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Biala TA, Afolabi YO, Khaliq AQM. How efficient is contact tracing in mitigating the spread of COVID-19? a mathematical modeling approach. APPLIED MATHEMATICAL MODELLING 2022; 103:714-730. [PMID: 34815616 PMCID: PMC8603240 DOI: 10.1016/j.apm.2021.11.011] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2020] [Revised: 10/24/2021] [Accepted: 11/07/2021] [Indexed: 05/26/2023]
Abstract
Contact Tracing (CT) is one of the measures taken by government and health officials to reduce the spread of the novel coronavirus. In this paper, we investigate its efficacy by developing a compartmental model for assessing its impact on mitigating the spread of the virus. We describe the impact on the reproduction number R 0 of COVID-19. In particular, we discuss the importance and relevance of parameters of the model such as the number of reported cases, effectiveness of tracking and monitoring policy, and the transmission rates to contact tracing. We describe the terms "perfect tracking", "perfect monitoring" and "perfect reporting" to indicate that traced contacts will be tracked while incubating, tracked contacts are efficiently monitored so that they do not cause secondary infections, and all infected persons are reported, respectively. We consider three special scenarios: (1) perfect monitoring and perfect tracking of contacts of a reported case, (2) perfect reporting of cases and perfect monitoring of tracked reported cases and (3) perfect reporting and perfect tracking of contacts of reported cases. Furthermore, we gave a lower bound on the proportion of contacts to be traced to ensure that the effective reproduction, R c , is below one and describe R c in terms of observable quantities such as the proportion of reported and traced cases. Model simulations using the COVID-19 data obtained from John Hopkins University for some selected states in the US suggest that even late intervention of CT may reasonably reduce the transmission of COVID-19 and reduce peak hospitalizations and deaths. In particular, our findings suggest that effective monitoring policy of tracked cases and tracking of traced contacts while incubating are more crucial than tracing more contacts. The use of CT coupled with other measures such as social distancing, use of face mask, self-isolation or quarantine and lockdowns will greatly reduce the spread of the epidemic as well as peak hospitalizations and total deaths.
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Affiliation(s)
- T A Biala
- Department of Mathematics, The Ohio State University, USA
| | - Y O Afolabi
- Department of Mathematics, University of Louisiana at Lafayette, USA
| | - A Q M Khaliq
- Department of Mathematical Sciences, Middle Tennessee State University, USA
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Dénes A, Ibrahim MA, Oluoch L, Tekeli M, Tekeli T. Impact of weather seasonality and sexual transmission on the spread of Zika fever. Sci Rep 2019; 9:17055. [PMID: 31745123 PMCID: PMC6863851 DOI: 10.1038/s41598-019-53062-z] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Accepted: 10/26/2019] [Indexed: 12/17/2022] Open
Abstract
We establish a compartmental model to study the transmission of Zika virus disease including spread through sexual contacts and the role of asymptomatic carriers. To incorporate the impact of the seasonality of weather on the spread of Zika, we apply a nonautonomous model with time-dependent mosquito birth rate and biting rate, which allows us to explain the differing outcome of the epidemic in different countries of South America: using Latin Hypercube Sampling for fitting, we were able to reproduce the different outcomes of the disease in various countries. Sensitivity analysis shows that, although the most important factors in Zika transmission are the birth rate of mosquitoes and the transmission rate from mosquitoes to humans, spread through sexual contacts also highly contributes to the transmission of Zika virus: our study suggests that the practice of safe sex among those who have possibly contracted the disease, can significantly reduce the number of Zika cases.
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Affiliation(s)
- Attila Dénes
- Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., Szeged, H-6720, Hungary.
| | - Mahmoud A Ibrahim
- Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., Szeged, H-6720, Hungary.,Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt
| | - Lillian Oluoch
- Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., Szeged, H-6720, Hungary
| | - Miklós Tekeli
- Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., Szeged, H-6720, Hungary
| | - Tamás Tekeli
- Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., Szeged, H-6720, Hungary
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Silva SYBE, Pinto ESG, Medeiros ERD, Rebouças DGDC, Paiva ACDS, Nascimento CPAD, Souza NLD. Strategies for the evaluation of interventions for the control of tuberculosis: integrative review. Rev Bras Enferm 2019; 72:1370-1377. [DOI: 10.1590/0034-7167-2017-0922] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2017] [Accepted: 03/05/2018] [Indexed: 11/21/2022] Open
Abstract
ABSTRACT Objective: Identifying the available evidence in the scientific literature about the strategies used in the evaluations of interventions for the control of tuberculosis. Method: Integrative review with searches in databases Lilacs, CINAHL and PubMed in August 2017. Thirty-three articles were selected and the theoretical referential of health assessment was used for analysis. Results: The prevalent interventions were health programs (60.7%), 69.7% focusing on results and 81.9% having quantitative character (81.9%). Final considerations: The evaluation of interventions for the control of tuberculosis is beneficial for the health services’ users and aids in the decision making of managers and health professionals.
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Guo J, Yang M, Wu Z, Shen X, Wang Y, Zhao G. High incidence and low case detection rate among contacts of tuberculosis cases in Shanghai, China. BMC Infect Dis 2019; 19:320. [PMID: 30975088 PMCID: PMC6460728 DOI: 10.1186/s12879-019-3942-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2017] [Accepted: 03/28/2019] [Indexed: 01/08/2023] Open
Abstract
Background To assess the effect of a contact investigation strategy by assessing the incidence of tuberculosis and the case detection rate among contacts of tuberculosis patients. Methods The pulmonary tuberculosis incidence among contacts was determined retrospectively from a tuberculosis information management system. For each detection method (symptom examination only, symptom examination plus chest radiography or other alternatives), the detection rate of pulmonary tuberculosis patients among contacts was derived from contact investigation form records. Results Sixty-nine cases of pulmonary tuberculosis were identified among a total of 8137 contacts after an average follow-up of 2.6 years (range: 0.25–5.25) during the period from 2010 to 2014. The incidence density was 329/100,000 person-years (PYs), and the 95% confidence interval (CI) was 256–419/100,000 PYs, which was significantly higher than the notification rate during the same period in the general population (29–30/100,000 PYs). The incidence density was higher (p < 0.0001) among male contacts (462/100,000 PYs) than among female contacts (236/100,000 PYs). The incidence density did not differ (p > 0.05) between contacts whose index case was sputum smear positive and those whose index case was sputum smear negative. Contacts who were biologically related family of the index cases exhibited a higher (p < 0.05) incidence density (475/100,000 PYs) than other contacts (281/100,000 PYs). Fifteen of the 69 incident cases were found through contact investigation, corresponding to a case detection rate via contact investigation of 22% (95% CI: 13–33%). The relevance ratio was 288/100,000 (12/4163) by both chest radiography and symptom survey, which was significantly higher than the rate detected by symptom survey alone, of 57/100,000 (2/3486), p = 0.028. The cumulative incidence in the contacts was 761/100,000 (62/8137) within 3 years from the time that the index cases were diagnosed with pulmonary tuberculosis, which was higher than the incidence rate of 210/100,000 (7/3328) recorded after 3 years (p < 0.001). Conclusions The contacts were at higher risk of pulmonary tuberculosis than the general population; however, only approximately 22% of the incident cases could be detected through contact investigation. Therefore, the contact investigation strategy must be improved for better detection of potential pulmonary tuberculosis cases.
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Affiliation(s)
- Juntao Guo
- Institute of Tuberculosis and HIV/AIDS Control and Prevention, Shanghai Municipal Center for Disease Control and Prevention, Shanghai, China.,Department of Epidemiology, School of Public Health, Fudan University, Shanghai, China
| | - Meixia Yang
- Department of Tuberculosis and HIV/AIDS Control and Prevention, Xuhui District Center for Disease Control and Prevention, Shanghai, China
| | - Zheyuan Wu
- Institute of Tuberculosis and HIV/AIDS Control and Prevention, Shanghai Municipal Center for Disease Control and Prevention, Shanghai, China
| | - Xin Shen
- Institute of Tuberculosis and HIV/AIDS Control and Prevention, Shanghai Municipal Center for Disease Control and Prevention, Shanghai, China
| | - Yuanhui Wang
- Department of Tuberculosis and HIV/AIDS Control and Prevention, Xuhui District Center for Disease Control and Prevention, Shanghai, China
| | - Genming Zhao
- Department of Epidemiology, School of Public Health, Fudan University, Shanghai, China.
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Baxter S, Goyder E, Chambers D, Johnson M, Preston L, Booth A. Interventions to improve contact tracing for tuberculosis in specific groups and in wider populations: an evidence synthesis. HEALTH SERVICES AND DELIVERY RESEARCH 2017. [DOI: 10.3310/hsdr05010] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
BackgroundThe tracing and screening of people who have had contact with an active case of tuberculosis (TB) is an important element of TB control strategies.ObjectivesThis study aimed to carry out a review of evidence regarding TB contact tracing, with a particular emphasis on research that was applicable to TB contact tracing in specific population groups in the UK.DesignAn evidence synthesis of literature of any study design on TB contact tracing in developed countries was carried out.SettingAny setting.PopulationIndividuals found to have active TB disease, and people who have come into contact with them.InterventionsContact-tracing investigations.Main outcome measuresAny outcome related to TB infection, contact investigations and/or the views of staff, people with TB disease, or their contacts.Data sourcesSearches for research published 1995 onwards were undertaken in the following databases: MEDLINE via Ovid SP, EMBASE via Ovid SP, EconLit via Ovid SP, PsycINFO via Ovid SP, Social Policy and Practice via Ovid SP, Cumulative Index to Nursing and Allied Health Literature via EBSCOhost, Science and Social Science Citation Indices via Web of Science and The Cochrane Library via Wiley Online Library.Review methodsThe study comprised a review of TB contact tracing in specific population groups and a review in wider populations. A narrative synthesis was completed and a logic model was developed from the literature.ResultsThere were 112 articles in the review: 23 related to specific populations and 89 related to wider populations. The literature was of limited quality, with much general description of investigations. We identified only two (uncontrolled) studies that could be considered evaluative. Although the limitations of the evidence should be recognised, the review suggested the following: the value of a location-based approach, working with local communities and the media, partnership working, using molecular epidemiological testing, ensuring adequate systems and addressing fear of stigma. The literature on investigations for specific populations has much concordance with that reporting findings from wider population groups. The recognised limitations of conventional investigation methods may, however, be exacerbated in specific populations.LimitationsThe English-language inclusion criterion may have limited the breadth of countries represented. A meta-analysis was not possible owing to the nature of the literature. Relevant studies may have been missed by our searches, which used terminology relating to contact tracing rather than to active case finding or screening.ConclusionsThe review identified a sizeable volume of literature relating to contact investigations. However, it is currently predominantly descriptive, with little evaluative work underpinning investigations in either specific or wider populations. Our findings are, therefore, based on limited evidence. Further research is required if robust conclusions are to be made.Future workResearch should further explore the development of measures that can be used to compare the effectiveness of different contact investigations, in studies using evaluative designs.FundingThe National Institute for Health Research Health Services and Delivery Research programme.
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Affiliation(s)
- Susan Baxter
- School of Health and Related Research, University of Sheffield, Sheffield, UK
| | - Elizabeth Goyder
- School of Health and Related Research, University of Sheffield, Sheffield, UK
| | - Duncan Chambers
- School of Health and Related Research, University of Sheffield, Sheffield, UK
| | - Maxine Johnson
- School of Health and Related Research, University of Sheffield, Sheffield, UK
| | - Louise Preston
- School of Health and Related Research, University of Sheffield, Sheffield, UK
| | - Andrew Booth
- School of Health and Related Research, University of Sheffield, Sheffield, UK
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Browne C, Gulbudak H, Webb G. Modeling contact tracing in outbreaks with application to Ebola. J Theor Biol 2015; 384:33-49. [PMID: 26297316 DOI: 10.1016/j.jtbi.2015.08.004] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2015] [Revised: 06/29/2015] [Accepted: 08/07/2015] [Indexed: 11/15/2022]
Abstract
Contact tracing is an important control strategy for containing Ebola epidemics. From a modeling perspective, explicitly incorporating contact tracing with disease dynamics presents challenges, and population level effects of contact tracing are difficult to determine. In this work, we formulate and analyze a mechanistic SEIR type outbreak model which considers the key features of contact tracing, and we characterize the impact of contact tracing on the effective reproduction number, Re, of Ebola. In particular, we determine how relevant epidemiological properties such as incubation period, infectious period and case reporting, along with varying monitoring protocols, affect the efficacy of contact tracing. In the special cases of either perfect monitoring of traced cases or perfect reporting of all cases, we derive simple formulae for the critical proportion of contacts that need to be traced in order to bring the effective reproduction number Re below one. Also, in either case, we show that Re can be expressed completely in terms of observable reported case/tracing quantities, namely Re = k((1-q)/q)+km where k is the number of secondary traced infected contacts per primary untraced reported case, km is the number of secondary traced infected contacts per primary traced reported case and (1-q)/q is the odds that a reported case is not a traced contact. These formulae quantify contact tracing as both an intervention strategy that impacts disease spread and a probe into the current epidemic status at the population level. Data from the West Africa Ebola outbreak is utilized to form real-time estimates of Re, and inform our projections of the impact of contact tracing, and other control measures, on the epidemic trajectory.
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Affiliation(s)
- Cameron Browne
- Department of Mathematics, Vanderbilt University, United States.
| | - Hayriye Gulbudak
- School of Biology, Georgia Institute of Technology, United States; School of Mathematics, Georgia Institute of Technology, United States
| | - Glenn Webb
- Department of Mathematics, Vanderbilt University, United States
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