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Abbas N, Zanib SA, Ramzan S, Nazir A, Shatanawi W. A conformable mathematical model of Ebola Virus Disease and its stability analysis. Heliyon 2024; 10:e35818. [PMID: 39247366 PMCID: PMC11379567 DOI: 10.1016/j.heliyon.2024.e35818] [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: 07/18/2023] [Revised: 07/25/2024] [Accepted: 08/05/2024] [Indexed: 09/10/2024] Open
Abstract
Ebola Virus Disease (EVD) is a viral hemorrhagic fever that affects humans and other primates. It is characterized by rapid virus spread in a short period of time. The disease has the potential to spread to many different regions of the world. In this paper, we have developed a modified mathematical model of the Ebola virus, adding the quarantine population as a control strategy. The quarantine population F and parametersρ 3 represent the rate at which individuals enter the quarantine compartment, which is vital in controlling the virus spread within society. The conformable derivatives have been applied to the modified model to observe the behavior of individuals for fractional derivative values between 0.7 and 1. For a modified model, the threshold parameter (R 0 ) has been determined using the Next-Generation Matrix (NGM) method. We have checked local and global stability at a disease-free equilibrium point using Routh-Herwitz (RH) criteria and Castillo-Chavez, respectively. Numerical results obtained through the Fourth-Order Runge Kutta Method (RK4) demonstrate, a decrease in the virus transmission rate after following the implementation of the quarantine strategy.
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Affiliation(s)
- Nadeem Abbas
- Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
| | - Syeda Alishwa Zanib
- Department of Mathematics, Riphah International University, Main Satyana Road, Faisalabad 44000, Pakistan
| | - Sehrish Ramzan
- Department of Mathematics, Government College University Faisalabad, Faisalabad 44000, Pakistan
| | - Aqsa Nazir
- Department of Engineering and Computer Science, National University of Modern Languages, Islamabad 44000, Pakistan
| | - Wasfi Shatanawi
- Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan
- Department of Mathematics, Faculty of Science, The Hashemite University, P.O Box 330127, Zarqa 13133, Jordan
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2
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Ithinji DG, Buchholz DW, Ezzatpour S, Monreal IA, Cong Y, Sahler J, Bangar AS, Imbiakha B, Upadhye V, Liang J, Ma A, Bradel-Tretheway B, Kaza B, Yeo YY, Choi EJ, Johnston GP, Huzella L, Kollins E, Dixit S, Yu S, Postnikova E, Ortega V, August A, Holbrook MR, Aguilar HC. Multivalent viral particles elicit safe and efficient immunoprotection against Nipah Hendra and Ebola viruses. NPJ Vaccines 2022; 7:166. [PMID: 36528644 PMCID: PMC9759047 DOI: 10.1038/s41541-022-00588-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2021] [Accepted: 12/05/2022] [Indexed: 12/23/2022] Open
Abstract
Experimental vaccines for the deadly zoonotic Nipah (NiV), Hendra (HeV), and Ebola (EBOV) viruses have focused on targeting individual viruses, although their geographical and bat reservoir host overlaps warrant creation of multivalent vaccines. Here we explored whether replication-incompetent pseudotyped vesicular stomatitis virus (VSV) virions or NiV-based virus-like particles (VLPs) were suitable multivalent vaccine platforms by co-incorporating multiple surface glycoproteins from NiV, HeV, and EBOV onto these virions. We then enhanced the vaccines' thermotolerance using carbohydrates to enhance applicability in global regions that lack cold-chain infrastructure. Excitingly, in a Syrian hamster model of disease, the VSV multivalent vaccine elicited safe, strong, and protective neutralizing antibody responses against challenge with NiV, HeV, or EBOV. Our study provides proof-of-principle evidence that replication-incompetent multivalent viral particle vaccines are sufficient to provide protection against multiple zoonotic deadly viruses with high pandemic potential.
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Affiliation(s)
- Duncan G Ithinji
- School for Global Animal Health, Washington State University, Pullman, WA, USA.,Kenya Agricultural and Livestock Research Organization, Nairobi, Kenya
| | - David W Buchholz
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY, USA
| | - Shahrzad Ezzatpour
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY, USA
| | - I Abrrey Monreal
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY, USA
| | - Yu Cong
- National Institute of Allergy and Infectious Diseases (NIAID) Integrated Research Facility, Ft Detrick, Frederick, MD, 21702, USA
| | - Julie Sahler
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY, USA
| | | | - Brian Imbiakha
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY, USA
| | - Viraj Upadhye
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY, USA
| | - Janie Liang
- National Institute of Allergy and Infectious Diseases (NIAID) Integrated Research Facility, Ft Detrick, Frederick, MD, 21702, USA
| | - Andrew Ma
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY, USA
| | | | - Benjamin Kaza
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY, USA
| | - Yao Yu Yeo
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY, USA
| | - Eun Jin Choi
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY, USA
| | - Gunner P Johnston
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY, USA
| | - Louis Huzella
- National Institute of Allergy and Infectious Diseases (NIAID) Integrated Research Facility, Ft Detrick, Frederick, MD, 21702, USA
| | - Erin Kollins
- National Institute of Allergy and Infectious Diseases (NIAID) Integrated Research Facility, Ft Detrick, Frederick, MD, 21702, USA
| | - Saurabh Dixit
- National Institute of Allergy and Infectious Diseases (NIAID) Integrated Research Facility, Ft Detrick, Frederick, MD, 21702, USA
| | - Shuiqing Yu
- National Institute of Allergy and Infectious Diseases (NIAID) Integrated Research Facility, Ft Detrick, Frederick, MD, 21702, USA
| | - Elena Postnikova
- National Institute of Allergy and Infectious Diseases (NIAID) Integrated Research Facility, Ft Detrick, Frederick, MD, 21702, USA
| | - Victoria Ortega
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY, USA
| | - Avery August
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY, USA
| | - Michael R Holbrook
- National Institute of Allergy and Infectious Diseases (NIAID) Integrated Research Facility, Ft Detrick, Frederick, MD, 21702, USA
| | - Hector C Aguilar
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY, USA.
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3
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Chebil D, Ben Hassine D, Melki S, Nouira S, Kammoun Rebai W, Hannachi H, Merzougui L, Ben Abdelaziz A. Place of distancing measures in containing epidemics: a scoping review. Libyan J Med 2022; 17:2140473. [PMID: 36325628 PMCID: PMC9639554 DOI: 10.1080/19932820.2022.2140473] [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: 07/18/2022] [Accepted: 10/22/2022] [Indexed: 11/06/2022] Open
Abstract
Distancing is one of the barrier measures in mitigating epidemics. We aimed to investigate the typology, effectiveness, and side effects of distancing rules during epidemics. Electronic searches were conducted on MEDLINE, PubMed in April 2020, using Mesh-Terms representing various forms of distancing ('social isolation', 'social distancing', 'quarantine') combining with 'epidemics'. PRISMA-ScR statement was consulted to report this review. A total of 314 titles were identified and 93 were finally included. 2009 influenza A and SARS-CoV-2 epidemics were the most studied. Distancing measures were mostly classified as case-based and community-based interventions. The combination of distancing rules, like school closure, home working, isolation and quarantine, has proven to be effective in reducing R0 and flattening the epidemic curve, also when initiated early at a high rate and combined with other non-pharmaceutical interventions. Epidemiological and modeling studies showed that Isolation and quarantine in the 2009 Influenza pandemic were effective measures to decrease attack rate also with high level of compliance but there was an increased risk of household transmission. lockdown was also effective to reduce R0 from 2.6 to 0.6 and to increase doubling time from 2 to 4 days in the covid-19 pandemic. The evidence for school closure and workplace distancing was moderate as single intervention. Psychological disorder, unhealthy behaviors, disruption of economic activities, social discrimination, and stigmatization were the main side effects of distancing measures. Earlier implementation of combined distancing measures leads to greater effectiveness in containing outbreaks. Their indication must be relevant and based on evidence to avoid adverse effects on the community. These results would help decision-makers to develop response plans based on the required experience and strengthen the capacity of countries to fight against future epidemics. Mesh words: Physical Distancing, Quarantine, Epidemics, Public Health, Scoping Review.
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Affiliation(s)
- Dhekra Chebil
- Infection Prevention Control Department, Ibn Al Jazzar University Hospital, Kairouan, Tunisia
- Research Laboratory, LR19SP01, Sousse, Tunisia
- Faculty of medicine of Sousse, University of Sousse, Sousse, Tunisia
| | - Donia Ben Hassine
- Research Laboratory, LR19SP01, Sousse, Tunisia
- Information System Direction (DSI), Sahloul University Hospital, Sousse, Tunisia
| | - Sarra Melki
- Research Laboratory, LR19SP01, Sousse, Tunisia
- Information System Direction (DSI), Sahloul University Hospital, Sousse, Tunisia
| | - Sarra Nouira
- Research Laboratory, LR19SP01, Sousse, Tunisia
- Information System Direction (DSI), Sahloul University Hospital, Sousse, Tunisia
| | - Wafa Kammoun Rebai
- Regional Training Center supported by WHO-TDR for East Mediterranean Region (EMR), Pasteur Institute of Tunis, Tunisia
| | - Hajer Hannachi
- Infection Prevention Control Department, Ibn Al Jazzar University Hospital, Kairouan, Tunisia
- Faculty of medicine of Sousse, University of Sousse, Sousse, Tunisia
| | - Latifa Merzougui
- Infection Prevention Control Department, Ibn Al Jazzar University Hospital, Kairouan, Tunisia
- Faculty of medicine of Sousse, University of Sousse, Sousse, Tunisia
| | - Ahmed Ben Abdelaziz
- Research Laboratory, LR19SP01, Sousse, Tunisia
- Faculty of medicine of Sousse, University of Sousse, Sousse, Tunisia
- Information System Direction (DSI), Sahloul University Hospital, Sousse, Tunisia
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Butt AIK, Imran M, Chamaleen D, Batool S. Optimal control strategies for the reliable and competitive mathematical analysis of Covid-19 pandemic model. MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2022; 46:MMA8593. [PMID: 36247229 PMCID: PMC9538878 DOI: 10.1002/mma.8593] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/31/2021] [Accepted: 07/11/2022] [Indexed: 06/16/2023]
Abstract
To understand dynamics of the COVID-19 disease realistically, a new SEIAPHR model has been proposed in this article where the infectious individuals have been categorized as symptomatic, asymptomatic, and super-spreaders. The model has been investigated for existence of a unique solution. To measure the contagiousness of COVID-19, reproduction numberR 0 is also computed using next generation matrix method. It is shown that the model is locally stable at disease-free equilibrium point whenR 0 < 1 and unstable forR 0 > 1 . The model has been analyzed for global stability at both of the disease-free and endemic equilibrium points. Sensitivity analysis is also included to examine the effect of parameters of the model on reproduction numberR 0 . A couple of optimal control problems have been designed to study the effect of control strategies for disease control and eradication from the society. Numerical results show that the adopted control approaches are much effective in reducing new infections.
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Affiliation(s)
- Azhar Iqbal Kashif Butt
- Department of MathematicsGovernment College UniversityLahorePakistan
- Department of Mathematics and Statistics, College of ScienceKing Faisal UniversityAl‐AhsaSaudi Arabia
| | - Muhammad Imran
- Department of MathematicsGovernment College UniversityLahorePakistan
| | - D.B.D. Chamaleen
- Department of MathematicsOpen University of Sri LankaNugegodaSri Lanka
| | - Saira Batool
- Department of MathematicsGovernment College UniversityLahorePakistan
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5
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Zhang M, Wang X, Hu L, Zhang Y, Zheng H, Wu H, Wang J, Luo L, Xiao H, Qiao C, Li X, Huang W, Wang Y, Feng J, Chen G. TIM-1 Augments Cellular Entry of Ebola Virus Species and Mutants, Which Is Blocked by Recombinant TIM-1 Protein. Microbiol Spectr 2022; 10:e0221221. [PMID: 35384693 PMCID: PMC9241846 DOI: 10.1128/spectrum.02212-21] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Accepted: 03/07/2022] [Indexed: 01/12/2023] Open
Abstract
Ebola virus, a member of the Filoviridae family, utilizes the attachment factors on host cells to support its entry and cause severe tissue damage. TIM-1 has been identified as a predominant attachment factor via interaction with phosphatidylserine (PS) localized on the viral envelope and glycoprotein (GP). In this study, we give the first demonstration that TIM-1 enhances the cellular entry of three species of Ebola virus, as well as those harboring GP mutations (A82V, T544I, and A82V T544I). Furthermore, two TIM-1 variants (i.e., TIM-1-359aa and TIM-1-364aa) had comparable effects on promoting Zaire Ebola virus (EBOV) attachment, internalization, and infection. Importantly, recombinant TIM-1 ectodomain (ECD) protein could decrease the infectivity of Ebola virus and display synergistic inhibitory effects with ADI-15946, a monoclonal antibody with broad neutralizing activity to Ebola virus. Of note, EBOV strains harboring GP mutations (K510E and D552N), which were refractory to antibody treatment, were still sensitive to TIM-1 protein-mediated impairment of infectivity, indicating that TIM-1 protein may represent an alternative therapeutic regimen when antibody evasion occurs. IMPORTANCE The viral genome has acquired numerous mutations with the potential to increase transmission during the 2013-to-2016 outbreak of Ebola virus. EBOV strains harboring GP mutations (A82V, T544I, and A82V T544I), which have been identified to increase viral infectivity in humans, have attracted our attention. Herein, we give the first report that polymorphic TIM-1 enhances the infectivity of three species of Ebola virus, as well as those harboring GP mutations (A82V, T544I, and A82V T544I). We show that recombinant TIM-1 ECD protein could decrease the infectivity of Ebola virus with or without a point mutation and displays synergistic inhibitory effects with ADI-15946. Furthermore, TIM-1 protein potently blocked cell entry of antibody-evading Ebola virus species. These findings highlight the role of TIM-1 in Ebola virus infection and indicate that TIM-1 protein represents a potential therapeutic avenue for Ebola virus and its mutated species.
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Affiliation(s)
- Min Zhang
- State Key Laboratory of Toxicology and Medical Countermeasures, Institute of Pharmacology and Toxicology, Beijing, China
| | - Xinwei Wang
- Inner Mongolia Key Lab of Molecular Biology, School of Basic Medical Sciences, Inner Mongolia Medical University, Hohhot, China
| | - Linhan Hu
- Inner Mongolia Key Lab of Molecular Biology, School of Basic Medical Sciences, Inner Mongolia Medical University, Hohhot, China
| | - Yuting Zhang
- Inner Mongolia Key Lab of Molecular Biology, School of Basic Medical Sciences, Inner Mongolia Medical University, Hohhot, China
| | - Hang Zheng
- Inner Mongolia Key Lab of Molecular Biology, School of Basic Medical Sciences, Inner Mongolia Medical University, Hohhot, China
| | - Haiyan Wu
- State Key Laboratory of Toxicology and Medical Countermeasures, Institute of Pharmacology and Toxicology, Beijing, China
| | - Jing Wang
- State Key Laboratory of Toxicology and Medical Countermeasures, Institute of Pharmacology and Toxicology, Beijing, China
| | - Longlong Luo
- State Key Laboratory of Toxicology and Medical Countermeasures, Institute of Pharmacology and Toxicology, Beijing, China
| | - He Xiao
- State Key Laboratory of Toxicology and Medical Countermeasures, Institute of Pharmacology and Toxicology, Beijing, China
| | - Chunxia Qiao
- State Key Laboratory of Toxicology and Medical Countermeasures, Institute of Pharmacology and Toxicology, Beijing, China
| | - Xinying Li
- State Key Laboratory of Toxicology and Medical Countermeasures, Institute of Pharmacology and Toxicology, Beijing, China
| | - Weijin Huang
- Division of HIV/AIDS and Sex-transmitted Virus Vaccines, National Institutes for Food and Drug Control, Beijing, China
| | - Youchun Wang
- Division of HIV/AIDS and Sex-transmitted Virus Vaccines, National Institutes for Food and Drug Control, Beijing, China
| | - Jiannan Feng
- State Key Laboratory of Toxicology and Medical Countermeasures, Institute of Pharmacology and Toxicology, Beijing, China
| | - Guojiang Chen
- State Key Laboratory of Toxicology and Medical Countermeasures, Institute of Pharmacology and Toxicology, Beijing, China
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6
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OUEMBA TASSÉ AJ, TSANOU B, LUBUMA J, WOUKENG JEANLOUIS, SIGNING FRANCIS. EBOLA VIRUS DISEASE DYNAMICS WITH SOME PREVENTIVE MEASURES: A CASE STUDY OF THE 2018–2020 KIVU OUTBREAK. J BIOL SYST 2022. [DOI: 10.1142/s0218339022500048] [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
To fight against Ebola virus disease, several measures have been adopted. Among them, isolation, safe burial and vaccination occupy a prominent place. In this paper, we present a model which takes into account these three control strategies as well as the indirect transmission through a polluted environment. The asymptotic behavior of our model is achieved. Namely, we determine a threshold value [Formula: see text] of the control reproduction number [Formula: see text], below which the disease is eliminated in the long run. Whenever the value of [Formula: see text] ranges from [Formula: see text] and 1, we prove the existence of a backward bifurcation phenomenon, which corresponds to the case, where a locally asymptotically stable positive equilibrium co-exists with the disease-free equilibrium, which is also locally asymptotically stable. The existence of this bifurcation complicates the control of Ebola, since the requirement of [Formula: see text] below one, although necessary, is no longer sufficient for the elimination of Ebola, more efforts need to be deployed. When the value of [Formula: see text] is greater than one, we prove the existence of a unique endemic equilibrium, locally asymptotically stable. That is the disease may persist and become endemic. Numerically, we fit our model to the reported data for the 2018–2020 Kivu Ebola outbreak which occurred in Democratic Republic of Congo. Through the sensitivity analysis of the control reproduction number, we prove that the transmission rates of infected alive who are outside hospital are the most influential parameters. Numerically, we explore the usefulness of isolation, safe burial combined with vaccination and investigate the importance to combine the latter control strategies to the educational campaigns or/and case finding.
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Affiliation(s)
- A. J. OUEMBA TASSÉ
- Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67, Dschang, Cameroon
| | - B. TSANOU
- Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67, Dschang, Cameroon
- Department of Science, Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20, Pretoria 0028, South Africa
- IRD Sorbonne University, UMMISCO, F-93143, Bondy, France
| | - J. LUBUMA
- School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa
| | - JEAN LOUIS WOUKENG
- Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67, Dschang, Cameroon
| | - FRANCIS SIGNING
- Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67, Dschang, Cameroon
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Ahmad W, Abbas M, Rafiq M, Baleanu D. Mathematical analysis for the effect of voluntary vaccination on the propagation of Corona virus pandemic. RESULTS IN PHYSICS 2021; 31:104917. [PMID: 34722138 PMCID: PMC8536489 DOI: 10.1016/j.rinp.2021.104917] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2021] [Revised: 10/10/2021] [Accepted: 10/13/2021] [Indexed: 05/04/2023]
Abstract
In this manuscript, a new nonlinear model for the rapidly spreading Corona virus disease (COVID-19) is developed. We incorporate an additional class of vaccinated humans which ascertains the impact of vaccination strategy for susceptible humans. A complete mathematical analysis of this model is conducted to predict the dynamics of Corona virus in the population. The analysis proves the effectiveness of vaccination strategy employed and helps public health services to control or to reduce the burden of corona virus pandemic. We first prove the existence and uniqueness and then boundedness and positivity of solutions. Threshold parameter for the vaccination model is computed analytically. Stability of the proposed model at fixed points is investigated analytically with the help of threshold parameter to examine epidemiological relevance of the pandemic. We apply LaSalle's invariance principle from the theory of Lyapunov function to prove the global stability of both the equilibria. Two well known numerical techniques namely Runge-Kutta method of order 4 (RK4), and the Non-Standard Finite Difference (NSFD) method are employed to solve the system of ODE's and to validate our obtained theoretical results. For different coverage levels of voluntary vaccination, we explored a complete quantitative analysis of the model. To draw our conclusions, the effect of proposed vaccination on threshold parameter is studied numerically. It is claimed that Corona virus disease could be eradicated faster if a human community selfishly adopts mandatory vaccination measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effect of vaccination strategy on a disease dynamics.
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Affiliation(s)
- W Ahmad
- Department of Mathematics, GC University, Lahore, Pakistan
| | - M Abbas
- Department of Mathematics, GC University, Lahore, Pakistan
| | - M Rafiq
- Department of Mathematics, Faculty of Sciences, University of Central Punjab Lahore, Pakistan
| | - D Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey
- Institute of Space Sciences, Magurele, Bucharest, Romania
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
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8
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Tang X, Musa SS, Zhao S, Mei S, He D. Using Proper Mean Generation Intervals in Modeling of COVID-19. Front Public Health 2021; 9:691262. [PMID: 34291032 PMCID: PMC8287506 DOI: 10.3389/fpubh.2021.691262] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Accepted: 05/19/2021] [Indexed: 12/17/2022] Open
Abstract
In susceptible-exposed-infectious-recovered (SEIR) epidemic models, with the exponentially distributed duration of exposed/infectious statuses, the mean generation interval (GI, time lag between infections of a primary case and its secondary case) equals the mean latent period (LP) plus the mean infectious period (IP). It was widely reported that the GI for COVID-19 is as short as 5 days. However, many works in top journals used longer LP or IP with the sum (i.e., GI), e.g., >7 days. This discrepancy will lead to overestimated basic reproductive number and exaggerated expectation of infection attack rate (AR) and control efficacy. We argue that it is important to use suitable epidemiological parameter values for proper estimation/prediction. Furthermore, we propose an epidemic model to assess the transmission dynamics of COVID-19 for Belgium, Israel, and the United Arab Emirates (UAE). We estimated a time-varying reproductive number [R0(t)] based on the COVID-19 deaths data and we found that Belgium has the highest AR followed by Israel and the UAE.
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Affiliation(s)
- Xiujuan Tang
- Shenzhen Center for Disease Control and Prevention, Shenzhen, China
| | - Salihu S. Musa
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China
- Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria
| | - Shi Zhao
- The Jockey Club School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
- Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China
| | - Shujiang Mei
- Shenzhen Center for Disease Control and Prevention, Shenzhen, China
| | - Daihai He
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China
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9
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Musa SS, Baba IA, Yusuf A, Sulaiman TA, Aliyu AI, Zhao S, He D. Transmission dynamics of SARS-CoV-2: A modeling analysis with high-and-moderate risk populations. RESULTS IN PHYSICS 2021; 26:104290. [PMID: 34026471 PMCID: PMC8131571 DOI: 10.1016/j.rinp.2021.104290] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Revised: 04/30/2021] [Accepted: 05/01/2021] [Indexed: 05/03/2023]
Abstract
Nigeria is second to South Africa with the highest reported cases of COVID-19 in sub-Saharan Africa. In this paper, we employ an SEIR-based compartmental model to study and analyze the transmission dynamics of SARS-CoV-2 outbreaks in Nigeria. The model incorporates different group of populations (that is, high- and- moderate risk populations) and is use to investigate the influence on each population on the overall transmission dynamics.The model, which is fitted well to the data, is qualitatively analyzed to evaluate the impacts of different schemes for controlstrategies. Mathematical analysis reveals that the model has two equilibria; i.e., disease-free equilibrium (DFE) which is local asymptotic stability (LAS) if the basic reproduction number (R 0 ) is less than 1; and unstable forR 0 > 1 , and an endemic equilibrium (EE) which is globally asymptotic stability (LAS) wheneverR 0 > 1 . Furthermore, we find that the model undergoes a phenomenon of backward bifurcation (BB, a coexistence of stable DFE and stable EE even if theR 0 < 1 ). We employ Partial Rank Correlation coefficients (PRCCs) for sensitivity analyses to evaluate the model's parameters. Our results highlight that proper surveillance, especially movement of individuals from high risk to moderate risk population, testing, as well as imposition of other NPIs measures are vital strategies for mitigating the COVID-19 epidemic in Nigeria. Besides, in the absence of an exact solution for the proposed model, we solve the model with the well-known ODE45 numerical solver and the effective numerical schemes such as Euler (EM), Runge-Kutta of order 2 (RK-2), and Runge-Kutta of order 4 (RK-4) in order to establish approximate solutions and to show the physical features of the model. It has been shown that these numerical schemes are very effective and efficient to establish superb approximate solutions for differential equations.
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Affiliation(s)
- Salihu S Musa
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong
- Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria
| | - Isa A Baba
- Department of Mathematics, Bayero University Kano, Nigeria
| | - Abdullahi Yusuf
- Department of Computer Engineering, Biruni University, Istanbul, Turkey
- Department of Mathematics, Science Faculty, Federal University Dutse, Jigawa, Nigeria
| | - Tukur A Sulaiman
- Department of Computer Engineering, Biruni University, Istanbul, Turkey
- Department of Mathematics, Science Faculty, Federal University Dutse, Jigawa, Nigeria
| | - Aliyu I Aliyu
- Department of Mathematics, Science Faculty, Federal University Dutse, Jigawa, Nigeria
| | - Shi Zhao
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong
- CUHK Shenzhen Research Institute, Shenzhen, China
| | - Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong
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Beigi A, Yousefpour A, Yasami A, Gómez-Aguilar JF, Bekiros S, Jahanshahi H. Application of reinforcement learning for effective vaccination strategies of coronavirus disease 2019 (COVID-19). EUROPEAN PHYSICAL JOURNAL PLUS 2021; 136:609. [PMID: 34094796 PMCID: PMC8166378 DOI: 10.1140/epjp/s13360-021-01620-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2021] [Accepted: 05/26/2021] [Indexed: 05/08/2023]
Abstract
Since December 2019, the new coronavirus has raged in China and subsequently all over the world. From the first days, researchers have tried to discover vaccines to combat the epidemic. Several vaccines are now available as a result of the contributions of those researchers. As a matter of fact, the available vaccines should be used in effective and efficient manners to put the pandemic to an end. Hence, a major problem now is how to efficiently distribute these available vaccines among various components of the population. Using mathematical modeling and reinforcement learning control approaches, the present article aims to address this issue. To this end, a deterministic Susceptible-Exposed-Infectious-Recovered-type model with additional vaccine components is proposed. The proposed mathematical model can be used to simulate the consequences of vaccination policies. Then, the suppression of the outbreak is taken to account. The main objective is to reduce the effects of Covid-19 and its domino effects which stem from its spreading and progression. Therefore, to reach optimal policies, reinforcement learning optimal control is implemented, and four different optimal strategies are extracted. Demonstrating the efficacy of the proposed methods, finally, numerical simulations are presented.
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Affiliation(s)
- Alireza Beigi
- School of Mechanical Engineering, College of Engineering, University of Tehran, 14399‒57131 Tehran, Iran
| | - Amin Yousefpour
- School of Mechanical Engineering, College of Engineering, University of Tehran, 14399‒57131 Tehran, Iran
| | - Amirreza Yasami
- School of Mechanical Engineering, College of Engineering, University of Tehran, 14399‒57131 Tehran, Iran
| | - J. F. Gómez-Aguilar
- CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Morelos Mexico
| | - Stelios Bekiros
- Department of Banking and Finance, FEMA, , University of Malta, Msida, MSD 2080 Malta
- Department of Economics, European University Institute, Via delle Fontanelle, 18, 50014 Florence, Italy
| | - Hadi Jahanshahi
- Department of Mechanical Engineering, University of Manitoba, Winnipeg, R3T 5V6 Canada
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11
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Wang R, Wang Q. Determination and estimation of optimal quarantine duration for infectious diseases with application to data analysis of COVID-19. Biometrics 2021; 78:691-700. [PMID: 33595842 PMCID: PMC8014886 DOI: 10.1111/biom.13444] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2020] [Revised: 01/24/2021] [Accepted: 02/03/2021] [Indexed: 01/24/2023]
Abstract
Quarantine measure is a commonly used nonpharmaceutical intervention during the outbreak of infectious diseases. A key problem for implementing quarantine measure is to determine the duration of the quarantine. Different from the existing methods that determine a constant quarantine duration for everyone, we develop an individualized quarantine rule that suggests different quarantine durations for individuals with different characteristics. The proposed quarantine rule is optimal in the sense that it minimizes the average quarantine duration of uninfected people with the constraint that the probability of symptom presentation for infected people attains the given value closing to 1. The optimal solution for the quarantine duration is obtained and estimated by some statistical methods with application to analyzing COVID‐19 data.
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Affiliation(s)
- Ruoyu Wang
- Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China.,University of Chinese Academy of Sciences, Beijing, China
| | - Qihua Wang
- Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China.,University of Chinese Academy of Sciences, Beijing, China
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12
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Ding C, Liu X, Yang S. The value of infectious disease modeling and trend assessment: a public health perspective. Expert Rev Anti Infect Ther 2021; 19:1135-1145. [PMID: 33522327 DOI: 10.1080/14787210.2021.1882850] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
INTRODUCTION Disease outbreaks of acquired immunodeficiency syndrome, severe acute respiratory syndrome, pandemic H1N1, H7N9, H5N1, Ebola, Zika, Middle East respiratory syndrome, and recently COVID-19 have raised the attention of the public over the past half-century. Revealing the characteristics and epidemic trends are important parts of disease control. The biological scenarios including transmission characteristics can be constructed and translated into mathematical models, which can help to predict and gain a deeper understanding of diseases. AREAS COVERED This review discusses the models for infectious diseases and highlights their values in the field of public health. This information will be of interest to mathematicians and clinicians, and make a significant contribution toward the development of more specific and effective models. Literature searches were performed using the online database of PubMed (inception to August 2020). EXPERT OPINION Modeling could contribute to infectious disease control by means of predicting the scales of disease epidemics, indicating the characteristics of disease transmission, evaluating the effectiveness of interventions or policies, and warning or forecasting during the pre-outbreak of diseases. With the development of theories and the ability of calculations, infectious disease modeling would play a much more important role in disease prevention and control of public health.
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Affiliation(s)
- Cheng Ding
- State Key Laboratory for Diagnosis and Treatment of Infectious Diseases,National Clinical Research Center for Infectious Diseases, Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, The First Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou, China
| | - Xiaoxiao Liu
- State Key Laboratory for Diagnosis and Treatment of Infectious Diseases,National Clinical Research Center for Infectious Diseases, Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, The First Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou, China
| | - Shigui Yang
- State Key Laboratory for Diagnosis and Treatment of Infectious Diseases,National Clinical Research Center for Infectious Diseases, Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, The First Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou, China.,Department of Epidemiology of Microbial Diseases, Yale School of Public Health, New Haven, CT, USA
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13
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Tambo E, El-Dessouky AG, Khater EIM, Xianonng Z. Enhanced surveillance and response approaches for pilgrims and local Saudi populations against emerging Nipah, Zika and Ebola viral diseases outbreaks threats. J Infect Public Health 2020; 13:674-678. [PMID: 32265162 PMCID: PMC7270858 DOI: 10.1016/j.jiph.2020.01.313] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2018] [Revised: 01/12/2020] [Accepted: 01/30/2020] [Indexed: 11/17/2022] Open
Abstract
Increasing emergence and spread of Nipah, ZIKV and Ebola case and potential outbreaks threats have been reported in several regions around the globe. Yet, emerging Nipah, Ebola and Zika viral diseases outbreaks have been indirectly linked to substantially globalization of trade and travel, climate change and intense urbanization impact, healthcare and socioeconomic inequities as well in affected community settings. Although no case has been documented in Saudi Arabia, there is a great risk of sudden emergence of any of these viruses and others via introducing among pilgrims coming from endemic regions during ritual ceremonies of mass gatherings. Consequently, promoting and investing on new and sensitive proven effective and innovative surveillance and monitoring approaches, including enhanced risk communication, improved integrated vectors surveillance in addition to improved sustainable highly pathogens surveillance control programs to human motility and environmental sanitation strategies all represent 'One Health' approach implementation strategic core. Initiation, development and implementation leaded by Saudi government and international stakeholders' of new partnership, coordinated response leadership and resource mobilization for multidisciplinary and intersectorial advocacy on emerging viral disease outbreaks, accompanied with R&D roadmap and taskforce is crucial. More efforts in epidemiological and laboratory early screening and surveillance of highly pathogenic germs/microbes, and confirmation of asymptomatic and syndromic cases amongst suspected Hajj and Umrah pilgrims, local vulnerable populations and expatriate workers is vital in generating reliable data and data sharing platform for timely risk communication and tourist information update, appropriate immunization campaigns or safe and efficacious care delivery implementation. Moreover, increase Hajj/Umrah mass gathering emergency outbreak preparedness, pilgrims health education and engagement outreach, pre-, during and post programs coverage and effectiveness is needed through One Health approach integration in attaining pilgrims and local population health safety and security, in advancing Saudi sustainable health development goals.
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Affiliation(s)
- Ernest Tambo
- Africa Disease Intelligence and Surveillance and Response Institute, Yaoundé, Cameroon; School of Public Health, University of Witwatersrand, Johannesburg, South Africa.
| | - Ashraf G El-Dessouky
- Microbiology Unit, Public Health Pests Laboratory, Jeddah Governate, Jeddah, Saudi Arabia; Biochemical Genetic Unit, Medical Genetics Center, Faculty of Medicine, Ain Shams University, Cairo, Egypt
| | - Emad I M Khater
- Department of Entomology, Faculty of Science, Ain Shams University, Cairo, Egypt
| | - Zhou Xianonng
- National Institute of Parasitic Diseases, Chinese Center for Disease Control and Prevention, Sanghai 200025, PR China
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Ryu S, Ali ST, Lim JS, Chun BC. Estimation of the Excess COVID-19 Cases in Seoul, South Korea by the Students Arriving from China. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2020; 17:E3113. [PMID: 32365703 PMCID: PMC7246702 DOI: 10.3390/ijerph17093113] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Revised: 04/17/2020] [Accepted: 04/25/2020] [Indexed: 01/04/2023]
Abstract
Background: In March 2020, overall, 37,000 international students from China, a country at risk of the 2019-novel coronavirus (COVID-19) infection has arrived in Seoul, South Korea. Individuals from the country at risk of COVID-19 infection have been included in the Korean home-quarantine program, but the efficacy of the program is uncertain. Methods: To estimate the possible number of infected individuals within the large influx of international students from China, we used a deterministic compartmental model for epidemic and performed a simulation-based search of different rates of compliance with home-quarantine. Results: Under the home-quarantine program, the number of the infected individuals would reach 40-72 from 12 March-24 March with the arrival of 0.2% of pre-infectious individuals. Furthermore, the number of isolated individuals would peak at 40-64 from 13 March-27 March in Seoul, South Korea. Our findings indicated when incoming international students showed strict compliance with quarantine, epidemics by the international student from China were less likely to occur in Seoul, South Korea. Conclusions: To mitigate possible epidemics, additional efforts to improve the compliance of home-quarantine of the individuals from countries with the virus risk are warranted along with other containment policies.
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Affiliation(s)
- Sukhyun Ryu
- Department of Preventive Medicine, College of Medicine, Konyang University, Daejeon 35365, Korea;
- Korean Society of Epidemiology 2019-nCoV Task Force Team, Korea
| | - Sheikh Taslim Ali
- WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong, China;
| | - Jun-Sik Lim
- College of Veterinary Medicine and Institute of Veterinary Science, Kangwon National University, Chuncheon 24341, Korea;
| | - Byung Chul Chun
- Korean Society of Epidemiology 2019-nCoV Task Force Team, Korea
- Department of Preventive Medicine, Korea University College of Medicine, Seoul 02841, Korea
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15
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Optimal Impulse Vaccination Approach for an SIR Control Model with Short-Term Immunity. MATHEMATICS 2019. [DOI: 10.3390/math7050420] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Vaccines are not administered on a continuous basis, but injections are practically introduced at discrete times often separated by an important number of time units, and this differs depending on the nature of the epidemic and its associated vaccine. In addition, especially when it comes to vaccination, most optimization approaches in the literature and those that have been subject to epidemic models have focused on treating problems that led to continuous vaccination schedules but their applicability remains debatable. In search of a more realistic methodology to resolve this issue, a control modeling design, where the control can be characterized analytically and then optimized, can definitely help to find an optimal regimen of pulsed vaccinations. Therefore, we propose a susceptible-infected-removed (SIR) hybrid epidemic model with impulse vaccination control and a compartment that represents the number of vaccinated individuals supposed to not acquire sufficient immunity to become permanently recovered due to the short-term effect of vaccines. A basic reproduction number, when the control is defined as a constant parameter, is calculated. Since we also need to find the optimal values of this impulse control when it is defined as a function of time, we start by stating a general form of an impulse version of Pontryagin’s maximum principle that can be adapted to our case, and then we apply it to our model. Finally, we provide our numerical simulations that are obtained via an impulse progressive-regressive iterative scheme with fixed intervals between impulse times (theoretical example of an impulse at each week), and we conclude with a discussion of our results.
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Area I, NdaÏrou F, J. Nieto J, J. Silva C, F. M. Torres D. Ebola model and optimal control with vaccination constraints. ACTA ACUST UNITED AC 2018. [DOI: 10.3934/jimo.2017054] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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Oluwagbemi O, Awe O. A comparative computational genomics of Ebola Virus Disease strains: In-silico Insight for Ebola control. INFORMATICS IN MEDICINE UNLOCKED 2018. [DOI: 10.1016/j.imu.2018.07.004] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022] Open
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More S, Bøtner A, Butterworth A, Calistri P, Depner K, Edwards S, Garin-Bastuji B, Good M, Gortázar Schmidt C, Michel V, Miranda MA, Nielsen SS, Raj M, Sihvonen L, Spoolder H, Stegeman JA, Thulke HH, Velarde A, Willeberg P, Winckler C, Baldinelli F, Broglia A, Beltrán Beck B, Kohnle L, Morgado J, Bicout D. Assessment of listing and categorisation of animal diseases within the framework of the Animal Health Law (Regulation (EU) No 2016/429): Ebola virus disease. EFSA J 2017; 15:e04890. [PMID: 32625555 PMCID: PMC7009972 DOI: 10.2903/j.efsa.2017.4890] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Ebola virus disease has been assessed according to the criteria of the Animal Health Law (AHL), in particular criteria of Article 7 on disease profile and impacts, Article 5 on the eligibility of Ebola virus disease to be listed, Article 9 for the categorisation of Ebola virus disease according to disease prevention and control rules as in Annex IV and Article 8 on the list of animal species related to Ebola virus disease. The assessment has been performed following a methodology composed of information collection and compilation, expert judgement on each criterion at individual and, if no consensus was reached before, also at collective level. The output is composed of the categorical answer, and for the questions where no consensus was reached, the different supporting views are reported. Details on the methodology used for this assessment are explained in a separate opinion. According to the assessment performed, Ebola virus disease can be considered eligible to be listed for Union intervention as laid down in Article 5(3) of the AHL. The disease would comply with the criteria as in Sections 4 and 5 of Annex IV of the AHL, for the application of the disease prevention and control rules referred to in points (d) and (e) of Article 9(1). The animal species to be listed for Ebola virus disease according to Article 8(3) criteria are some species of non-human primates, pigs and rodents as susceptible species and some species of fruit bats as reservoir, as indicated in the present opinion.
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