Table 3.
Name of first author [publication] | Location, time of data | Type of data | Objective | Methods | Assumptions | Reproductive number type | Estimated reproductive number |
---|---|---|---|---|---|---|---|
Zhao [34] | China, 2005–2016 | CDC data | To investigate the impact of age on TB transmission | SEIR model with age structure; use least squares to get parameters that align with TB data in China; use Latin hypercube sampling to get CI | Although the susceptible compartment was stratified by age, the other compartments were not age-stratified thus assuming no difference in age for those compartments | Basic | 1.786 (95% CI 1.775–1.796) |
Liu [35] | China, 2004–2014 | Annual TB case data | To use modelling to investigate the impact of different vaccination strategies (constant or pulse BCG) on TB transmission | Compartmental models with vaccination compartments | Assumptions made for all parameter values | Basic | 1.19 |
Yang [36] | Shaanxi, China, 2004–2012 | Notifiable active TB cases by month | Study the seasonality impact on TB transmission dynamics | A seasonality TB compartmental model: subjects either entered latent or diseased compartment; contact rate, reactivation rate and disease-induced death rate are periodic continuous functions | Parameter values for recruitment rate, natural death rate, recovery rate | Basic | Dependent on parameter values |
Nebenzahl-Guimaraes [28] | The Netherlands, 1993–2011 | Surveillance and RFLP data | Determine if mycobacterial lineages affect infection risk, clustering and disease progression among Mycobacterium tuberculosis cases | Descriptive and regression approach; DNA fingerprinting to link cases | All secondary cases captured in surveillance data; genetic matching accurately reflects transmission patterns | Effective | Range: 0.17–1.04 |
Narula [37] | India, 2006–2011 | Quarterly reported data from Central TB Division | Estimate basic R0 for TB | Compartmental model with Bayesian melding technique to estimate parameters; Susceptible, latent, infected compartments instead of SIR | Some parameter values assumed with reference in the differential equations | Basic | 0.92, averaged for India overall with range 0.72–0.98 |
Zhang [38] | China, 2005–2012 | Monthly case reporting data from CDC | Estimate effective R0 of TB by year | Compartmental model adding hospitalised compartment; Chi-square test for optimal parameters | An upper bound for number of initially susceptible people, natural death rate, initial number of latent individuals | Effective | Range from 3.318 to 4.302 from year 2005 to 2012 |
Ypma [39] | The Netherlands, 1993–2007 | RFLP data | Explore the high heterogeneity in the number of secondary cases caused per infectious individual for TB | Model ‘superspreading’ parameter as a negative binomial distribution | Immigrants who have been in the country for less than 6 months at diagnosis are index cases themselves | Fingerprint reproductive number as a function of the effective reproductive number and the probability that the fingerprint of the infected person is different than its infector | 0.48 (95% CI 0.44–0.59) |
Andrews [40] | Cape Town, South Africa, 2011 | Carbon dioxide data, public transit usage data from national survey | Estimate risk of TB transmission on 3 modes of public transit | Modified Wells-Riley model for airborne disease transmission | Duration of infectiousness of 1 year; used TB and HIV parameters from studies in the same area; natural history parameters from the literature | Basic | Dependent on duration of infectiousness and frequency of transit usage |
Okuonghae [41] | Benin city, Nigeria, 2008 | Survey data | Assess how control strategies on addressing TB transmission parameters can minimise incidence | Compartmental model adding compartments of disease awareness level, identified infectiousness | Model parameter values such as recruitment rate, recovery rate from the literature | Basic, under treatment | Dependent on parameter values |
Liao [42] | Taiwan, 2005–2010 | Monthly data from CDC | Estimate MDR-TB infection risk | Mathematical probabilistic two-strain model with compartments for drug-sensitive and drug-resistant subjects; dose–response model for relationship between R0 and total proportion of infected population | Some model parameter values from data, some from the literature; assumed 0.99 of people latently infected were drug sensitive and 0.01 were drug resistant | Basic |
Hwalien County: 0.89 (95% CI 0.23–2.17) for drug sensitive; 0.38 (95% CI 0.05–1.30) for multi-drug resistant; Taitung County: 0.94 (95% CI 0.24–2.28) for drug sensitive; 0.38 (95% CI 0.05–1.33) for multi-drug resistant; Pingtung County: 0.85 (95% CI 0.21–2.08) for drug sensitive; 0.34 (95% CI 0.04–1.13) for multi-drug resistant; Taipei City: 0.84 (95% CI 0.21–2.00) for drug sensitive; 0.30 (95% CI 0.04–0.97) for multi-drug resistant; |
Liao [43] | Taiwan, 2004–2008; selected three areas with the highest incidence, one with the lowest incidence | Monthly disease burden TB data from Taiwan CDC | Examine TB population dynamics and assess potential infection risk | Compartmental model with susceptible, latently infected, infectious, non-infectious and recovered compartments; incorporated reactivation, relapse and reinfection | Some parameter values taken from the literature, some estimated from data | Basic, estimated as sum of fast, slow and relapse | Highest R0 total in Hwalien: 1.65 with 95th percentile range 0.45–6.45; Taipei lowest at 1.5 (0.45–4.98); Taitung: 1.72; Pingtung: 1.65 |
Liu [44] | China, 2000–2008 | Data from the National Bureau of Statistics | Incorporate migration to study TB transmission | SEIR compartments for rural residents, migrant workers and urban population | Model parameters calculated from website data; migration rates | Basic | No explicit estimate |
Borgdorff [29] | The Netherlands, 1993–2007 | RFLP data | Determine to what extent tuberculosis trends in the Netherlands depend on secular trend, immigration and recent transmission | DNA fingerprinting to link cases | All secondary cases captured in surveillance data; genetic matching accurately reflects transmission patterns | Basic | 0.24 (95% CI 0.21–0.26) |
Liu [45] | China, Jan, 2005–Dec, 2008 | Monthly notification data from Ministry of Health | Develop a model incorporating seasonality and define basic reproduction ratio | Used periodic infection rate and reactivation rate to incorporate seasonality in the compartmental model; considered fast and slow progression | Parameters such as recruitment rate, natural death rate were assumed to be constants; some parameter values assumed and some taken from the literature | Basic | Dependent on parameter values with range 0.4–2.6 |
Brooks-Pollock [46] | Ukraine, 1959 and 2006 | Mortality data | Explore the effect of age structure on TB infection and disease prevalence, basic reproductive number and impact of intervention | Basic SEIR mathematical model with assumptions about survivorship | A survivorship function which could be described in terms of age and life expectancy | Basic | Dependent on progression rate with range 0–0.85 |
Basu [47] | KwaZulu-Natal, South Africa | Extensively drug-resistant TB data (XDR-TB) | Model XDR-TB transmission dynamics | Model XDR-TB incorporating the existing XDR detection rate and treatment system | Even mixing of air; range of key parameters in the model | Effective | 1.97, range 0.7–4.6; 1.23, range 0.4–3.1 when combining screening and therapy; 1.38, range 0.6–3.3 with South African strategic plan alone. |
Furuya [7] | Japan, 2000–2005 | Exposure data | Quantify the risk of TB infection in an internet café where people without homes stayed overnight | Wells-Riley model to estimate the reproductive number | Patients stayed in a confined space for 150 days; some values in the Wells-Riley equation assumed, others from the literature | Estimated as a function of exposure period | Dependent on exposure period |
Long [9] | Southern India, 2004–2006 | HIV-TB co-epidemics data | Model HIV-TB co-epidemics and explore hypothetical treatment effect | First model: susceptibility to either or both diseases compartments; second model: SII*SEI | A linear relationship between treatment levels and the associated parameters; model parameters from the literature | Basic | R = 3.55 when no active treatment for TB |
Borgdorff [48] | The Netherlands, 1995–2002 | RFLP data | Assess progress towards TB elimination | DNA fingerprinting to link cases; survival analysis | All secondary cases captured in surveillance data; genetic matching accurately reflects transmission patterns | Basic | Dutch index cases: 0.23, non-Dutch index cases: 0.25 |
Borgdorff [49] | San Francisco, USA, 1991–1996 | RFLP data | Determine tuberculosis transmission dynamics in San Francisco and its association with country of birth and ethnicity | Define effective reproductive number as a function of transmission index, which is a function of number of secondary cases and potential source cases in a given subgroup | Each cluster originates from a single source case in the database; either the first case of a cluster was its source case, or that the probability of being a source case declined exponentially over time by 0.77% per day | Effective, recent transmission | 0.24 (95% CI 0.17–0.31) |
Davidow [50] | New York City, 1989–1993 | TB and AIDS surveillance data | Evaluate the importance of recent M. tuberculosis transmission | Estimated # of TB infectious cases 1 year ago and computed short-term R0; R0 = the average # of new infections caused by each case per year of infectiousness*the average duration of infectiousness*the probability of progressing to active TB within 1 year after infection | Some clinical assumptions; parameter values in equation taken from the literature or calculated from neighbourhood-specific data | Short-term | No explicit estimates; focused on percentage of TB cases due to infection 1 year ago |
Vynnycky [51] | England and Wales, 1900 | Surveillance data; age and time-specific mortality rates | Describe transmission dynamics of all forms of pulmonary TB | Age-structured mathematical model with compartments for endogenous and exogenous diseases | General relationship between: first primary episode and age at infection, risk of exogenous disease and age at reinfection, endogenous disease and current age; risk of reinfection and first infection are identical; parameter values from the literature | Basic and net which is the same as effective | Net R at about 1 from 1900–1950; basic R0 declined from about 3 in 1900, reached 2 by 1950, and first fell below 1 in about 1960 |
Salpeter [52] | USA, 1930–1995 | Case rates, correction for rates before 1975 | Estimate time delay from infection to disease and R | Estimate R as a function of case rate and the shape of the delay function | R and case rate constant with calendar time t; incidence rate of latent infection is independent of the age | Effective | 0.55, range 0.4–0.7 in sensitivity analysis |
Borgdorff [27] | Netherlands, 1993–1995 | RFLP data | Quantifying transmission of TB between and within nationalities | Effective R0 estimated as a function of transmission index | Probability of a patient being the source of a cluster was proportional to the incidence rate of potential sources times the probability that a potential source would give rise to a cluster | Effective | 0.26, 95% CI (0.20–0.32); also estimated for different nationalities |