Pendekatan Pemodelan Matematika Penyebaran Tuberkulosis Sensitif Obat (TB-SO) dan Tuberkulosis Resisten Obat (TB-RO) dengan Vaksinasi dan Isolasi
Abstract
Tuberculosis (TB) remains a serious public health problem. Based on bacterial susceptibility to anti-tuberculosis drugs, TB is classified into drug-susceptible TB (DS-TB) and drug-resistant TB (DR-TB), where the presence of DR-TB poses a challenge for control because its management is more complex and it has the potential to sustain transmission within a population. Mathematical models can be used to understand the transmission dynamics of DS-TB and DR-TB. This study analyzes the model The novelty of this research lies in the development of a two-strain TB model that simultaneously incorporates strain-specific latent phase separation, differences in transmission rates between strains, and TB-RO-specific isolation interventions within a single framework. The analysis include determining equilibrium points, the reproduction number using next generation matrix, stability analysis, and numerical simulations. Three equilibrium points are obtained: disease-free, TB-RO mono-existence, and coexistence of both strains. Stability analysis at each equilibrium point is carried out using the value of . The analysis is performed through parameter conditions related to the transmission rate of DS-TB and the transmission rate of DR-TB . Sensitivity analysis shows that reducing and has a major impact on suppressing the transmission of DS-TB and DR-TB. In addition, increasing substantially reduces DR-TB transmission by enhancing the isolation of DR-TB cases.
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