Mathematical Analysis of the Transmission Dynamics of Tuberculosis

Nayeem, Jannatun; Sultana, Israt

doi:10.4236/ajcm.2019.93012

Cited by 4 publications

(4 citation statements)

References 11 publications

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“…To integrate (21), refs. [23,33] have applied two-step Lagrange interpolation to solve this integration, and we use similar knowledge to write our proposed model (1) in the following form as [20]:…”

Section: Numerical Simulationmentioning

confidence: 99%

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Mathematical Modelling of Tuberculosis Outbreak in an East African Country Incorporating Vaccination and Treatment

Oshinubi,

Peter,

Addai

et al. 2023

Computation

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In this paper, we develop a deterministic mathematical epidemic model for tuberculosis outbreaks in order to study the disease’s impact in a given population. We develop a qualitative analysis of the model by showing that the solution of the model is positive and bounded. The global stability analysis of the model uses Lyapunov functions and the threshold quantity of the model, which is the basic reproduction number is estimated. The existence and uniqueness analysis for Caputo fractional tuberculosis outbreak model is presented by transforming the deterministic model to a Caputo sense model. The deterministic model is used to predict real data from Uganda and Rwanda to see how well our model captured the dynamics of the disease in the countries considered. Furthermore, the sensitivity analysis of the parameters according to R0 was considered in this study. The normalised forward sensitivity index is used to determine the most sensitive variables that are important for infection control. We simulate the Caputo fractional tuberculosis outbreak model using the Adams–Bashforth–Moulton approach to investigate the impact of treatment and vaccine rates, as well as the disease trajectory. Overall, our findings imply that increasing vaccination and especially treatment availability for infected people can reduce the prevalence and burden of tuberculosis on the human population.

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Section: Numerical Simulationmentioning

confidence: 99%

“…MDR-TB treatment and prevention have become increasingly important in recent years, and they comprise the focus of this article [18] . Other articles that deal with the modelling of TB can be found in [19][20][21][22][23] .…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling of Tuberculosis Outbreak in an East African Country Incorporating Vaccination and Treatment

Oshinubi,

Peter,

Addai

et al. 2023

Computation

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show abstract

“…Te use of mathematical models to capture the causes and the control of infectious diseases has been studied widely [10][11][12][13]. Mathematical deterministic models have considerably been applied to comprehend the behaviour of infections both at population and within host levels including proposing strategic intervention approaches.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling of Tuberculosis and Hepatitis C Coinfection Dynamics with No Intervention

Kizito,

Nampala,

Ariho

2024

Journal of Mathematics

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In this study, a deterministic tuberculosis (TB)-hepatitis C (HCV) coinfection mathematical model with no intervention is analysed purposely to examine the dynamics of TB-HCV coinfection so as to find conditions for reducing the transmission of both TB and HCV. A unique solution to the model exists; it is positive and is bounded. The analytical and numerical analysis show that for basic reproduction number, R0=maxRT,RH<1, the TB and HCV disease-free equilibrium points are stable. Further analysis shows that when the TB-HCV coinfection basic reproduction number is greater than 1, the endemic equilibrium point is stable. Sensitivity analysis reveals that interventions to reduce TB or HCV infection need to aim and concentrate on minimizing the numbers of the effective contact rate with TB- or HCV-infected humans and the rate of progress from latent TB or acute HCV to infectious TB or chronic HCV stage. Numerical simulations reveal that over time, the number of TB latent humans, acute HCV humans, and the number of dually infected humans have a linear relationship with the effective contact and the progression rates for both TB- and HCV-infected humans. We recommend that health education campaigns to communities aimed at reducing the transmission rates of TB and HCV be conducted. These could include screening and isolation, wearing of face masks for TB cases and screening, sterilization of surgical instruments, and use of condoms for HCV-infected humans.

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“…Nayeem and Sultana (2019) developed a dynamical model to understand the underlying dynamics of Tuberculosis infection at the population level by incorporating treatment of individuals, the infection of latent and recovery individuals. Their analysis revealed that the model exhibits a backward bifurcation when TB treatment remains in the infected class.…”

mentioning

confidence: 99%

A Mathematical Model for Tuberculosis Infection Transmission Dynamics in the Presence of Testing and Therapy, Isolation and Treatment

Okolo,

Makama,

Abah

2023

FJS

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In this study, a mathematical model for Tuberculosis infection transmission dynamics is developed by incorporating testing and therapy of latent individuals, the isolation of infectious individuals and the treatment of the isolated individuals. The basic reproduction number was computed using the next generation matrix method. Analysis of the model at the disease-free equilibrium state and the endemic equilibrium states shows that it is locally and globally asymptomatically stable whenever the basic reproduction number is less than unity at the disease -free equilibrium state and locally and globally asymptotically stable whenever the basic reproduction number is greater than unity. The result from the sensitivity index of show that the infection transmission parameter and other control parameters such as early detection and therapy, the isolation of infected individuals and treatment are crucial parameters to tuberculosis management. It is shown from numerical simulations that the early detection and therapy, isolation and treatment of infected individuals will reduce the infection transmission. Further numerical results show that the combination of early detection and therapy, isolation and treatment of infectious individuals will decrease the infection transmission and its eventual eradication from the human population.

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Mathematical Analysis of the Transmission Dynamics of Tuberculosis

Cited by 4 publications

References 11 publications

Mathematical Modelling of Tuberculosis Outbreak in an East African Country Incorporating Vaccination and Treatment

Mathematical Modelling of Tuberculosis Outbreak in an East African Country Incorporating Vaccination and Treatment

Mathematical Modelling of Tuberculosis and Hepatitis C Coinfection Dynamics with No Intervention

A Mathematical Model for Tuberculosis Infection Transmission Dynamics in the Presence of Testing and Therapy, Isolation and Treatment

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