Modeling Tuberculosis Among Healthcare Workers
A mathematical model for transmission dynamics of tuberculosis among healthcare workers is formulated. Tuberculosis is an airborne disease caused by Mycobacterium tuberculosis bacteria that affect the lungs of a host. Previous research had concentrated on mathematical modeling of transmission dynami...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2019-12-01
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| Series: | Moroccan Journal of Pure and Applied Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/mjpaa-2019-0014 |
| _version_ | 1818280585258336256 |
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| author | Faniran T.S. Falade A.O. Alakija T.O. |
| author_facet | Faniran T.S. Falade A.O. Alakija T.O. |
| author_sort | Faniran T.S. |
| collection | DOAJ |
| description | A mathematical model for transmission dynamics of tuberculosis among healthcare workers is formulated. Tuberculosis is an airborne disease caused by Mycobacterium tuberculosis bacteria that affect the lungs of a host. Previous research had concentrated on mathematical modeling of transmission dynamics of tuberculosis without considering the impact of compliance rate to particulate respirator by healthcare workers on the transmission. Therefore, how compliance rate to particulate respirator reduces the transmission of tuberculosis is an active question, and we develop a new system of ordinary differential equations that explicitly explores the impact of compliance rate to particulate respirator by healthcare workers upon transmission. Rigorous analysis of the model shows that the disease-free equilibrium point is locally asymptotically stable when the basic reproduction number, Ro < 1. This is established through the analysis of characteristic equation. Basic reproduction, Ro is the number of new cases that an existing case generates on average over the infectious period in a susceptible population. We also show that the endemic equilibrium point is locally asymptotically stable for Ro > 1, by using Routh-Hurwitz criteria for stability. Sensitivity analysis is carried out to determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity analysis shows that the most sensitive parameter is β (Human-to-human transmission rate), followed by Λ (Human recruitment rate). Also, the result shows that increase in ψ (compliance rate to particulate respirator by healthcare workers) leads to decrease in Ro which reduces tuberculosis spread among healthcare workers. |
| first_indexed | 2024-12-12T23:51:34Z |
| format | Article |
| id | doaj.art-8a9db897af594c2b8f49c37d85203c80 |
| institution | Directory Open Access Journal |
| issn | 2351-8227 |
| language | English |
| last_indexed | 2024-12-12T23:51:34Z |
| publishDate | 2019-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Moroccan Journal of Pure and Applied Analysis |
| spelling | doaj.art-8a9db897af594c2b8f49c37d85203c802022-12-22T00:06:41ZengSciendoMoroccan Journal of Pure and Applied Analysis2351-82272019-12-015218619610.2478/mjpaa-2019-0014Modeling Tuberculosis Among Healthcare WorkersFaniran T.S.0Falade A.O.1Alakija T.O.2Department of Computer Science, Lead City University, Lagos-Ibadan Expressway, Ibadan, Oyo State, Nigeria.Department of Mathematics, African Institute for Mathematical Sciences, Mbour, Senegal.Department of Statistics, Yaba College of Technology, Lagos State, Nigeria.A mathematical model for transmission dynamics of tuberculosis among healthcare workers is formulated. Tuberculosis is an airborne disease caused by Mycobacterium tuberculosis bacteria that affect the lungs of a host. Previous research had concentrated on mathematical modeling of transmission dynamics of tuberculosis without considering the impact of compliance rate to particulate respirator by healthcare workers on the transmission. Therefore, how compliance rate to particulate respirator reduces the transmission of tuberculosis is an active question, and we develop a new system of ordinary differential equations that explicitly explores the impact of compliance rate to particulate respirator by healthcare workers upon transmission. Rigorous analysis of the model shows that the disease-free equilibrium point is locally asymptotically stable when the basic reproduction number, Ro < 1. This is established through the analysis of characteristic equation. Basic reproduction, Ro is the number of new cases that an existing case generates on average over the infectious period in a susceptible population. We also show that the endemic equilibrium point is locally asymptotically stable for Ro > 1, by using Routh-Hurwitz criteria for stability. Sensitivity analysis is carried out to determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity analysis shows that the most sensitive parameter is β (Human-to-human transmission rate), followed by Λ (Human recruitment rate). Also, the result shows that increase in ψ (compliance rate to particulate respirator by healthcare workers) leads to decrease in Ro which reduces tuberculosis spread among healthcare workers.https://doi.org/10.2478/mjpaa-2019-0014tuberculosisrespiratorbasic reproduction numberstabilitysensitivity analysis34c2022e3092d30 |
| spellingShingle | Faniran T.S. Falade A.O. Alakija T.O. Modeling Tuberculosis Among Healthcare Workers Moroccan Journal of Pure and Applied Analysis tuberculosis respirator basic reproduction number stability sensitivity analysis 34c20 22e30 92d30 |
| title | Modeling Tuberculosis Among Healthcare Workers |
| title_full | Modeling Tuberculosis Among Healthcare Workers |
| title_fullStr | Modeling Tuberculosis Among Healthcare Workers |
| title_full_unstemmed | Modeling Tuberculosis Among Healthcare Workers |
| title_short | Modeling Tuberculosis Among Healthcare Workers |
| title_sort | modeling tuberculosis among healthcare workers |
| topic | tuberculosis respirator basic reproduction number stability sensitivity analysis 34c20 22e30 92d30 |
| url | https://doi.org/10.2478/mjpaa-2019-0014 |
| work_keys_str_mv | AT fanirants modelingtuberculosisamonghealthcareworkers AT faladeao modelingtuberculosisamonghealthcareworkers AT alakijato modelingtuberculosisamonghealthcareworkers |