Analysis of a mathematical model for tuberculosis: What could be done to increase case detection

Okuonghae, D.; Omosigho, Sunday E.

doi:10.1016/j.jtbi.2010.09.044

Cited by 48 publications

(40 citation statements)

References 20 publications

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“…Generally, reducing the incidence and prevalence of TB in a population hinges on successful treatment and high case detection rates (Okuonghae and Omosigho, 2010 , 2011 ; World Health Organization, 2014 ; Okuonghae, 2015 ). It fact, it is seriously encouraged that effort should be concentrated on ensuring that all TB cases are detected, notified and commence treatment immediately (World Health Organization, 2014 ).…”

Section: Introductionmentioning

confidence: 99%

“… This work extends a mathematical model for the transmission dynamics of tuberculosis that examined the impact of certain factors on tuberculosis case detection (Okuonghae and Omosigho, 2011 ). The extended model now classifies the latently infected individuals by their level of tuberculosis awareness (as was done for the susceptible sub-population) and further expands the number of key factors that can positively affect the tuberculosis case detection rate.…”

mentioning

confidence: 96%

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Dynamics of a Mathematical Model for Tuberculosis with Variability in Susceptibility and Disease Progressions Due to Difference in Awareness Level

Okuonghae

Ikhimwin

2016

Front. Microbiol.

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This work extends a mathematical model for the transmission dynamics of tuberculosis that examined the impact of certain factors on tuberculosis case detection (Okuonghae and Omosigho, 2011). The extended model now classifies the latently infected individuals by their level of tuberculosis awareness (as was done for the susceptible sub-population) and further expands the number of key factors that can positively affect the tuberculosis case detection rate. The effect of these identified factors on the associated reproduction number of the model is considered. It is shown that the system can undergo the phenomenon of backward bifurcation when the associated reproduction number of the model is less than unity; in a special case, the effect of exogenous re-infection on the backward bifurcation phenomenon is significantly dictated by the level of awareness of the latently infected individuals. Qualitative and quantitative analysis of the model showed the effect of key identified factors on the dynamics of tuberculosis while suggesting a serious concentration on tuberculosis awareness programmes, active case finding strategies and use of active cough identification for identifying likely TB cases and sustaining awareness campaigns over a long period of time.

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 96%

Dynamics of a Mathematical Model for Tuberculosis with Variability in Susceptibility and Disease Progressions Due to Difference in Awareness Level

Okuonghae

Ikhimwin

2016

Front. Microbiol.

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“…In later research, we will choose monthly data. Although our model take into account factors such as slow-fast process [40][41][42], vaccination [23][24][25], reinfection [20][21][22], reactivated [28,29] and undiagnosed infection [20,43], these factors are not enough. We did not take into account factors such as interactions with HIV [26,27], immigration [73,74] and drug-resistant TB bacilli [65,75,76].…”

Section: Deficiencymentioning

confidence: 99%

“…In 1962, Waaler et al established the first dynamic model of TB based on a susceptible-infected-recovered (SIR) model [19]. From then on, many models, which take multiple influencing factors into consideration, have been established, such as reinfection [20][21][22], vaccination [23][24][25], interactions with HIV [26,27], reactivated [28,29], Chemoprophylaxis [18] and so on [30][31][32][33]. Revelle et al considered prophylaxis, cure and BCG vaccination to research the optimal strategy to fight against TB, which was then extensively used to study the epidemic model of transmission for infectious disease in 1967 [34].…”

Section: Introductionmentioning

confidence: 99%

“…These people are more likely to develop multi-drug resistance relative to the diagnosed infectious population [20,39]. According to the actual situation of TB in the United States, we considered several factors: slow-fast process [40][41][42], vaccination [23][24][25], reinfection [20][21][22], reactivated [28,29] and undiagnosed infection [20,43]. Then we referenced the modeling thought from D.P.…”

Section: Introductionmentioning

confidence: 99%

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The Prevention and Control of Tuberculosis: An Analysis Based On a Tuberculosis Dynamic Model Derived from the Cases of Americans

Huang

Wang

et al. 2020

Preprint

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Background: Tuberculosis (TB), a preventable and curable disease, is claimed as the second largest number of fatalities, and there are 9,025 cases reported in the United States in 2018. Many researchers have done a lot of research and achieved remarkable results, but TB is still a severe problem to the human beings. The study is a further exploration of the prevention and control of tuberculosis.Methods: In the paper, we propose a new dynamic model to study the transmission dynamics of TB, and then use global differential evolution and local sequential quadratic programming (DESQP) optimization algorithm to estimate parameters of the model. Finally, we use Latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCC) to analyze the influence of parameters on the basic reproduction number (R0) and the total infectious (including the diagnosed, undiagnosed and incomplete treatment infectious), respectively.Results: According to the research, the basic reproduction is computed as 2.3597, which means TB will be an epidemic in the US. The diagnosed rate is 0.6082, which means the undiagnosed will be diagnosed after 1.6442 years. The diagnosed will recover after an average of 1.9912 years. Moreover, some diagnosed will end the treatment after 1.7550 years for some reason. From the study, it’s shown that 2.4% of the recovered will be reactivated, and 13.88% of the newborn will be vaccinated. However, the immune system will be lost after about 19.6078 years.Conclusion: Through the results of this study, we give some suggestions to help prevent and control the TB epidemic in the United States, such as prolonging the protection period of the vaccine by developing new and more effective vaccines to prevent TB; using the Chemoprophylaxis for incubation patients to prevent their conversion into active TB; raising people’s awareness of the prevention and control of TB and treatment after illness; isolating the infected to reduce the spread of TB. According to the latest report in the announcement that came at the first WHO Global Ministerial Conference on Ending tuberculosis in the Sustainable Development Era, we predict that it is challenging to control TB in 2030.

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A tuberculosis model with early and late latency, imperfect vaccination, and relapse: An application to China

Jiang

Liu

Wang

et al. 2023

Math Methods in App Sciences

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Screening those individuals who are latent but at higher risk of rapidly developing active tuberculosis (TB) is one of the intervention measures to control the spread of TB. This work proposes a TB SVELIT (S-Susceptible, V-Vaccinated, E-Early latent, L-Late latent, I-Infected, T-Treated) transmission model with relapse. In particular, a complete threshold dynamical analysis for the model is performed and the existence of optimal control is obtained. Meanwhile, the validity of the model is shown by comparing the real data with the fitted curve and the future trend in the incidence of TB in China is predicted. More importantly, the effects of four strategies, including vaccination, media propaganda, screening latent individuals, and receiving treatment, are evaluated numerically. The results suggest that the above four strategies can effectively control TB and shorten the duration of the epidemic. Interestingly, treatment is more effective than vaccination in controlling TB, but media propaganda and latent screening are cheaper and easier to implement.

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Analysis of a mathematical model for tuberculosis: What could be done to increase case detection

Cited by 48 publications

References 20 publications

Dynamics of a Mathematical Model for Tuberculosis with Variability in Susceptibility and Disease Progressions Due to Difference in Awareness Level

Dynamics of a Mathematical Model for Tuberculosis with Variability in Susceptibility and Disease Progressions Due to Difference in Awareness Level

The Prevention and Control of Tuberculosis: An Analysis Based On a Tuberculosis Dynamic Model Derived from the Cases of Americans

A tuberculosis model with early and late latency, imperfect vaccination, and relapse: An application to China

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