A mathematical model of tuberculosis and COVID-19 coinfection with the effect of isolation and treatment
In this research, we developed a coinfection model of tuberculosis and COVID-19 with the effect of isolation and treatment. We obtained two equilibria, namely, disease-free equilibrium and endemic equilibrium. Disease-free equilibrium is a state in which no infection of tuberculosis and COVID-19 occ...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-08-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2022.958081/full |
| _version_ | 1817998407326760960 |
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| author | Fatuh Inayaturohmat Nursanti Anggriani Asep K. Supriatna |
| author_facet | Fatuh Inayaturohmat Nursanti Anggriani Asep K. Supriatna |
| author_sort | Fatuh Inayaturohmat |
| collection | DOAJ |
| description | In this research, we developed a coinfection model of tuberculosis and COVID-19 with the effect of isolation and treatment. We obtained two equilibria, namely, disease-free equilibrium and endemic equilibrium. Disease-free equilibrium is a state in which no infection of tuberculosis and COVID-19 occurs. Endemic equilibrium is a state in which there occurs not only the infection of tuberculosis and COVID-19 but also the coinfection of tuberculosis and COVID-19. We assumed that the parameters follow the uniform distribution, and then, we took 1,000 samples of each parameter using Latin hypercube sampling (LHS). Next, the samples were sorted by ranking. Finally, we used the partial rank correlation coefficient (PRCC) to find the correlation between the parameters with compartments. We analyzed the PRCC for three compartments, namely, individuals infected with COVID-19, individuals infected with tuberculosis, and individuals coinfected with COVID-19 and tuberculosis. The most sensitive parameters are the recovery rate and the infection rate of each COVID-19 and tuberculosis. We performed the optimal control in the form of prevention for COVID-19 and tuberculosis. The numerical simulation shows that these controls effectively reduce the infected population. We also concluded that the effect of isolation has an immediate impact on reducing the number of COVID-19 infections, while the effect of treatment has an impact that tends to take a longer time. |
| first_indexed | 2024-04-14T02:53:10Z |
| format | Article |
| id | doaj.art-0aee6382b6b747d294261447f1c178e4 |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-04-14T02:53:10Z |
| publishDate | 2022-08-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-0aee6382b6b747d294261447f1c178e42022-12-22T02:16:13ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872022-08-01810.3389/fams.2022.958081958081A mathematical model of tuberculosis and COVID-19 coinfection with the effect of isolation and treatmentFatuh Inayaturohmat0Nursanti Anggriani1Asep K. Supriatna2Master of Mathematics Study Program, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang, IndonesiaIn this research, we developed a coinfection model of tuberculosis and COVID-19 with the effect of isolation and treatment. We obtained two equilibria, namely, disease-free equilibrium and endemic equilibrium. Disease-free equilibrium is a state in which no infection of tuberculosis and COVID-19 occurs. Endemic equilibrium is a state in which there occurs not only the infection of tuberculosis and COVID-19 but also the coinfection of tuberculosis and COVID-19. We assumed that the parameters follow the uniform distribution, and then, we took 1,000 samples of each parameter using Latin hypercube sampling (LHS). Next, the samples were sorted by ranking. Finally, we used the partial rank correlation coefficient (PRCC) to find the correlation between the parameters with compartments. We analyzed the PRCC for three compartments, namely, individuals infected with COVID-19, individuals infected with tuberculosis, and individuals coinfected with COVID-19 and tuberculosis. The most sensitive parameters are the recovery rate and the infection rate of each COVID-19 and tuberculosis. We performed the optimal control in the form of prevention for COVID-19 and tuberculosis. The numerical simulation shows that these controls effectively reduce the infected population. We also concluded that the effect of isolation has an immediate impact on reducing the number of COVID-19 infections, while the effect of treatment has an impact that tends to take a longer time.https://www.frontiersin.org/articles/10.3389/fams.2022.958081/fullmathematical modeltuberculosisCOVID-19coinfectionisolationtreatment |
| spellingShingle | Fatuh Inayaturohmat Nursanti Anggriani Asep K. Supriatna A mathematical model of tuberculosis and COVID-19 coinfection with the effect of isolation and treatment Frontiers in Applied Mathematics and Statistics mathematical model tuberculosis COVID-19 coinfection isolation treatment |
| title | A mathematical model of tuberculosis and COVID-19 coinfection with the effect of isolation and treatment |
| title_full | A mathematical model of tuberculosis and COVID-19 coinfection with the effect of isolation and treatment |
| title_fullStr | A mathematical model of tuberculosis and COVID-19 coinfection with the effect of isolation and treatment |
| title_full_unstemmed | A mathematical model of tuberculosis and COVID-19 coinfection with the effect of isolation and treatment |
| title_short | A mathematical model of tuberculosis and COVID-19 coinfection with the effect of isolation and treatment |
| title_sort | mathematical model of tuberculosis and covid 19 coinfection with the effect of isolation and treatment |
| topic | mathematical model tuberculosis COVID-19 coinfection isolation treatment |
| url | https://www.frontiersin.org/articles/10.3389/fams.2022.958081/full |
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