Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis
The long and binding treatment of tuberculosis (TB) at least 6–8 months for the new cases, the partial immunity given by BCG vaccine, the loss of immunity after a few years doing that strategy of TB control via vaccination and treatment of infectious are not sufficient to eradicate TB. TB is an infe...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2019-01-01
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| Series: | Journal of Biological Dynamics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/17513758.2018.1563218 |
| _version_ | 1818133312368017408 |
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| author | Leontine Nkague Nkamba Thomas Timothee Manga Franklin Agouanet Martin Luther Mann Manyombe |
| author_facet | Leontine Nkague Nkamba Thomas Timothee Manga Franklin Agouanet Martin Luther Mann Manyombe |
| author_sort | Leontine Nkague Nkamba |
| collection | DOAJ |
| description | The long and binding treatment of tuberculosis (TB) at least 6–8 months for the new cases, the partial immunity given by BCG vaccine, the loss of immunity after a few years doing that strategy of TB control via vaccination and treatment of infectious are not sufficient to eradicate TB. TB is an infectious disease caused by the bacillus Mycobacterium tuberculosis. Adults are principally attacked. In this work, we assess the impact of vaccination in the spread of TB via a deterministic epidemic model (SV ELI) (Susceptible, Vaccinated, Early latent, Late latent, Infectious). Using the Lyapunov–Lasalle method, we analyse the stability of epidemic system (SV ELI) around the equilibriums (disease-free and endemic). The global asymptotic stability of the unique endemic equilibrium whenever $ \mathcal R_{0} \gt 1 $ is proved, where $ \mathcal R_{0} $ is the reproduction number. We prove also that when $ \mathcal R_{0} $ is less than 1, TB can be eradicated. Numerical simulations, using some TB data found in the literature in relation with Cameroon, are conducted to approve analytic results, and to show that vaccination coverage is not sufficient to control TB, effective contact rate has a high impact in the spread of TB. |
| first_indexed | 2024-12-11T08:50:43Z |
| format | Article |
| id | doaj.art-a874090b75b446828d6640009ab2b6b2 |
| institution | Directory Open Access Journal |
| issn | 1751-3758 1751-3766 |
| language | English |
| last_indexed | 2024-12-11T08:50:43Z |
| publishDate | 2019-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Biological Dynamics |
| spelling | doaj.art-a874090b75b446828d6640009ab2b6b22022-12-22T01:14:02ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662019-01-01131264210.1080/17513758.2018.15632181563218Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosisLeontine Nkague Nkamba0Thomas Timothee Manga1Franklin Agouanet2Martin Luther Mann Manyombe3University of Yaoundé IAIDEPY Association des Ingénieurs Diplomés de l'Ecole Polytechnique de YaoundéUniversity of Yaoundé IUniversity of Yaoundé IThe long and binding treatment of tuberculosis (TB) at least 6–8 months for the new cases, the partial immunity given by BCG vaccine, the loss of immunity after a few years doing that strategy of TB control via vaccination and treatment of infectious are not sufficient to eradicate TB. TB is an infectious disease caused by the bacillus Mycobacterium tuberculosis. Adults are principally attacked. In this work, we assess the impact of vaccination in the spread of TB via a deterministic epidemic model (SV ELI) (Susceptible, Vaccinated, Early latent, Late latent, Infectious). Using the Lyapunov–Lasalle method, we analyse the stability of epidemic system (SV ELI) around the equilibriums (disease-free and endemic). The global asymptotic stability of the unique endemic equilibrium whenever $ \mathcal R_{0} \gt 1 $ is proved, where $ \mathcal R_{0} $ is the reproduction number. We prove also that when $ \mathcal R_{0} $ is less than 1, TB can be eradicated. Numerical simulations, using some TB data found in the literature in relation with Cameroon, are conducted to approve analytic results, and to show that vaccination coverage is not sufficient to control TB, effective contact rate has a high impact in the spread of TB.http://dx.doi.org/10.1080/17513758.2018.1563218effective contact ratevaccinationtuberculosisbasic reproduction numberglobal stability |
| spellingShingle | Leontine Nkague Nkamba Thomas Timothee Manga Franklin Agouanet Martin Luther Mann Manyombe Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis Journal of Biological Dynamics effective contact rate vaccination tuberculosis basic reproduction number global stability |
| title | Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis |
| title_full | Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis |
| title_fullStr | Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis |
| title_full_unstemmed | Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis |
| title_short | Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis |
| title_sort | mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis |
| topic | effective contact rate vaccination tuberculosis basic reproduction number global stability |
| url | http://dx.doi.org/10.1080/17513758.2018.1563218 |
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