https://doi.org/10.1140/epjp/s13360-023-04754-z
Regular Article
A tuberculosis model incorporating the impact of information, saturated treatment and multiple reinfections
Department of Mathematics, Indian Institute of Technology Patna, 801103, Patna, India
Received:
17
July
2023
Accepted:
26
November
2023
Published online:
28
December
2023
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 
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.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
