Ren [53] |
Develop SEIR model for imperfect treatment with age-dependent latency and relapse |
SEIR model |
TB infectious in latent period; age-dependence |
Basic |
Dependent on parameters |
Jabbari [54] |
To set up a model that can examine two TB strains (DS and DR) with multiple latent stages |
Mathematical compartmental model with compartments for latency stages |
The drug-sensitive strain will not play a role in the process of exogenous reinfection for the drug-resistant strain |
Basic |
Dependent on parameters |
Okuonghae [55] |
Study the effects of additional heterogeneities from the level of TB awareness on TB transmission dynamics and case detection rate |
Expanding [34] by dividing both susceptible and latently infected compartment by level of TB awareness |
Reasonable values and bounds for parameters such as transmission rate, recovery rate from the literature |
Effective |
Dependent on parameters such as active case finding rate and treatment rate |
Liu [56] |
Evaluate effect of treatment for TB |
Compartmental model with treatment and two latent periods incorporated |
Once the treatment of active TB cases is interrupted, there is no more treatment; specified model parameter values and their relationship with one another |
Basic |
Dependent on transmission coefficients |
Silva [57] |
Study optimal strategies for the controlling active TB infectious and persistent latent individuals |
Compartmental model considering reinfection and post-exposure interventions with the addition of early latent and persistent latent compartments |
Parameter values taken from the literature |
Basic |
Dependent on transmission coefficient |
Hu [58] |
Study the threshold dynamics of TB |
Compartmental model with periodic functions for reactivation rate and infection rate; include additional compartment for treated people that do not return to the hospital for examination |
NA |
Basic |
Dependent on transmission coefficient |
Emvudu [59] |
Address the problem of optimal control for TB transmission dynamics |
Compartmental model with an additional compartment for loss to follow-up |
Half of the parameter values were assumed; others taken from the Cameroon literature |
Basic |
Dependent on parameters such as transmission rate |
Sergeev [60] |
How drug-sensitive and drug-resistant strains mixed together can impacts long-term TB dynamics |
Compartmental with the three compartments for both latent and infected: drug-resistant, drug-sensitive and mixed strains |
Reasonable values for many parameters; few data exist to inform model parameters |
Basic; estimated for drug-resistant, drug-sensitive and mixed strains |
Dependent on model parameters |
Roeger [61] |
Model TB and HIV co-infection |
Compartmental model for joint dynamics of TB and HIV and compute independent reproductive numbers for the two diseases |
Probability of infection is the same for those treated with TB and those susceptible; assumed relationship among model parameters |
Overall R0 as the max of R0 for TB and HIV |
Dependent on model parameters |
Gerberry [62] |
Study the trade-off between BCG and detection, treatment of TB |
Compartmental model with additional compartments for latently infected and unvaccinated, latently infected and vaccinated; establish thresholds for basic R0
|
Throughout the duration of the vaccine's efficacy, latent TB completely undetectable |
Basic |
Dependent on model parameters |
Bhunu [63] |
Model HIV/AIDS and TB coinfection |
Compartmental model for TB, HIV separately without intervention; full model with intervention |
Parameter values from Central Statistics Office of Zimbabwe and literature; relationship amongst parameters in the model |
Basic |
Dependent on model parameters |
Bhunu [8] |
Model the effect of pre-exposure and post-exposure vaccines |
Compartmental model with additional compartments for susceptible (vaccinated or not) and latent (history of vaccine or not) |
Homogeneous mixing; recovered people would not develop disease from reinfection, but could be re-infected; parameter values taken from Central Statistics Office and literature |
Basic |
Dependent on model parameters |
Sharomi [64] |
Address the interaction between HIV and TB |
TB-only, HIV-only and full model analysed with both susceptible and latent compartments divided according to TB and HIV status |
Dually infected people could not transmit both diseases; some parameters taken from the literature, others assumed |
Basic |
Dependent on model parameters |
McCluskey [65] |
Address global stability of high dimensional TB model |
Use Lyapunov function to demonstrate the stability of the endemic equilibria in mathematical models for TB: SEIR, SEIS and SIR; fast and slow progression incorporated |
|
Basic |
No explicit estimate |
Martcheva [66] |
Address the issue of an infected person being subject to further contacts with infectious individuals—‘super infection’ |
Subdivide the latent stage into one where the disease progresses and one where the disease development is on hold |
Relationship among model parameters |
Basic |
No explicit estimate |
Aparicio [67] |
Express basic R0 as a function of cluster size |
Divide individuals into either active clusters or otherwise |
Homogeneous mixing |
Basic |
No explicit estimate; expressed as a function of household size |
Feng [68] |
Examine how exogenous reinfection changes the TB transmission dynamics |
Include additional parameters in the mathematical model to model exogenous reinfection |
Constant per capita removal rate to focus on the role of reinfection |
Basic |
No explicit estimate; analytical expression |
Beatriz [69] |
Assess the effects of heterogeneous infectivity |
Divide infective period into k stages |
Homogenous mixing; bilinear incidence rate |
Basic |
No explicit estimate; analytical expression |
Castillo-Chavez [70] |
Use an age-structure model to study the dynamics of TB |
Use age-specific parameters in the compartmental model; transmission dynamics studied for with and without vaccine |
Mixing between individuals is proportional to their age-dependent activity level; disease-induced death rate neglected |
Net and basic |
No explicit estimate; analytical expression |
Lietman [71] |
Test the hypothesis that exposure to TB leads to disappearance of leprosy |
Add in leprosy compartment in the mathematical model |
Cross-immunity is symmetric: same immunity for TB and leprosy |
Basic |
Dependent on R0 of leprosy and cross-protection rate |
Sanchez [72] |
Evaluate the effects of parameter estimation uncertainty on the value of R0
|
Latin hypercube sampling used on parameters in the compartmental model in Blower [72] to evaluate uncertainty of R0
|
Range for parameters in the compartmental model |
Sum of R0 for fast, slow and relapse |
Dependent on parameters in the model |
Gumel [10] |
Study the transmission dynamics of TB with multiple strains, in the presence of exogenous reinfection |
Included drug-sensitive and resistant strains in the compartmental model; exogenous reinfection incorporated |
Homogenous mixing |
Effective R0 for the two strains |
Dependent on parameters in the model |
Singer [73] |
Study the impact of different reinfection levels of latently infected individuals on TB transmission dynamics |
Compartmental model for heterogeneous population: one group more susceptible to infection than the other |
Parameter range uniformly distributed according to previous papers |
Basic |
No explicit estimate |
Trauer [74] |
Model TB transmission for highly endemic regions of the Asia-Pacific where HIV-coinfection is low |
Compartmental models with compartments for immunisation, latency, reinfection, drug-resistance, etc. |
Parameters fixed values according to papers and WHO |
Basic |
Dependent on parameters; computed as 8.34 for drug-susceptible and 5.84 for drug resistant at baseline |
Dye [75] |
To establish criteria for MDR-TB control |
Compartmental models with compartments for drug-susceptible, drug-resistant, treatment failure, etc. |
Parameters calculated from different populations |
Basic |
Dependent on parameters; best estimated of the model parameters yielded R0 = 1.6 (95% CI 1.02–2.67) |
Blower [76] |
Track the emergence and evolution of multiple strains of drug-resistant TB |
Non-compartmental mathematical model |
NA |
Basic |
Dependent on drug susceptibility of TB |
Blower [77] |
Model the transmission dynamics of TB |
Compartmental models with latently infected, infectious, non-infectious, recovered compartments |
Some model parameters assumed; some taken from references |
Basic; defined as the sum of slow progression, recent transmission and relapse |
Median of 4.47, range: 0.74–18.58 |
Blower [78] |
Understand, predict and control TB |
Compartmental models with drug-sensitive and drug-resistant compartments |
NA |
Basic |
Dependent on model parameters |
Aparicio [67] |
Evaluate homogeneous mixing and heterogeneous mixing models for TB |
Three types of compartmental models: a standard incidence homogenous mixing mode; a heterogeneous mixing model; an age-structured model |
Assumptions on model parameters |
Basic |
Dependent on model parameters |