Analysis and simulation of a mathematical model of tuberculosis transmission in Democratic Republic of the Congo
Abstract According to the World Health Organization reports, tuberculosis (TB) remains one of the top 10 deadly diseases of recent decades in the world. In this paper, we present the modeling, analysis and simulation of a mathematical model of TB transmission in a population incorporating several fa...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-11-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-03091-0 |
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| author | Selain Kasereka Kabunga Emile F. Doungmo Goufo Vinh Ho Tuong |
| author_facet | Selain Kasereka Kabunga Emile F. Doungmo Goufo Vinh Ho Tuong |
| author_sort | Selain Kasereka Kabunga |
| collection | DOAJ |
| description | Abstract According to the World Health Organization reports, tuberculosis (TB) remains one of the top 10 deadly diseases of recent decades in the world. In this paper, we present the modeling, analysis and simulation of a mathematical model of TB transmission in a population incorporating several factors and study their impact on the disease dynamics. The spread of TB is modeled by eight compartments including different groups, which are too often not taken into account in the projections of tuberculosis incidence. The rigorous mathematical analysis of this model is provided, the basic reproduction number ( R 0 $\mathcal{R}_{0}$ ) is obtained and used for TB dynamics control. The results obtained show that lost to follow-up and transferred individuals constitute a risk, but less than the cases carrying germs. Rapidly evolving latent/exposed cases are responsible for the incidence increasing in the short and medium term, while slower evolving latent/exposed cases will be responsible for the persistent long-term incidence and maintenance of TB and delay elimination in the population. The numerical simulations of the model show that, with certain parameters, TB will die out or sensibly reduce in the entire Democratic Republic of the Congo (DRC) population. The strategies on which the DRC’s health system is currently based to fight this disease show their weaknesses because the TB situation in the DRC remains endemic. But monitoring contact, detection of latent individuals and their treatment are actions to be taken to reduce the incidence of the disease and thus effectively control it in the population. |
| first_indexed | 2024-12-11T16:14:16Z |
| format | Article |
| id | doaj.art-33db0e61d4f2494185a45a83cfa2a492 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-11T16:14:16Z |
| publishDate | 2020-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-33db0e61d4f2494185a45a83cfa2a4922022-12-22T00:58:59ZengSpringerOpenAdvances in Difference Equations1687-18472020-11-012020111910.1186/s13662-020-03091-0Analysis and simulation of a mathematical model of tuberculosis transmission in Democratic Republic of the CongoSelain Kasereka Kabunga0Emile F. Doungmo Goufo1Vinh Ho Tuong2Department of Mathematical Sciences, College of Science, Engineering & Technology, University of South AfricaDepartment of Mathematical Sciences, College of Science, Engineering & Technology, University of South AfricaInstitut Francophone International, Vietnam National UniversityAbstract According to the World Health Organization reports, tuberculosis (TB) remains one of the top 10 deadly diseases of recent decades in the world. In this paper, we present the modeling, analysis and simulation of a mathematical model of TB transmission in a population incorporating several factors and study their impact on the disease dynamics. The spread of TB is modeled by eight compartments including different groups, which are too often not taken into account in the projections of tuberculosis incidence. The rigorous mathematical analysis of this model is provided, the basic reproduction number ( R 0 $\mathcal{R}_{0}$ ) is obtained and used for TB dynamics control. The results obtained show that lost to follow-up and transferred individuals constitute a risk, but less than the cases carrying germs. Rapidly evolving latent/exposed cases are responsible for the incidence increasing in the short and medium term, while slower evolving latent/exposed cases will be responsible for the persistent long-term incidence and maintenance of TB and delay elimination in the population. The numerical simulations of the model show that, with certain parameters, TB will die out or sensibly reduce in the entire Democratic Republic of the Congo (DRC) population. The strategies on which the DRC’s health system is currently based to fight this disease show their weaknesses because the TB situation in the DRC remains endemic. But monitoring contact, detection of latent individuals and their treatment are actions to be taken to reduce the incidence of the disease and thus effectively control it in the population.http://link.springer.com/article/10.1186/s13662-020-03091-0TuberculosisMathematical modelModeling-simulationDRCEquation-based modelDifferential equations |
| spellingShingle | Selain Kasereka Kabunga Emile F. Doungmo Goufo Vinh Ho Tuong Analysis and simulation of a mathematical model of tuberculosis transmission in Democratic Republic of the Congo Advances in Difference Equations Tuberculosis Mathematical model Modeling-simulation DRC Equation-based model Differential equations |
| title | Analysis and simulation of a mathematical model of tuberculosis transmission in Democratic Republic of the Congo |
| title_full | Analysis and simulation of a mathematical model of tuberculosis transmission in Democratic Republic of the Congo |
| title_fullStr | Analysis and simulation of a mathematical model of tuberculosis transmission in Democratic Republic of the Congo |
| title_full_unstemmed | Analysis and simulation of a mathematical model of tuberculosis transmission in Democratic Republic of the Congo |
| title_short | Analysis and simulation of a mathematical model of tuberculosis transmission in Democratic Republic of the Congo |
| title_sort | analysis and simulation of a mathematical model of tuberculosis transmission in democratic republic of the congo |
| topic | Tuberculosis Mathematical model Modeling-simulation DRC Equation-based model Differential equations |
| url | http://link.springer.com/article/10.1186/s13662-020-03091-0 |
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