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

Dhiraj Kumar Das and T.K. Kar

Chaos, Solitons & Fractals, 2021, vol. 146, issue C

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.

Keywords: Tuberculosis model; Smear positive and negative TB; Basic reproduction number; Global asymptotic stability (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002320

DOI: 10.1016/j.chaos.2021.110879

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