Quantifying TB transmission: a systematic review of reproduction number and serial interval estimates for tuberculosis

Abstract Tuberculosis (TB) is the leading global infectious cause of death. Understanding TB transmission is critical to creating policies and monitoring the disease with the end goal of TB elimination. To our knowledge, there has been no systematic review of key transmission parameters for TB. We carried out a systematic review of the published literature to identify studies estimating either of the two key TB transmission parameters: the serial interval (SI) and the reproductive number. We identified five publications that estimated the SI and 56 publications that estimated the reproductive number. The SI estimates from four studies were: 0.57, 1.42, 1.44 and 1.65 years; the fifth paper presented age-specific estimates ranging from 20 to 30 years (for infants <1 year old) to <5 years (for adults). The reproductive number estimates ranged from 0.24 in the Netherlands (during 1933–2007) to 4.3 in China in 2012. We found a limited number of publications and many high TB burden settings were not represented. Certain features of TB dynamics, such as slow transmission, complicated parameter estimation, require novel methods. Additional efforts to estimate these parameters for TB are needed so that we can monitor and evaluate interventions designed to achieve TB elimination.

[1]  C. Castillo-Chavez,et al.  Transmission and dynamics of tuberculosis on generalized households. , 2000, Journal of theoretical biology.

[2]  C. Castillo-Chavez,et al.  A two-strain TB model with multiple latent stages. , 2016, Mathematical biosciences and engineering : MBE.

[3]  Margaret L. Brandeau,et al.  Controlling Co-Epidemics: Analysis of HIV and Tuberculosis Infection Dynamics , 2008, Oper. Res..

[4]  N. Nagelkerke,et al.  Analysis of tuberculosis transmission between nationalities in the Netherlands in the period 1993-1995 using DNA fingerprinting. , 1998, American journal of epidemiology.

[5]  Chung-Min Liao,et al.  A Probabilistic Transmission and Population Dynamic Model to Assess Tuberculosis Infection Risk , 2012, Risk analysis : an official publication of the Society for Risk Analysis.

[6]  A. Dirksen,et al.  Molecular evidence of endogenous reactivation of Mycobacterium tuberculosis after 33 years of latent infection. , 2002, The Journal of infectious diseases.

[7]  T. Stadler Inferring Epidemiological Parameters on the Basis of Allele Frequencies , 2011, Genetics.

[8]  Sanling Yuan,et al.  Analysis of Transmission and Control of Tuberculosis in Mainland China, 2005–2016, Based on the Age-Structure Mathematical Model , 2017, International journal of environmental research and public health.

[9]  Karen E. Clark,et al.  Update on latent tuberculosis infection. , 2014, American family physician.

[10]  J. Wallinga,et al.  Different Epidemic Curves for Severe Acute Respiratory Syndrome Reveal Similar Impacts of Control Measures , 2004, American journal of epidemiology.

[11]  C. Castillo-Chavez,et al.  Global stability of an age-structure model for TB and its applications to optimal vaccination strategies. , 1998, Mathematical biosciences.

[12]  Tanja Stadler,et al.  Exact vs. Approximate Computation: Reconciling Different Estimates of Mycobacterium tuberculosis Epidemiological Parameters , 2014, Genetics.

[13]  Epco Hasker,et al.  Recurrence in tuberculosis: relapse or reinfection? , 2003, The Lancet. Infectious diseases.

[14]  E. Lyons,et al.  Pandemic Potential of a Strain of Influenza A (H1N1): Early Findings , 2009, Science.

[15]  S. Blower,et al.  Uncertainty and sensitivity analysis of the basic reproductive rate. Tuberculosis as an example. , 1997, American journal of epidemiology.

[16]  T. Chou,et al.  Modeling the emergence of the 'hot zones': tuberculosis and the amplification dynamics of drug resistance , 2004, Nature Medicine.

[17]  J. Wallinga,et al.  Serial intervals of respiratory infectious diseases: a systematic review and analysis. , 2014, American journal of epidemiology.

[18]  Angélique Stéphanou,et al.  Towards the Design of a Patient-Specific Virtual Tumour , 2016, Comput. Math. Methods Medicine.

[19]  C. Castillo-Chavez,et al.  A model for tuberculosis with exogenous reinfection. , 2000, Theoretical population biology.

[20]  Ronald B Geskus,et al.  The incubation period distribution of tuberculosis estimated with a molecular epidemiological approach. , 2011, International journal of epidemiology.

[21]  D. van Soolingen,et al.  Progress towards tuberculosis elimination: secular trend, immigration and transmission , 2010, European Respiratory Journal.

[22]  Séverine Ansart,et al.  Transmission parameters of the A/H1N1 (2009) influenza virus pandemic: a review , 2011, Influenza and other respiratory viruses.

[23]  David J. Gerberry Trade-off between BCG vaccination and the ability to detect and treat latent tuberculosis. , 2009, Journal of theoretical biology.

[24]  S. Blower,et al.  The intrinsic transmission dynamics of tuberculosis epidemics , 1995, Nature Medicine.

[25]  Carlos Castillo-Chavez,et al.  Modeling TB and HIV co-infections. , 2009, Mathematical biosciences and engineering : MBE.

[26]  Tetsu Watanabe,et al.  Use of a mathematical model to estimate tuberculosis transmission risk in an Internet café , 2009, Environmental health and preventive medicine.

[27]  P. Lio’,et al.  Bayesian Melding Approach to Estimate the Reproduction Number for Tuberculosis Transmission in Indian States and Union Territories , 2015, Asia-Pacific journal of public health.

[28]  Tianhua Zhang,et al.  Seasonality Impact on the Transmission Dynamics of Tuberculosis , 2016, Comput. Math. Methods Medicine.

[29]  Shanjing Ren Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse. , 2017, Mathematical biosciences and engineering : MBE.

[30]  H M Yang,et al.  The basic reproduction ratio for a model of directly transmitted infections considering the virus charge and the immunological response. , 2000, IMA journal of mathematics applied in medicine and biology.

[31]  P. Alcabes,et al.  The contribution of recently acquired Mycobacterium tuberculosis infection to the New York City tuberculosis epidemic, 1989-1993. , 2000, Epidemiology.

[32]  J. Wallinga,et al.  A Sign of Superspreading in Tuberculosis: Highly Skewed Distribution of Genotypic Cluster Sizes , 2013, Epidemiology.

[33]  Jason R Andrews,et al.  Modeling the role of public transportation in sustaining tuberculosis transmission in South Africa. , 2013, American journal of epidemiology.

[34]  Baojun Song,et al.  Existence of multiple-stable equilibria for a multi-drug-resistant model of Mycobacterium tuberculosis. , 2008, Mathematical biosciences and engineering : MBE.

[35]  Yong Li,et al.  Mathematical modeling of tuberculosis data of China. , 2015, Journal of theoretical biology.

[36]  C. Bhunu,et al.  Modeling HIV/AIDS and Tuberculosis Coinfection , 2009, Bulletin of mathematical biology.

[37]  Maia Martcheva,et al.  Progression age enhanced backward bifurcation in an epidemic model with super-infection , 2003, Journal of mathematical biology.

[38]  D. van Soolingen,et al.  Transmission and Progression to Disease of Mycobacterium tuberculosis Phylogenetic Lineages in The Netherlands , 2015, Journal of Clinical Microbiology.

[39]  Jianhong Wu,et al.  The impact of migrant workers on the tuberculosis transmission: general models and a case study for China. , 2012, Mathematical biosciences and engineering : MBE.

[40]  D van Soolingen,et al.  Estimation of serial interval and incubation period of tuberculosis using DNA fingerprinting. , 1999, The international journal of tuberculosis and lung disease : the official journal of the International Union against Tuberculosis and Lung Disease.

[41]  Dany Djeudeu,et al.  Optimal Control of the Lost to Follow Up in a Tuberculosis Model , 2011, Comput. Math. Methods Medicine.

[42]  Andrew R. Francis,et al.  Using Approximate Bayesian Computation to Estimate Tuberculosis Transmission Parameters From Genotype Data , 2006, Genetics.

[43]  Xiao-Qiang Zhao,et al.  A Tuberculosis Model with Seasonality , 2010, Bulletin of mathematical biology.

[44]  Ellen Brooks-Pollock,et al.  The Impact of Realistic Age Structure in Simple Models of Tuberculosis Transmission , 2010, PloS one.

[45]  C. Bhunu,et al.  Modelling the effects of pre-exposure and post-exposure vaccines in tuberculosis control. , 2008, Journal of theoretical biology.

[46]  N. Nagelkerke,et al.  Transmission of tuberculosis in San Francisco and its association with immigration and ethnicity. , 2000, The international journal of tuberculosis and lung disease : the official journal of the International Union against Tuberculosis and Lung Disease.

[47]  C. Fraser,et al.  Transmission Dynamics of the Etiological Agent of SARS in Hong Kong: Impact of Public Health Interventions , 2003, Science.

[48]  Denis Kouame,et al.  New Estimators and Guidelines for Better Use of Fetal Heart Rate Estimators with Doppler Ultrasound Devices , 2014, Comput. Math. Methods Medicine.

[49]  D. Okuonghae,et al.  Analysis of a mathematical model for tuberculosis: What could be done to increase case detection. , 2011, Journal of theoretical biology.

[50]  S. Cauchemez,et al.  Estimates of the reproduction number for seasonal, pandemic, and zoonotic influenza: a systematic review of the literature , 2014, BMC Infectious Diseases.

[51]  P. Hopewell,et al.  Tuberculosis and latent tuberculosis infection in close contacts of people with pulmonary tuberculosis in low-income and middle-income countries: a systematic review and meta-analysis. , 2008, The Lancet. Infectious diseases.

[52]  G. Marks,et al.  Contact investigation for tuberculosis: a systematic review and meta-analysis , 2012, European Respiratory Journal.

[53]  C. McCluskey,et al.  Lyapunov functions for tuberculosis models with fast and slow progression. , 2006, Mathematical biosciences and engineering : MBE.

[54]  Yong Li,et al.  Mixed vaccination strategy for the control of tuberculosis: A case study in China. , 2016, Mathematical biosciences and engineering : MBE.

[55]  Ellen Brooks-Pollock,et al.  Epidemiologic inference from the distribution of tuberculosis cases in households in Lima, Peru. , 2011, The Journal of infectious diseases.

[56]  Derrick W. Crook,et al.  A Quantitative Evaluation of MIRU-VNTR Typing Against Whole-Genome Sequencing for Identifying Mycobacterium tuberculosis Transmission: A Prospective Observational Cohort Study , 2018, bioRxiv.

[57]  P E Fine,et al.  Lifetime risks, incubation period, and serial interval of tuberculosis. , 2000, American journal of epidemiology.

[58]  Dick van Soolingen,et al.  Tuberculosis Elimination in the Netherlands , 2005, Emerging infectious diseases.

[59]  S. Blower,et al.  Leprosy and tuberculosis: the epidemiological consequences of cross-immunity. , 1997, American journal of public health.

[60]  Emma S McBryde,et al.  Construction of a mathematical model for tuberculosis transmission in highly endemic regions of the Asia-Pacific. , 2014, Journal of theoretical biology.

[61]  P E Fine,et al.  The long-term dynamics of tuberculosis and other diseases with long serial intervals: implications of and for changing reproduction numbers , 1998, Epidemiology and Infection.

[62]  Delfim F. M. Torres,et al.  Optimal control for a tuberculosis model with reinfection and post-exposure interventions. , 2013, Mathematical biosciences.

[63]  G. Schoolnik,et al.  The epidemiology of tuberculosis in San Francisco. A population-based study using conventional and molecular methods. , 1994, The New England journal of medicine.

[64]  L Forsberg White,et al.  A likelihood‐based method for real‐time estimation of the serial interval and reproductive number of an epidemic , 2008, Statistics in medicine.

[65]  E. Salpeter,et al.  Mathematical model for the epidemiology of tuberculosis, with estimates of the reproductive number and infection-delay function. , 1998, American journal of epidemiology.

[66]  Xin-li Hu Threshold dynamics for a tuberculosis model with seasonality. , 2011, Mathematical biosciences and engineering : MBE.

[67]  C. Liao,et al.  Assessing the transmission risk of multidrug-resistant Mycobacterium tuberculosis epidemics in regions of Taiwan. , 2012, International journal of infectious diseases : IJID : official publication of the International Society for Infectious Diseases.

[68]  K. Kam,et al.  Transmission of multidrug-resistant and extensively drug-resistant tuberculosis in a metropolitan city , 2012, European Respiratory Journal.

[69]  S. Basu,et al.  Averting epidemics of extensively drug-resistant tuberculosis , 2009, Proceedings of the National Academy of Sciences.

[70]  Mayetri Gupta,et al.  The Impact of Prior Information on Estimates of Disease Transmissibility Using Bayesian Tools , 2015, PloS one.

[71]  Benjamin H Singer,et al.  Influence of backward bifurcation on interpretation of r(0) in a model of epidemic tuberculosis with reinfection. , 2004, Mathematical biosciences and engineering : MBE.

[72]  J. Hyman,et al.  The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda. , 2004, Journal of theoretical biology.

[73]  B G Williams,et al.  Criteria for the control of drug-resistant tuberculosis. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[74]  R. Horsburgh,et al.  Priorities for the treatment of latent tuberculosis infection in the United States. , 2004, The New England journal of medicine.

[75]  Baojun Song,et al.  Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment. , 2008, Mathematical biosciences and engineering : MBE.

[76]  T. Cohen,et al.  Models to understand the population-level impact of mixed strain M. tuberculosis infections. , 2011, Journal of theoretical biology.

[77]  J. Gerberding,et al.  Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: a theoretical framework , 1998, Journal of Molecular Medicine.

[78]  D. Okuonghae,et al.  Dynamics of a Mathematical Model for Tuberculosis with Variability in Susceptibility and Disease Progressions Due to Difference in Awareness Level , 2016, Front. Microbiol..

[79]  Chenxue Yang,et al.  A Mathematical Model of Cancer Treatment by Radiotherapy , 2014, Comput. Math. Methods Medicine.

[80]  M. Pagano,et al.  Estimation of the reproductive number and the serial interval in early phase of the 2009 influenza A/H1N1 pandemic in the USA , 2009, Influenza and other respiratory viruses.