Mathematical Model Of Tuberculosis Transmission Research Articles

Sensitivity analysis and random dynamics for a mathematical model of tuberculosis transmission

In this study, a recent mathematical model for the spread of tuberculosis disease will be analyzed under random conditions. The sensitivity of the basic reproduction number to the changes in the parameters will be analyzed using the forward normalized sensitivity index. Additionally, random disease transmission dynamics will be analyzed by using simulations of the random differential equation system. Random behavior of disease transmission such as expected compartment sizes and coefficients of variations will be investigated to comment on the randomness of the spread.

The potential impact of urine-LAM diagnostics on tuberculosis incidence and mortality: A modelling analysis

BackgroundLateral flow urine lipoarabinomannan (LAM) tests could offer important new opportunities for the early detection of tuberculosis (TB). The currently licensed LAM test, Alere Determine TB LAM Ag (‘LF-LAM’), performs best in the sickest people living with HIV (PLHIV). However, the technology continues to improve, with newer LAM tests, such as Fujifilm SILVAMP TB LAM (‘SILVAMP-LAM’) showing improved sensitivity, including amongst HIV-negative patients. It is important to anticipate the epidemiological impact that current and future LAM tests may have on TB incidence and mortality.Methods and findingsConcentrating on South Africa, we examined the impact that widening LAM test eligibility would have on TB incidence and mortality. We developed a mathematical model of TB transmission to project the impact of LAM tests, distinguishing ‘current’ tests (with sensitivity consistent with LF-LAM), from hypothetical ‘future’ tests (having sensitivity consistent with SILVAMP-LAM). We modelled the impact of both tests, assuming full adoption of the 2019 WHO guidelines for the use of these tests amongst those receiving HIV care. We also simulated the hypothetical deployment of future LAM tests for all people presenting to care with TB symptoms, not restricted to PLHIV. Our model projects that 2,700,000 (95% credible interval [CrI] 2,000,000–3,600,000) and 420,000 (95% CrI 350,000–520,000) cumulative TB incident cases and deaths, respectively, would occur between 2020 and 2035 if the status quo is maintained. Relative to this comparator, current and future LAM tests would respectively avert 54 (95% CrI 33–86) and 90 (95% CrI 55–145) TB deaths amongst inpatients between 2020 and 2035, i.e., reductions of 5% (95% CrI 4%–6%) and 9% (95% CrI 7%–11%) in inpatient TB mortality. This impact in absolute deaths averted doubles if testing is expanded to include outpatients, yet remains <1% of country-level TB deaths. Similar patterns apply to incidence results. However, deploying a future LAM test for all people presenting to care with TB symptoms would avert 470,000 (95% CrI 220,000–870,000) incident TB cases (18% reduction, 95% CrI 9%–29%) and 120,000 (95% CrI 69,000–210,000) deaths (30% reduction, 95% CrI 18%–44%) between 2020 and 2035. Notably, this increase in impact arises largely from diagnosis of TB amongst those with HIV who are not yet in HIV care, and who would thus be ineligible for a LAM test under current guidelines. Qualitatively similar results apply under an alternative comparator assuming expanded use of GeneXpert MTB/RIF (‘Xpert’) for TB diagnosis. Sensitivity analysis demonstrates qualitatively similar results in a setting like Kenya, which also has a generalised HIV epidemic, but a lower burden of HIV/TB coinfection. Amongst limitations of this analysis, we do not address the cost or cost-effectiveness of future tests. Our model neglects drug resistance and focuses on the country-level epidemic, thus ignoring subnational variations in HIV and TB burden.ConclusionsThese results suggest that LAM tests could have an important effect in averting TB deaths amongst PLHIV with advanced disease. However, achieving population-level impact on the TB epidemic, even in high-HIV-burden settings, will require future LAM tests to have sufficient performance to be deployed more broadly than in HIV care.

Analysis and simulation of a mathematical model of tuberculosis transmission in Democratic Republic of the Congo

According to the World Health Organization reports, tuberculosis (TB) remains one of the top 10 deadly diseases of recent decades in the world. In this paper, we present the modeling, analysis and simulation of a mathematical model of TB transmission in a population incorporating several factors and study their impact on the disease dynamics. The spread of TB is modeled by eight compartments including different groups, which are too often not taken into account in the projections of tuberculosis incidence. The rigorous mathematical analysis of this model is provided, the basic reproduction number (mathcal{R}_{0}) is obtained and used for TB dynamics control. The results obtained show that lost to follow-up and transferred individuals constitute a risk, but less than the cases carrying germs. Rapidly evolving latent/exposed cases are responsible for the incidence increasing in the short and medium term, while slower evolving latent/exposed cases will be responsible for the persistent long-term incidence and maintenance of TB and delay elimination in the population. The numerical simulations of the model show that, with certain parameters, TB will die out or sensibly reduce in the entire Democratic Republic of the Congo (DRC) population. The strategies on which the DRC’s health system is currently based to fight this disease show their weaknesses because the TB situation in the DRC remains endemic. But monitoring contact, detection of latent individuals and their treatment are actions to be taken to reduce the incidence of the disease and thus effectively control it in the population.

The potential impact of the COVID-19 pandemic on the tuberculosis epidemic a modelling analysis.

BackgroundRoutine services for tuberculosis (TB) are being disrupted by stringent lockdowns against the novel SARS-CoV-2 virus. We sought to estimate the potential long-term epidemiological impact of such disruptions on TB burden in high-burden countries, and how this negative impact could be mitigated.MethodsWe adapted mathematical models of TB transmission in three high-burden countries (India, Kenya and Ukraine) to incorporate lockdown-associated disruptions in the TB care cascade. The anticipated level of disruption reflected consensus from a rapid expert consultation. We modelled the impact of these disruptions on TB incidence and mortality over the next five years, and also considered potential interventions to curtail this impact.FindingsEven temporary disruptions can cause long-term increases in TB incidence and mortality. If lockdown-related disruptions cause a temporary 50% reduction in TB transmission, we estimated that a 3-month suspension of TB services, followed by 10 months to restore to normal, would cause, over the next 5 years, an additional 1⋅19 million TB cases (Crl 1⋅06–1⋅33) and 361,000 TB deaths (CrI 333–394 thousand) in India, 24,700 (16,100–44,700) TB cases and 12,500 deaths (8.8–17.8 thousand) in Kenya, and 4,350 (826–6,540) cases and 1,340 deaths (815–1,980) in Ukraine. The principal driver of these adverse impacts is the accumulation of undetected TB during a lockdown. We demonstrate how long term increases in TB burden could be averted in the short term through supplementary “catch-up” TB case detection and treatment, once restrictions are eased.InterpretationLockdown-related disruptions can cause long-lasting increases in TB burden, but these negative effects can be mitigated with rapid restoration of TB services, and targeted interventions that are implemented as soon as restrictions are lifted.FundingUSAID and Stop TB Partnership

The Potential Impact of the COVID-19 Pandemic on the Tuberculosis Epidemic: A Modelling Analysis

Background: Routine services for tuberculosis (TB) are being disrupted by stringent lockdowns against the novel SARS-CoV-2 virus. We sought to estimate the potential long-term epidemiological impact of such disruptions on TB burden in high-burden countries, and how this negative impact could be mitigated. Methods: We adapted mathematical models of TB transmission in three high-burden countries (India, Kenya and Ukraine) to incorporate lockdown-associated disruptions in the TB care cascade. The anticipated level of disruption reflected consensus from a rapid expert consultation. We modelled the impact of these disruptions on TB incidence and mortality over the next five years, and also considered potential interventions to curtail this impact. Results: Even temporary disruptions can cause long-term increases in TB incidence and mortality. We estimated that a 3-month lockdown, followed by 10 months to restore normal TB services, would cause, over the next 5 years, an additional 1.65 million TB cases (Crl 1.49– 1.85) and 438,000 TB deaths (CrI 403 – 483 thousand) in India, 41,400 (28,900–62,200) TB cases and 14,800 deaths (10.5 – 19.2 thousand) in Kenya, and 7,960 (6,250 – 9,880) cases and 2,050 deaths (1,610 - 2,360) in Ukraine. However, any such negative impacts could be averted through supplementary “catch-up” TB case detection and treatment, once restrictions are eased. Interpretation: Lockdown-related disruptions can cause long-lasting increases in TB burden, but these negative effects can be mitigated with targeted interventions implemented rapidly once lockdowns are lifted.Funding Statement: USAID and Stop TB Partnership.Declaration of Interests: The authors declare no conflict of interest.

A mathematical model of tuberculosis transmission in Thailand with vaccination and anti-drug treatment

A mathematical model of tuberculosis transmission in Thailand with vaccination and anti-drug treatment

Strategic Planning for Tuberculosis Control in the Republic of Fiji.

The tuberculosis (TB) health burden in Fiji has been declining in recent years, although challenges remain in improving control of the diabetes co-epidemic and achieving adequate case detection across the widely dispersed archipelago. We applied a mathematical model of TB transmission to the TB epidemic in Fiji that captured the historical reality over several decades, including age stratification, diabetes, varying disease manifestations, and incorrect diagnoses. Next, we simulated six intervention scenarios that are under consideration by the Fiji National Tuberculosis Program. Our findings show that the interventions were able to achieve only modest improvements in disease burden, with awareness raising being the most effective intervention to reduce TB incidence, and treatment support yielding the highest impact on mortality. These improvements would fall far short of the ambitious targets that have been set by the country, and could easily be derailed by moderate increases in the diabetes burden. Furthermore, the effectiveness of the interventions was limited by the extensive pool of latent TB infection, because the programs were directed at only active cases, and thus were unlikely to achieve the desired reductions in burden. Therefore, it is essential to address the co-epidemic of diabetes and treat people with latent TB infection.

Strategies for ending tuberculosis in the South-East Asian Region: A modelling approach.

Background & objectives:To support recent political commitments to end tuberculosis (TB) in the World Health Organization South-East Asian Region (SEAR), there is a need to understand by what measures, and with what investment, these goals could be reached. These questions were addressed by using mathematical models of TB transmission by doing the analysis on a country-by-country basis in SEAR.Methods:A dynamical model of TB transmission was developed, in consultation with each of the 11 countries in the SEAR. Three intervention scenarios were examined: (i) strengthening basic TB services (including private sector engagement), (ii) accelerating TB case-finding and notification, and (iii) deployment of a prognostic biomarker test by 2025, to guide mass preventive therapy of latent TB infection. Each scenario was built on the preceding ones, in successive combination.Results:Comprehensive improvements in basic TB services by 2020, in combination with accelerated case-finding to increase TB detection by at least two-fold by 2020, could lead to a reduction in TB incidence rates in SEAR by 67.3 per cent [95% credible intervals (CrI) 65.3-69.8] and TB deaths by 80.9 per cent (95% CrI 77.9-84.7) in 2035, relative to 2015. These interventions alone would require an additional investment of at least US$ 25 billion. However, their combined effect is insufficient to reach the end TB targets of 80 per cent by 2030 and 90 per cent by 2035. Model projections show how additionally, deployment of a biomarker test by 2025 could end TB in the region by 2035. Targeting specific risk groups, such as slum dwellers, could mitigate the coverage needed in the general population, to end TB in the Region.Interpretation & conclusions:While the scale-up of currently available strategies may play an important role in averting TB cases and deaths in the Region, there will ultimately be a need for novel, mass preventive measures, to meet the end TB goals. Achieving these impacts will require a substantial escalation in funding for TB control in the Region.

A numerical algorithm of parameter identification in mathematical model of tuberculosis transmission with control programs

A numerical algorithm of parameter identification in mathematical model of tuberculosis transmission with control programs

Benefits of continuous isoniazid preventive therapy may outweigh resistance risks in a declining tuberculosis/HIV coepidemic.

Extending the duration of isoniazid preventive therapy (IPT) among people living with HIV (PLHIV) may improve its effectiveness at both individual and population levels, but could also increase selective pressure in favor of isoniazid-resistant tuberculosis (TB) strains. The objective of this study was to determine the relative importance of these two effects. Transmission dynamic model. We created a mathematical model of TB transmission incorporating HIV incidence and treatment, mixed strain latent TB infections, and four different phenotypes of TB drug resistance (pan-susceptible, isoniazid monoresistant, rifampicin monoresistant, and multidrug resistant). We used this model to project the effects of IPT duration on the incidence of isoniazid-sensitive and isoniazid-resistant TB as well as mortality among PLHIV. We evaluated the sensitivity of our baseline model, which was calibrated to data from Botswana, to different assumptions about the future trajectory of the TB epidemic. Our model suggests that, in the context of a declining TB epidemic such as that currently observed in Botswana, the incidence and mortality benefits of continuous IPT for PLHIV are likely to outweigh the potential resistance risks associated with long-duration IPT. However, should TB epidemics fail to remain in control, as was observed during the initial emergence of HIV, the selective pressure imposed by widespread use of continuous IPT on isoniazid-resistant TB incidence may erode its initial benefits. Resistance concerns are likely insufficient to rule out use of continuous IPT when coupled with effective TB treatment, case finding, and HIV control.

Feasibility of achieving the 2025 WHO global tuberculosis targets in South Africa, China, and India: a combined analysis of 11 mathematical models.

SummaryBackgroundThe post-2015 End TB Strategy proposes targets of 50% reduction in tuberculosis incidence and 75% reduction in mortality from tuberculosis by 2025. We aimed to assess whether these targets are feasible in three high-burden countries with contrasting epidemiology and previous programmatic achievements.Methods11 independently developed mathematical models of tuberculosis transmission projected the epidemiological impact of currently available tuberculosis interventions for prevention, diagnosis, and treatment in China, India, and South Africa. Models were calibrated with data on tuberculosis incidence and mortality in 2012. Representatives from national tuberculosis programmes and the advocacy community provided distinct country-specific intervention scenarios, which included screening for symptoms, active case finding, and preventive therapy.FindingsAggressive scale-up of any single intervention scenario could not achieve the post-2015 End TB Strategy targets in any country. However, the models projected that, in the South Africa national tuberculosis programme scenario, a combination of continuous isoniazid preventive therapy for individuals on antiretroviral therapy, expanded facility-based screening for symptoms of tuberculosis at health centres, and improved tuberculosis care could achieve a 55% reduction in incidence (range 31–62%) and a 72% reduction in mortality (range 64–82%) compared with 2015 levels. For India, and particularly for China, full scale-up of all interventions in tuberculosis-programme performance fell short of the 2025 targets, despite preventing a cumulative 3·4 million cases. The advocacy scenarios illustrated the high impact of detecting and treating latent tuberculosis.InterpretationMajor reductions in tuberculosis burden seem possible with current interventions. However, additional interventions, adapted to country-specific tuberculosis epidemiology and health systems, are needed to reach the post-2015 End TB Strategy targets at country level.FundingBill and Melinda Gates Foundation

The Potential Impact of Up-Front Drug Sensitivity Testing on India's Epidemic of Multi-Drug Resistant Tuberculosis.

BackgroundIn India as elsewhere, multi-drug resistance (MDR) poses a serious challenge in the control of tuberculosis (TB). The End TB strategy, recently approved by the world health assembly, aims to reduce TB deaths by 95% and new cases by 90% between 2015 and 2035. A key pillar of this approach is early diagnosis of tuberculosis, including use of higher-sensitivity diagnostic testing and universal rapid drug susceptibility testing (DST). Despite limitations of current laboratory assays, universal access to rapid DST could become more feasible with the advent of new and emerging technologies. Here we use a mathematical model of TB transmission, calibrated to the TB epidemic in India, to explore the potential impact of a major national scale-up of rapid DST. To inform key parameters in a clinical setting, we take GeneXpert as an example of a technology that could enable such scale-up. We draw from a recent multi-centric demonstration study conducted in India that involved upfront Xpert MTB/RIF testing of all TB suspects.ResultsWe find that widespread, public-sector deployment of high-sensitivity diagnostic testing and universal DST appropriately linked with treatment could substantially impact MDR-TB in India. Achieving 75% access over 3 years amongst all cases being diagnosed for TB in the public sector alone could avert over 180,000 cases of MDR-TB (95% CI 44187 – 317077 cases) between 2015 and 2025. Sufficiently wide deployment of Xpert could, moreover, turn an increasing MDR epidemic into a diminishing one. Synergistic effects were observed with assumptions of simultaneously improving MDR-TB treatment outcomes. Our results illustrate the potential impact of new and emerging technologies that enable widespread, timely DST, and the important effect that universal rapid DST in the public sector can have on the MDR-TB epidemic in India.

Tuberculosis control and economic recession: longitudinal study of data from 21 European countries, 1991-2012.

ObjectiveTo investigate whether the economic recession affected the control of tuberculosis in the European Union.MethodsMultivariate regression models were used to quantify the association between gross domestic product, public health expenditure and tuberculosis case detection rates, using data from 21 European Union member states (1991–2012). The estimated changes in case detection attributable to the recession were combined with mathematical models of tuberculosis transmission, to project the potential influence of the recession on tuberculosis epidemiology until 2030.FindingsBetween 1991 and 2007, detection rates for sputum-smear-positive tuberculosis in the European Union were stable at approximately 85%. During the economic recession (2008–2011) detection rates declined by a mean of 5.22% (95% confidence interval, CI: 2.54–7.90) but treatment success rates showed no significant change (P = 0.62). A fall in economic output of 100 United States dollars per capita was associated with a 0.22% (95% CI: 0.05–0.39) mean reduction in the tuberculosis case detection rate. An equivalent fall in spending on public health services was associated with a 2.74% (95% CI: 0.31–5.16) mean reduction in the detection rate. Mathematical models suggest that the recession and consequent austerity policies will lead to increases in tuberculosis prevalence and tuberculosis-attributable mortality that are projected to persist for over a decade.ConclusionAcross the European Union, reductions in spending on public health services appear to have reduced tuberculosis case detection and to have increased the long-term risk of a resurgence in the disease.

A mathematical model of tuberculosis transmission with heterogeneity in disease susceptibility and progression under a treatment regime for infectious cases

The effect of difference in susceptibility on the dynamics of tuberculosis is an ongoing study. Several genes in TB co-receptors (e.g. HLA and non-HLA) have been correlated with susceptibility and resistance to tuberculosis and rate of progression to active TB. In this paper, we present a novel mathematical model that distinguishes between susceptibility amongst the population. The model classifies the susceptibles as having no, partial or full natural resistance to tuberculosis and the latently infecteds as rapid, normal or very slow (or no) progressors to active TB depending on the genes. The goal of this paper is to investigate the impact of such heterogeneity on the spread of tuberculosis and to identify key parameters that could be used in understanding these heterogeneities more fully. We derived the reproduction number RT for the model and examine the relative contributions to RT from the three latently infected classes as well as the infectious classes. The effect of treatment under the heterogeneity is also examined.

How host heterogeneity governs tuberculosis reinfection?

Recurrent episodes of tuberculosis (TB) can be due to relapse of latent infection or exogenous reinfection, and discrimination is crucial for control planning. Molecular genotyping of Mycobacterium tuberculosis isolates offers concrete opportunities to measure the relative contribution of reinfection in recurrent disease. Here, a mathematical model of TB transmission is fitted to data from 14 molecular epidemiology studies, enabling the estimation of relevant epidemiological parameters. Meta-analysis reveals that rates of reinfection after successful treatment are higher than rates of new TB, raising an important question about the underlying mechanism. We formulate two alternative mechanisms within our model framework: (i) infection increases susceptibility to reinfection or (ii) infection affects individuals differentially, thereby recruiting high-risk individuals to the group at risk for reinfection. The second mechanism is better supported by the fittings to the data, suggesting that reinfection rates are inflated through a population phenomenon that occurs in the presence of heterogeneity in individual risk of infection. As a result, rates of reinfection are higher when measured at the population level even though they might be lower at the individual level. Finally, differential host recruitment is modulated by transmission intensity, being less pronounced when incidence is high.

A Probabilistic Transmission and Population Dynamic Model to Assess Tuberculosis Infection Risk

The purpose of this study was to examine tuberculosis (TB) population dynamics and to assess potential infection risk in Taiwan. A well-established mathematical model of TB transmission built on previous models was adopted to study the potential impact of TB transmission. A probabilistic risk model was also developed to estimate site-specific risks of developing disease soon after recent primary infection, exogenous reinfection, or through endogenous reactivation (latently infected TB) among Taiwan regions. Here, we showed that the proportion of endogenous reactivation (53-67%) was larger than that of exogenous reinfection (32-47%). Our simulations showed that as epidemic reaches a steady state, age distribution of cases would finally shift toward older age groups dominated by latently infected TB cases as a result of endogenous reactivation. A comparison of age-weighted TB incidence data with our model simulation output with 95% credible intervals revealed that the predictions were in an apparent agreement with observed data. The median value of overall basic reproduction number (R₀) in eastern Taiwan ranged from 1.65 to 1.72, whereas northern Taiwan had the lowest R₀ estimate of 1.50. We found that total TB incidences in eastern Taiwan had 25-27% probabilities of total proportion of infected population exceeding 90%, whereas there were 36-66% probabilities having exceeded 20% of total proportion of infected population attributed to latently infected TB. We suggested that our Taiwan-based analysis can be extended to the context of developing countries, where TB remains a substantial cause of elderly morbidity and mortality.