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Global dynamics of a tuberculosis model with sensitivity of the smear microscopy

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  • Das, Dhiraj Kumar
  • Kar, T.K.

Abstract

Sputum smear microscopy and chest X-ray are the key TB diagnosis methods available in resource-constrained health settings of many developing countries worldwide. The test has moderate sensitivity towards the detection of pulmonary tuberculosis (PTB) cases. However, the undetected cases are also capable of transmitting the disease with a reduced transmission possibility. In this work, a five-dimensional compartmental model is formulated considering the infectivity of both smear-positive and negative individuals. The next-generation matrix method yields the expression of basic reproduction number R0. The global asymptotic stability of the disease-free equilibrium point ξ0 for R0<1 and that of endemic equilibrium point for R0>1 are established with suitably constructed Lyapunov functions. The sensitivity indices of the associated parameters of R0 are obtained with a suitable choice of parameter values. It has been found that neglecting the transmission capacity of smear-negative individuals underestimates the value of R0, whereas ignoring the smear-negative compartment overestimates the same quantity.

Suggested Citation

  • Das, Dhiraj Kumar & Kar, T.K., 2021. "Global dynamics of a tuberculosis model with sensitivity of the smear microscopy," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002320
    DOI: 10.1016/j.chaos.2021.110879
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    References listed on IDEAS

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    1. Berhe, Hailay Weldegiorgis & Makinde, Oluwole Daniel & Theuri, David Mwangi, 2019. "Co-dynamics of measles and dysentery diarrhea diseases with optimal control and cost-effectiveness analysis," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 903-921.
    2. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Dynamics of a stochastic tuberculosis model with antibiotic resistance," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 223-230.
    3. Seidu, Baba & Bornaa, C.S. & Makinde, Oluwole D., 2020. "An Ebola model with hyper-susceptibility," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "The impact of the media awareness and optimal strategy on the prevalence of tuberculosis," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    5. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "Transmission dynamics of tuberculosis with multiple re-infections," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    6. Khajanchi, Subhas & Das, Dhiraj Kumar & Kar, Tapan Kumar, 2018. "Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 52-71.
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    1. Majee, Suvankar & Jana, Soovoojeet & Das, Dhiraj Kumar & Kar, T.K., 2022. "Global dynamics of a fractional-order HFMD model incorporating optimal treatment and stochastic stability," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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