopted. CONCLUSIONS Screening and culling infected poultry is a critical measure for preventing human H7N9 infections in the long term. This model may provide important insights for decision-making on a national intervention strategy for the long-term control of the H7N9 virus epidemic.
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Affiliation(s)
- Zhifei Liu
- School of Public Health, Lanzhou University, Lanzhou, mainland China
| | - Chi-Tai Fang
- Institute of Epidemiology and Preventive Medicine, College of Public Health, National Taiwan University, 17 Xu-Zhou Road, Taipei 100, Taiwan; Division of Infectious Diseases, Department of Internal Medicine, National Taiwan University Hospital, Taipei, Taiwan.
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Abstract
In March 2013 the first cases of human avian influenza A(H7N9) were reported to the World Health Organization. Since that time, over 650 cases have been reported. Infections are associated with considerable morbidity and mortality, particularly within certain demographic groups. This rapid increase in cases over a brief time period is alarming and has raised concerns about the pandemic potential of the H7N9 virus. Three major factors influence the pandemic potential of an influenza virus: (1) its ability to cause human disease, (2) the immunity of the population to the virus, and (3) the transmission potential of the virus. This paper reviews what is currently known about each of these factors with respect to avian influenza A(H7N9). Currently, sustained human-to-human transmission of H7N9 has not been reported; however, population immunity to the virus is considered very low, and the virus has significant ability to cause human disease. Several statistical and geographical modelling studies have estimated and predicted the spread of the H7N9 virus in humans and avian species, and some have identified potential risk factors associated with disease transmission. Additionally, assessment tools have been developed to evaluate the pandemic potential of H7N9 and other influenza viruses. These tools could also hypothetically be used to monitor changes in the pandemic potential of a particular virus over time.
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Global dynamics of avian influenza epidemic models with psychological effect. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2015; 2015:913726. [PMID: 25861378 PMCID: PMC4377454 DOI: 10.1155/2015/913726] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/17/2014] [Revised: 02/09/2015] [Accepted: 02/12/2015] [Indexed: 01/14/2023]
Abstract
Cross-sectional surveys conducted in Thailand and China after the outbreaks of the avian influenza A H5N1 and H7N9 viruses show a high degree of awareness of human avian influenza in both urban and rural populations, a higher level of proper hygienic practice among urban residents, and in particular a dramatically reduced number of visits to live markets in urban population after the influenza A H7N9 outbreak in China in 2013. In this paper, taking into account the psychological effect toward avian influenza in the human population, a bird-to-human transmission model in which the avian population exhibits saturation effect is constructed. The dynamical behavior of the model is studied by using the basic reproduction number. The results demonstrate that the saturation effect within avian population and the psychological effect in human population cannot change the stability of equilibria but can affect the number of infected humans if the disease is prevalent. Numerical simulations are given to support the theoretical results and sensitivity analyses of the basic reproduction number in terms of model parameters that are performed to seek for effective control measures for avian influenza.
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Hsieh YH, Wu J, Fang J, Yang Y, Lou J. Quantification of bird-to-bird and bird-to-human infections during 2013 novel H7N9 avian influenza outbreak in China. PLoS One 2014; 9:e111834. [PMID: 25479054 PMCID: PMC4257544 DOI: 10.1371/journal.pone.0111834] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2014] [Accepted: 09/30/2014] [Indexed: 11/18/2022] Open
Abstract
From February to May, 2013, 132 human avian influenza H7N9 cases were identified in China resulting in 37 deaths. We developed a novel, simple and effective compartmental modeling framework for transmissions among (wild and domestic) birds as well as from birds to human, to infer important epidemiological quantifiers, such as basic reproduction number for bird epidemic, bird-to-human infection rate and turning points of the epidemics, for the epidemic via human H7N9 case onset data and to acquire useful information regarding the bird-to-human transmission dynamics. Estimated basic reproduction number for infections among birds is 4.10 and the mean daily number of human infections per infected bird is 3.16*10-5 [3.08*10-5, 3.23*10-5]. The turning point of 2013 H7N9 epidemic is pinpointed at April 16 for bird infections and at April 9 for bird-to-human transmissions. Our result reveals very low level of bird-to-human infections, thus indicating minimal risk of widespread bird-to-human infections of H7N9 virus during the outbreak. Moreover, the turning point of the human epidemic, pinpointed at shortly after the implementation of full-scale control and intervention measures initiated in early April, further highlights the impact of timely actions on ending the outbreak. This is the first study where both the bird and human components of an avian influenza epidemic can be quantified using only the human case data.
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Affiliation(s)
- Ying-Hen Hsieh
- Department of Public Health, China Medical University, Taichung, Taiwan
- Center for Infectious Disease Education and Research, China Medical University, Taichung, Taiwan
| | - Jianhong Wu
- Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada
- Centre for Disease Modelling, York University, Toronto, Ontario, Canada
| | - Jian Fang
- Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada
- Centre for Disease Modelling, York University, Toronto, Ontario, Canada
- Department of Mathematics, Harbin Institute of Technology, Harbin, China
| | - Yong Yang
- Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada
| | - Jie Lou
- Department of Mathematics, Shanghai University, Shanghai, China
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Determination of original infection source of H7N9 avian influenza by dynamical model. Sci Rep 2014; 4:4846. [PMID: 24786135 PMCID: PMC5381286 DOI: 10.1038/srep04846] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2014] [Accepted: 04/11/2014] [Indexed: 01/03/2023] Open
Abstract
H7N9, a newly emerging virus in China, travels among poultry and human. Although H7N9 has not aroused massive outbreaks, recurrence in the second half of 2013 makes it essential to control the spread. It is believed that the most effective control measure is to locate the original infection source and cut off the source of infection from human. However, the original infection source and the internal transmission mechanism of the new virus are not totally clear. In order to determine the original infection source of H7N9, we establish a dynamical model with migratory bird, resident bird, domestic poultry and human population, and view migratory bird, resident bird, domestic poultry as original infection source respectively to fit the true dynamics during the 2013 pandemic. By comparing the date fitting results and corresponding Akaike Information Criterion (AIC) values, we conclude that migrant birds are most likely the original infection source. In addition, we obtain the basic reproduction number in poultry and carry out sensitivity analysis of some parameters.
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