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Abstract This study has been carried out using a novel mathematical model on the dynamics of tuberculosis (TB) transmission considering vaccination, endogenous re-activation of the dormant infection, and exogenous re-infection. We can comprehend the behavior of TB under the influence of vaccination from this article. We compute the basic reproduction number ( $${\mathcal {R}}_0$$ R 0 ) as well as the vaccination reproduction number ( $${\mathcal {R}}_v$$ R v ) using the next-generation matrix (NGM) approach. The theoretical analysis demonstrates that the disease-free equilibrium point is locally asymptotically stable, and the fractional order system is Ulam–Hyers type stable. We perform numerical simulation of our model using the Adams-Bashforth 3-step method to verify the theoretical results and to show the model outputs graphically. By performing data fitting, we observe that our formulated model produces results that closely match real-world data. Our findings indicate that vaccinating a limited segment of the population can effectively eradicate the disease. The numerical simulations also show that vaccination can reduce the number of susceptible and infectious individuals in the population. Moreover, the graphical representations illustrate that the number of infected individuals rises due to both exogenous reinfection and endogenous reactivation.

This study has been carried out using a novel mathematical model on the dynamics of tuberculosis (TB) transmission considering vaccination, endogenous re-activation of the dormant infection, and exogenous re-infection. We can comprehend the behavior of TB under the influence of vaccination from this article. We compute the basic reproduction number ( R 0 ) as well as the vaccination reproduction number ( R v ) using the next-generation matrix (NGM) approach. The theoretical analysis demonstrates that the disease-free equilibrium point is locally asymptotically stable, and the fractional order system is Ulam–Hyers type stable. We perform numerical simulation of our model using the Adams-Bashforth 3-step method to verify the theoretical results and to show the model outputs graphically. By performing data fitting, we observe that our formulated model produces results that closely match real-world data. Our findings indicate that vaccinating a limited segment of the population can effectively eradicate the disease. The numerical simulations also show that vaccination can reduce the number of susceptible and infectious individuals in the population. Moreover, the graphical representations illustrate that the number of infected individuals rises due to both exogenous reinfection and endogenous reactivation. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear mathematical model for tuberculosis transmission, which incorporates multiple saturated exogenous reinfections, is proposed and explored. The existence of disease-free and endemic steady states is investigated. Disease-free equilibrium (DFE) is locally asymptotically stable (LAS) but not globally asymptotically stable (GAS) when the basic reproduction number, ℛ 0 < 1. However, it is GAS only when there is no exogenous reinfection. The local asymptotic stability and global asymptotic stability of the unique endemic equilibrium point (EEP) are established under certain conditions when ℛ 0 > 1. Further, the EEP is GAS when ℛ 0 > 1 , provided there is no exogenous reinfection. When ℛ 0 is below unity, the presence of multiple endemic equilibria is found which leads to backward bifurcation. It is demonstrated that the system encounters a Hopf-bifurcation when the transmission rate β crosses a critical value, resulting in the formation of limit cycles, i.e. periodic solutions bifurcate around the EEP when β passes a critical value. The stability and direction of Hopf-bifurcation are also studied. The results of the analytical work are validated through numerical simulations. A numerical simulation illustrates that EEP losses its stability via Hopf-bifurcation for specific parameters. However, when the bifurcation parameter β is increased further, the EEP regains its stability. In addition, Hopf-bifurcation occurs due to exogenous reinfection rates p and . Thus, our model shows some important nonlinear dynamical behaviors. [ABSTRACT FROM AUTHOR]

COVID-19 and Tuberculosis (TB) are among the major global public health problems and diseases with major socioeconomic impacts. The dynamics of these diseases are spread throughout the world with clinical similarities which makes them difficult to be mitigated. In this study, we formulate and analyze a mathematical model containing several epidemiological characteristics of the co-dynamics of COVID-19 and TB. Sufficient conditions are derived for the stability of both COVID-19 and TB sub-models equilibria. Under certain conditions, the TB sub-model could undergo the phenomenon of backward bifurcation whenever its associated reproduction number is less than one. The equilibria of the full TB-COVID-19 model are locally asymptotically stable, but not globally, due to the possible occurrence of backward bifurcation. The incorporation of exogenous reinfection into our model causes effects by allowing the occurrence of backward bifurcation for the basic reproduction number R0 η∗). The analytical results show that reducing R0

COVID-19 and Tuberculosis (TB) are among the major global public health problems and diseases with major socioeconomic impacts. The dynamics of these diseases are spread throughout the world with clinical similarities which makes them difficult to be mitigated. In this study, we formulate and analyze a mathematical model containing several epidemiological characteristics of the co-dynamics of COVID-19 and TB. Sufficient conditions are derived for the stability of both COVID-19 and TB sub-models equilibria. Under certain conditions, the TB sub-model could undergo the phenomenon of backward bifurcation whenever its associated reproduction number is less than one. The equilibria of the full TBCOVID-19 model are locally asymptotically stable, but not globally, due to the possible occurrence of backward bifurcation. The incorporation of exogenous reinfection into our model causes effects by allowing the occurrence of backward bifurcation for the basic reproduction number R0 < 1 and the exogenous reinfection rate greater than a threshold (h > h*). The analytical results show that reducing R0 < 1 may not be sufficient to eliminate the disease from the community. The optimal control strategies were proposed to minimize the disease burden and related costs. The existence of optimal controls and their characterization are established using Pontryagin's Minimum Principle. Moreover, different numerical simulations of the control induced model are carried out to observe the effects of the control strategies. It reveals the usefulness of the optimization strategies in reducing COVID-19 infection and the co-infection of both diseases in the community. [ABSTRACT FROM AUTHOR]

Background: Although phenotypic drug susceptibility testing (DST) of Mycobacterium tuberculosis (Mtb) takes up to 6–8 weeks, little is known about how drug susceptibility is affected during this period. Methods: We performed a prospective cohort study to investigate the development of drug resistance (DR) during turnaround time (TAT), including 359 pulmonary tuberculosis (PTB) patients with a baseline DST result of an Mtb isolate collected at TB diagnosis and a follow-up DST result of an Mtb isolate collected when baseline DST result was available between 2013 and 2018. Whole-genome sequencing (WGS) was used to differentiate between acquired drug resistance, exogenous reinfection, and mixed infection. Results: Among the studied patients, during TAT for DST, 116 (32.3%) developed DR to four first-line drugs (rifampicin, isoniazid, pyrazinamide, ethambutol). Among 116 pairs of isolates included for WGS, 21 pairs were classified as acquired drug resistance with single nucleotide polymorphisms (SNPs) differences less than 12. Four pairs with an intermediate SNPs differences displayed minor differences in related genotypes and were assessed as mixed infection. The remaining 91 pairs had high SNPs differences consistent with exogenous reinfection. Conclusions: The exogenous reinfection of drug-resistant strains played a vital role in the development of DR of Mtb isolates during TAT for DST, highlighting the need for both rapid DST methods and improved infection control.

Little is known about how additional second-line drug resistance emerges during multidrug-resistant tuberculosis (MDR-TB) treatment. The present study aimed to investigate the influence of microevolution, exogenous reinfection and mixed infection on second-line drug resistance during the recommended 2-year MDR-TB treatment. Individuals with MDR-TB were enrolled between 2013 and 2016 in a multicentre prospective observational cohort study and were followed up for 2 years until treatment completion. Whole-genome sequencing (WGS) was applied for serial Mycobacterium tuberculosis isolates from study participants throughout the treatment, to study the role of microevolution, exogenous reinfection and mixed infection in the development of second-line drug resistance. Of the 286 enrolled patients with MDR-TB, 63 (22.0%) M. tuberculosis isolates developed additional drug resistance during the MDR-TB treatment, including 5 that fulfilled the criteria of extensively drug-resistant TB. By comparing WGS data of serial isolates retrieved from the patients throughout treatment, 41 (65.1%) of the cases of additional second-line drug resistance were the result of exogenous reinfection, 18 (28.6%) were caused by acquired drug resistance, i.e. microevolution, while the remaining 4 (6.3%) were caused by mixed infections with drug-resistant and drug-susceptible strains. In multivariate analysis, previous TB treatment (adjusted hazard ratio (aHR) 2.51, 95% CI 1.51–4.18), extensive disease on chest X-ray (aHR 3.39, 95% CI 2.03–5.66) and type 2 diabetes mellitus (aHR 4.00, 95% CI 2.22–7.21) were independent risk factors associated with the development of additional second-line drug resistance. A large proportion of additional second-line drug resistance emerging during MDR-TB treatment was attributed to exogenous reinfection, indicating the urgency of infection control in health facilities as well as the need for repeated drug susceptibility testing throughout MDR-TB treatment. [ABSTRACT FROM AUTHOR]

Background Previously treated (ie, recurrent) tuberculosis (TB) cases account for approximately 7%–8% of incident TB globally and in Singapore. Molecular fingerprinting has enabled the differentiation of these patients into relapsed or reinfection cases. Methods Patient demographics, disease characteristics, and treatment information were obtained from the national TB notification registry and TB Control Unit. We performed a retrospective, case-control study to evaluate factors associated with recurrent TB disease in Singapore citizens and permanent residents with culture-positive TB from 2006 to 2013 and who developed a second episode of culture-positive TB up to 2016 using multivariable logistic regression analyses. Results Ninety-one cases with culture-positive first and recurrent TB disease episodes were identified. Recurrent TB was associated with age ≥60 years (adjusted odds ratio [aOR], 1.98 [95% confidence interval {CI}, 1.09–3.61), male sex (aOR, 2.29 [95% CI, 1.22–4.51]), having concomitant pulmonary and extrapulmonary TB (aOR, 3.10 [95% CI, 1.59–6.10]) and extrapulmonary TB alone (aOR, 3.82 [95% CI, 1.12–13.31]), and was less likely in non-Malays (aOR, 0.52 [95% CI,.27–.99]). DNA fingerprinting results for both episodes in 49 cases differentiated these into 28 relapsed and 21 reinfection cases. Relapse was associated with having concomitant pulmonary and extrapulmonary TB (aOR, 9.24 [95% CI, 2.50–42.42]) and positive sputum acid-fast bacilli smear (aOR, 3.95 [95% CI, 1.36–13.10]). Conclusions Relapse and reinfection contributed to 57% and 43%, respectively, of recurrent TB in Singapore. Our study highlights the underappreciated association of concomitant pulmonary and extrapulmonary TB as a significant risk factor for disease relapse. [ABSTRACT FROM AUTHOR]

In this article, a novel fractional order model has been introduced in Caputo sense for HIV-TB co-infection in the presence of exogenous reinfection and recurrent TB along with the treatment for both HIV and TB. The main aim of considering the fractional order model is to incorporate the memory effect of both diseases. We have analyzed both sub-models separately with fractional order. The basic reproduction number, which measures the contagiousness of the disease, is determined. The HIV sub-model is shown to have a locally asymptotically stable disease-free equilibrium point when the corresponding reproduction number, R H , is less than unity, whereas, for R H > 1 , the endemic equilibrium point comes into existence. For the TB sub-model, the disease-free equilibrium point has been proved to be locally asymptotically stable for R T < 1 . The existence of TB endemic equilibrium points in the presence of reinfection and recurrent TB for R T < 1 justifies the existence of backward bifurcation under certain restrictions on the parameters. Further, we numerically simulate the fractional order model to verify the analytical results and highlight the role of fractional order in co-infection modeling. The fractional order derivative is shown to have a crucial role in determining the transmission dynamics of HIV-TB co-infection. It is concluded that the memory effect plays a significant role in reducing the infection prevalence of HIV-TB co-infection. An increment in the number of recovered individuals can also be observed when the memory effect is taken into consideration by introducing fractional order model. [ABSTRACT FROM AUTHOR]

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We propose an extended mathematical model for tuberculosis dynamics including five groups as susceptible individuals, S(t); latent, infected with TB but not infectious individuals, E(t); individuals who have active TB and treated at home, I 1 (t) ; individuals who have active TB and treated in hospital I 2 (t) and recovered individuals R(t). We incorporate exogenous reinfection and infection of recovered individuals to extend the model. Since healthcare facilities are limited and treatment in hospital might hard to afford for the people living in resource-poor countries, being treated at home or hospital are two important cases affecting the transmission and eradication of the disease. Therefore, an optimal control problem (OCP) is constructed governed by the extended TB model where the importance of being treated at home and in hospital can be revealed and the success of the treatment can be measured mathematically in case of limited number of healthcare facilities and treatment expenses. The aim of applying optimal control strategy to this new SEIR model is to minimize the number of latent and infectious individuals as well as the cost of applying three controls, namely distancing control, u 1 (t) ; effort that prevents the failure of treatment at home for active TB infectious individuals, u 2 (t) ; and effort that prevents the failure of treatment in hospital for active TB infectious individuals, u 3 (t) . We set two different controls u 2 (t) and u 3 (t) special to the subgroups I 1 (t) and I 2 (t) so that we can catch the contribution of being treated in hospital or being treated at home. While constructing the OCP, the form of the reproduction number is used so that we can construct the OCP in a way to decrease the reproduction number. In addition, local asymptotic stability of the disease-free equilibrium (DFE) point is proven with the use of the reproduction number; but, global asymptotic stability of the DFE point may not be achieved due to exogenous reinfection. It means that the disease might become persistent even if there is a small infectious group of people in the population. Therefore, the need for optimal control strategy is revealed even for a small infectious subgroup. At the end, we present some numerical results to obtain the optimal intervention strategies in case the transition rate from/to home to/from hospital is large. [ABSTRACT FROM AUTHOR]

Recurrent tuberculosis is an important indicator of the effectiveness of tuberculosis control and can occur by relapse or exogenous reinfection. We conducted a retrospective cohort study on all bacteriologically confirmed tuberculosis cases that were successfully treated between 2000 and 2012 in Shanghai, an urban area with a high number but a low prevalence rate of tuberculosis cases and a low prevalence of HIV infection. Genotyping the Mycobacterium tuberculosis from clinical isolates was used to distinguish between relapse and reinfection. In total, 5.3% (710/13,417) of successfully treated cases had a recurrence, a rate of 7.55 (95% CI 7.01–8.13) episodes per 1000 person-years, more than 18 times the rate of tuberculosis in the general population. Patients who were male, age 30–59, retreatment cases, had cavitation, diabetes, drug-resistant or multidrug-resistant tuberculosis in their initial episode of tuberculosis, were at high risk for a recurrence. Among 141 recurrent cases that had paired isolates, 59 (41.8%) had different genotypes, indicating reinfection with a different strain. Patients who completed treatment were still at high risk of another episode of tuberculosis and exogenous reinfection contributed a significant proportion of the recurrent tuberculosis cases. Targeted control strategies are needed to prevent new tuberculosis infections in this setting. [ABSTRACT FROM AUTHOR]

Purpose: Recurrence of tuberculosis (TB) can be the consequence of relapse or exogenous reinfection. The study aimed to assess the factors associated with exogenous TB reinfection. Methods: Prospective cohort study based on the TB database, maintained at the Division of Infectious Diseases, Luigi Sacco Hospital (Milan, Italy). Time period: 1995-2010. Inclusion criteria: (1) ≥2 episodes of culture-confirmed TB; (2) cure of the first episode of TB; (3) availability of one Mycobacterium tuberculosis isolate for each episode. Genotyping of the M. tuberculosis strains to differentiate relapse and exogenous reinfection. Logistic regression analysis was used to assess the influence of risk factors on exogenous reinfections. Result: Of the 4682 patients with TB, 83 were included. Of these, exogenous reinfection was diagnosed in 19 (23 %). It was independently associated with absence of multidrug resistance at the first episode [0, 10 (0.01-0.95), p = 0.045] and with prolonged interval between the first TB episode and its recurrence [7.38 (1.92-28.32) p = 0.004]. However, TB relapses occurred until 4 years after the first episode. The risk associated with being foreign born, extrapulmonary site of TB, and HIV infection was not statistically significant. In the relapse and re-infection cohort, one-third of the patients showed a worsened drug resistance profile during the recurrent TB episode. Conclusions: Exogenous TB reinfections have been documented in low endemic areas, such as Italy. A causal association with HIV infection could not be confirmed. Relapses and exogenous reinfections shared an augmented risk of multidrug resistance development, frequently requiring the use of second-line anti-TB regimens. [ABSTRACT FROM AUTHOR]

Summary: A public-private partnership (PPP) involving Stellenbosch University in South Africa and GlaxoSmithKline (GSK) has benefited both research and a local community where tuberculosis (TB) is endemic. The venture, part of GSK''s Action TB programme, enabled the University''s Desmond Tutu TB Centre to establish an epidemiological field site in two suburbs of Cape Town where the annual risk of TB infection is 3.5%. Collaboration between the centre and GSK focused on the development of a surrogate marker model able to predict patient outcome with relative accuracy. Such models may be useful tools for diagnosis/prognosis and for shortening clinical trials of novel TB agents. Other research findings stemming from the Action TB partnership suggest that exogenous reinfection is responsible for the majority of relapse cases and that adults often have infection with multiple strains. The local community has been empowered by the implementation of the Directly Observed Treatment, Short-course (DOTS) programme and benefited from improved education about health in general and TB in particular. The centre has also provided employment for many local people in field work and other roles. Meanwhile, national and international publicity about the centre''s work has aided in generating the essential political will to allocate resources and shape healthcare priorities, benefiting this impoverished community. [Copyright &y& Elsevier]

The importance of exogenous reinfection versus endogenous reactivation for the resurgence of tuberculosis (TB) has been a matter of ongoing debate. Previous mathematical models of TB give conflicting results on the possibility of multiple stable equilibria in the presence of reinfection, and hence the failure to control the disease even when the basic reproductive number is less than unity. The present study reconsiders the effect of exogenous reinfection, by extending previous studies to incorporate a generalized rate of reinfection as a function of the number of actively infected individuals. A mathematical model is developed to include all possible routes to the development of active TB (progressive primary infection, endogenous reactivation, and exogenous reinfection). The model is qualitatively analyzed to show the existence of multiple equilibria under realistic assumptions and plausible range of parameter values. Two examples, of unbounded and saturated incidence rates of reinfection, are given, and simulation results using estimated parameter values are presented. The results reflect exogenous reinfection as a major cause of TB emergence, especially in high prevalence areas, with important public health implications for controlling its spread. [ABSTRACT FROM AUTHOR]

Treatment of drug-resistant tuberculosis requires extended use of more toxic and less effective drugs and may result in retreatment cases due to failure, abandonment or disease recurrence. It is therefore important to understand the evolutionary process of drug resistance in Mycobacterium tuberculosis. We here in describe the microevolution of drug resistance in serial isolates from six previously treated patients. Drug resistance was initially investigated through phenotypic methods, followed by genotypic approaches. The use of whole-genome sequencing allowed the identification of mutations in the katG , rpsL and rpoB genes associated with drug resistance, including the detection of rare mutations in katG and mixed populations of strains. Molecular docking simulation studies of the impact of observed mutations on isoniazid binding were also performed. Whole-genome sequencing detected 266 single nucleotide polymorphisms between two isolates obtained from one patient, suggesting a case of exogenous reinfection. In conclusion, sequencing technologies can detect rare mutations related to drug resistance, identify subpopulations of resistant strains, and identify diverse populations of strains due to exogenous reinfection, thus improving tuberculosis control by guiding early implementation of appropriate clinical and therapeutic interventions. [ABSTRACT FROM AUTHOR]

• A nonlinear adaptive control method is proposed for controlling Tuberculosis, considering the uncertainty in system parameters. • The stability of the system is proved by the Lyapunov theorem and confirmed by simulation. • The proposed control system has the ability to control active infectious and persistent latent groups. Tuberculosis is one of deadly diseases in many countries that attacks to the human body and causes damage to the lung, causing bloody coughing and if left untreated, it will kill half of the affected people. Tuberculosis bacteria can stay latent and reactivate after passing appropriate conditions. For this reason, control of this disease and treatment of infected people has a significant importance, and observing health issues can prevent the spread of it. In this paper, a nonlinear adaptive control method is proposed for the first time in order to control and treat tuberculosis outbreak subjected to the modeling uncertainty. To design a control system being robust against uncertainties, an adaptation law is defined to update values of estimated parameters and ensures the whole system stability. The treatment achievement and stability of the closed-loop system is proved by the Lyapunov theorem and confirmed by some simulations. The proposed strategy has the capability to control the tuberculosis outbreak by reducing the numbers of active infectious and persistent latent individuals based on their desired values in the society. [ABSTRACT FROM AUTHOR]