An SVEIRE Model of Tuberculosis to Assess the Effect of an Imperfect Vaccine and Other Exogenous Factors

Sulayman, Fatima; Abdullah, Farah Aini; Mohd, Mohd Hafiz

doi:10.3390/math9040327

Cited by 32 publications

(23 citation statements)

References 73 publications

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“…Since at , the DFE of the TB only sub-model ( 7 ) may undergo backward bifurcation (Wangari and Stone 2018 ; Sulayman et al. 2021 ), we wish to investigate (1) whether the sub-model ( 7 ) could also exhibit that phenomenon (2) the forward/transcritical or backward/subcritical direction of the bifurcation.…”

Section: Model Analysismentioning

confidence: 99%

Mathematical modeling and optimal control of SARS-CoV-2 and tuberculosis co-infection: a case study of Indonesia

Rwezaura

Diagne

Omame

et al. 2022

Model. Earth Syst. Environ.

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A new mathematical model incorporating epidemiological features of the co-dynamics of tuberculosis (TB) and SARS-CoV-2 is analyzed. Local asymptotic stability of the disease-free and endemic equilibria are shown for the sub-models when the respective reproduction numbers are below unity. Bifurcation analysis is carried out for the TB only sub-model, where it was shown that the sub-model undergoes forward bifurcation. The model is fitted to the cumulative confirmed daily SARS-CoV-2 cases for Indonesia from February 11, 2021 to August 26, 2021. The fitting was carried out using the fmincon optimization toolbox in MATLAB. Relevant parameters in the model are estimated from the fitting. The necessary conditions for the existence of optimal control and the optimality system for the co-infection model is established through the application of Pontryagin’s Principle. Different control strategies: face-mask usage and SARS-CoV-2 vaccination, TB prevention as well as treatment controls for both diseases are considered. Simulations results show that: (1) the strategy against incident SARS-CoV-2 infection averts about 27,878,840 new TB cases; (2) also, TB prevention and treatment controls could avert 5,397,795 new SARS-CoV-2 cases. (3) In addition, either SARS-CoV-2 or TB only control strategy greatly mitigates a significant number of new co-infection cases.

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Section: Model Analysismentioning

confidence: 99%

Mathematical modeling and optimal control of SARS-CoV-2 and tuberculosis co-infection: a case study of Indonesia

Rwezaura

Diagne

Omame

et al. 2022

Model. Earth Syst. Environ.

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“…e basic reproduction number of system model (4) was calculated using the next generation operator approach (see [25,26]), where it is obtained to be…”

Section: Analysis Ofmentioning

confidence: 99%

Analysis of a Tuberculosis Infection Model considering the Influence of Saturated Recovery (Treatment)

Sulayman

Abdullah

2021

Complexity

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Tuberculosis (TB) is a serious global health threat that is caused by the bacterium Mycobacterium tuberculosis, is extremely infectious, and has a high mortality rate. In this paper, we developed a model of TB infection to predict the impact of saturated recovery. The existence of equilibrium and its stability has been investigated based on the effective reproduction number R C . The model displays interesting dynamics, including backward bifurcation and Hopf bifurcation, which further results in the stable disease-free and stable endemic equilibria to be coexisting. Bifurcation analysis demonstrates that the saturation parameter is accountable for the phenomenon of backward bifurcation. We derive a condition that guarantees that the model is globally asymptotically stable using the Lyapunov function approach to global stability. The numerical simulation also reveals that the extent of saturation of TB infection is the mechanism that is fuelling TB disease in the population.

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“…Egonmwan et al [ 36 ] established a new-fangled TB model to inspect the effect of diagnosis and treatment for the infectious mass of TB. The study in [ 12 ] shows that diagnosis, proper vaccination drives, and treatments can restrain uncertain aspects of TB; however [ 40 ] mentions that even deficient vaccination of tuberculosis plays a role in inhibiting the spread of the disease. Robert studied a TB system with the consequence of reversion of infection [ 49 ].…”

Section: Introductionmentioning

confidence: 99%

A noninteger order SEITR dynamical model for TB

2022

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This research paper designs the noninteger order SEITR dynamical model in the Caputo sense for tuberculosis. The authors of the article have classified the infection compartment into four different compartments such as newly infected unrecognized individuals, diagnosed patients, highly infected patients, and patients with delays in treatment which provide better detail of the TB infection dynamic. We estimate the model parameters using the least square curve fitting and demonstrate that the proposed model provides a good fit to tuberculosis confirmed cases of India from the year 2000 to 2020. Further, we compute the basic reproduction number as $\Re _{0} \approx 1.73$ ℜ 0 ≈ 1.73 of the model using the next-generation matrix method and the model equilibria. The existence and uniqueness of the approximate solution for the SEITR model is validated using the generalized Adams–Bashforth–Moulton method. The graphical representation of the fractional order model is given to validate the result using the numerical simulation. We conclude that the fractional order model is more realistic than the classical integer order model and provide more detailed information about the real data of the TB disease dynamics.

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An SVEIRE Model of Tuberculosis to Assess the Effect of an Imperfect Vaccine and Other Exogenous Factors

Cited by 32 publications

References 73 publications

Mathematical modeling and optimal control of SARS-CoV-2 and tuberculosis co-infection: a case study of Indonesia

Mathematical modeling and optimal control of SARS-CoV-2 and tuberculosis co-infection: a case study of Indonesia

Analysis of a Tuberculosis Infection Model considering the Influence of Saturated Recovery (Treatment)

A noninteger order SEITR dynamical model for TB

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