A tuberculosis model with the impact of sputum smear microscopy
Abstract This paper proposes and analyzes a five-dimensional tuberculosis model incorporating slow-fast progression, endogenous reactivation, exogenous reinfection, and the assumption that infectives pass the smear microscopy test. This study disseminates information regarding how the presence and infectiousness of smear-negative patients in a tuberculosis epidemic significantly affect the threshold epidemic quantity %${\mathcal {R}_0}%$ (basic reproduction number). Stability and bifurcation analysis is carried out, and we find that the exogenous reinfection causes backward bifurcation and multiple endemic steady states in the system. We analytically and numerically explored the case of the periodic oscillations in the population via Hopf bifurcation for %${\mathcal {R}_0<1}%$ as well as %${\mathcal {R}_0>1}.%$.
| Medienart: |
E-Artikel |
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| Erscheinungsjahr: |
2024 |
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| Erschienen: |
2024 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:70 |
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| Enthalten in: |
Journal of applied mathematics and computing - 70(2024), 1 vom: 22. Jan., Seite 711-740 |
| Sprache: |
Englisch |
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| Beteiligte Personen: |
Srivastava, Akriti [VerfasserIn] |
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| Links: |
Volltext [lizenzpflichtig] |
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| Themen: |
Bifurcation analysis |
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| Anmerkungen: |
© The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2024. 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. |
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| doi: |
10.1007/s12190-023-01984-3 |
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| funding: |
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| Förderinstitution / Projekttitel: |
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SPR054667577 |
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| 520 | |a Abstract This paper proposes and analyzes a five-dimensional tuberculosis model incorporating slow-fast progression, endogenous reactivation, exogenous reinfection, and the assumption that infectives pass the smear microscopy test. This study disseminates information regarding how the presence and infectiousness of smear-negative patients in a tuberculosis epidemic significantly affect the threshold epidemic quantity %${\mathcal {R}_0}%$ (basic reproduction number). Stability and bifurcation analysis is carried out, and we find that the exogenous reinfection causes backward bifurcation and multiple endemic steady states in the system. We analytically and numerically explored the case of the periodic oscillations in the population via Hopf bifurcation for %${\mathcal {R}_0<1}%$ as well as %${\mathcal {R}_0>1}.%$ | ||
| 650 | 4 | |a Tuberculosis model |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Stability analysis |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Bifurcation analysis |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Smear positive and negative tuberculosis |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Srivastava, Prashant K. |0 (orcid)0000-0002-7651-5639 |4 aut | |
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