An Epidemiological Model for Tuberculosis Considering Environmental Transmission and Reinfection
As tuberculosis (TB) patients do not have lifetime immunity, environmental transmission is one of the key reasons why TB has not been entirely eradicated. In this study, an SVEIRB model of recurrent TB considering environmental transmission was developed to explore the transmission kinetics of recur...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/11/2423 |
| _version_ | 1797597133175521280 |
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| author | Qiuyun Li Fengna Wang |
| author_facet | Qiuyun Li Fengna Wang |
| author_sort | Qiuyun Li |
| collection | DOAJ |
| description | As tuberculosis (TB) patients do not have lifetime immunity, environmental transmission is one of the key reasons why TB has not been entirely eradicated. In this study, an SVEIRB model of recurrent TB considering environmental transmission was developed to explore the transmission kinetics of recurrent TB in the setting of environmental transmission, exogenous infection, and prophylaxis. A more thorough explanation of the effect of environmental transmission on recurrent TB can be found in the model’s underlying regeneration numbers. The global stability of disease-free and local equilibrium points can be discussed by looking at the relevant characteristic equations. The Lyapunov functions and the LaSalle invariance principle are used to show that the local equilibrium point is globally stable, and TB will persist if the basic reproduction number is larger. Conversely, the disease will disappear if the basic reproduction number is less than one. The impact of environmental transmission on the spread of tuberculosis was further demonstrated by numerical simulations, which also demonstrated that vaccination and reducing the presence of the virus in the environment are both efficient approaches to control the disease’s spread. |
| first_indexed | 2024-03-11T03:02:29Z |
| format | Article |
| id | doaj.art-40b69f136ebb473aa7ea1311073215a4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T03:02:29Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-40b69f136ebb473aa7ea1311073215a42023-11-18T08:11:50ZengMDPI AGMathematics2227-73902023-05-011111242310.3390/math11112423An Epidemiological Model for Tuberculosis Considering Environmental Transmission and ReinfectionQiuyun Li0Fengna Wang1Institute of Information and Computation, School of Mathematics and Physics, North China Electric Power University, Beijing 102206, ChinaInstitute of Information and Computation, School of Mathematics and Physics, North China Electric Power University, Beijing 102206, ChinaAs tuberculosis (TB) patients do not have lifetime immunity, environmental transmission is one of the key reasons why TB has not been entirely eradicated. In this study, an SVEIRB model of recurrent TB considering environmental transmission was developed to explore the transmission kinetics of recurrent TB in the setting of environmental transmission, exogenous infection, and prophylaxis. A more thorough explanation of the effect of environmental transmission on recurrent TB can be found in the model’s underlying regeneration numbers. The global stability of disease-free and local equilibrium points can be discussed by looking at the relevant characteristic equations. The Lyapunov functions and the LaSalle invariance principle are used to show that the local equilibrium point is globally stable, and TB will persist if the basic reproduction number is larger. Conversely, the disease will disappear if the basic reproduction number is less than one. The impact of environmental transmission on the spread of tuberculosis was further demonstrated by numerical simulations, which also demonstrated that vaccination and reducing the presence of the virus in the environment are both efficient approaches to control the disease’s spread.https://www.mdpi.com/2227-7390/11/11/2423tuberculosis modelenvironmental transmissionbasic regeneration numberstability analysis |
| spellingShingle | Qiuyun Li Fengna Wang An Epidemiological Model for Tuberculosis Considering Environmental Transmission and Reinfection Mathematics tuberculosis model environmental transmission basic regeneration number stability analysis |
| title | An Epidemiological Model for Tuberculosis Considering Environmental Transmission and Reinfection |
| title_full | An Epidemiological Model for Tuberculosis Considering Environmental Transmission and Reinfection |
| title_fullStr | An Epidemiological Model for Tuberculosis Considering Environmental Transmission and Reinfection |
| title_full_unstemmed | An Epidemiological Model for Tuberculosis Considering Environmental Transmission and Reinfection |
| title_short | An Epidemiological Model for Tuberculosis Considering Environmental Transmission and Reinfection |
| title_sort | epidemiological model for tuberculosis considering environmental transmission and reinfection |
| topic | tuberculosis model environmental transmission basic regeneration number stability analysis |
| url | https://www.mdpi.com/2227-7390/11/11/2423 |
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