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A tuberculosis model incorporating the impact of information, saturated treatment and multiple reinfections

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Abstract

This study investigates a novel tuberculosis (TB) model by integrating key factors that contribute to the spread of TB, such as endogenous reactivation, reinfection of recovered individuals, slow-fast progression of TB via non-monotonic information-induced incidence term, saturation in treatment function, and exogenous reinfection. The mathematical analysis of the model is carried out, and both transcritical and backward bifurcation are obtained conditionally, which infers that \({\mathcal {R}}_0<1\) is not sufficient for TB eradication. The combined impact of reinfections and treatment saturation on backward bifurcation is illustrated, along with the presence of exogenous reinfection. Further analysis shows that the model system exhibits interesting rich and complex nonlinear dynamics, such as bistability, multistability, Hopf bifurcation, and Hopf–Hopf bifurcation (stability switches). Analytical results are further explored and supplemented with numerical findings. The model system is fitted with real-time data of India and Turkey. It is observed that our model fits well and is reasonably accurate for short-term prediction.

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Acknowledgements

AS acknowledges financial support from the Indian Institute of Technology Patna.

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  1. Department of Mathematics, Indian Institute of Technology Patna, Patna, 801103, India

    Akriti Srivastava & Prashant K. Srivastava

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  1. Akriti Srivastava
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Correspondence to Prashant K. Srivastava.

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Srivastava, A., Srivastava, P.K. A tuberculosis model incorporating the impact of information, saturated treatment and multiple reinfections. Eur. Phys. J. Plus 138, 1156 (2023). https://doi.org/10.1140/epjp/s13360-023-04754-z

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