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| A Mathematical Modeling of Two-Strain Tuberculosis Transmission: Deterministic and Stochastic Approaches to Screening, Treatment, and Quarantine Strategies |
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| KeyWord:Deterministic model, stochastic model, screening, treatment, quarantine |
| Author Name | Affiliation | | A. Muhammad Mu'adz | Department of Mathematics, Hasanuddin University, Perintis Kemerdekaan Km.10, 90245, Makassar, South Sulawesi, Indonesia | | Kasbawati | Department of Mathematics, Hasanuddin University, Perintis Kemerdekaan Km.10, 90245, Makassar, South Sulawesi, Indonesia | | Syamsuddin Toaha | Department of Mathematics, Hasanuddin University, Perintis Kemerdekaan Km.10, 90245, Makassar, South Sulawesi, Indonesia | | Muhammad Rifqy Adha Nurdiansyah | Department of Mathematics, Hasanuddin University, Perintis Kemerdekaan Km.10, 90245, Makassar, South Sulawesi, Indonesia |
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| Abstract: |
| This research observes the transmission dynamics of drug-sensitive tuberculosis (DS-TB), drug-resistant tuberculosis (DR-TB) and undiagnosed tuberculosis infections using deterministic and stochastic models. The study focuses on the impacts of contact rates, screening of latent individuals or high-risk groups, treatment, and quarantine measures on the basic reproduction rate ($R_0$) and the estimated number of infected individuals ($m$). The results show that undiagnosed infected individuals are the greatest factor on the spread of tuberculosis within the system, which emphasizes the importance of screening on latent individuals. Analysis on the effects of screening on latent individuals also emphasizes the importance of treatment and quarantine for both DS-TB and DR-TB infections, respectively. However, analysis on the effects of both treatment and quarantine states that relying on either treatment or quarantine efforts is not enough to stop the spread of the two-strain TB within the system; thus a combined strategies is required to help eradicate the disease. |
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