Journal of innovative applied mathematics and computational sciences
Volume 4, Numéro 1, Pages 63-85
2024-09-25
A Discrete-time Epidemic Model To Analyze And Control Multidrug-resistant And Extensively Drug-resistant Tuberculosis In Russia And India
Authors : Chennaf Bouchra . Abdelouahab Mohammed Salah .
Abstract
Despite significant progress in preventing and treating Tuberculosis (TB), it continues to be a leading cause of death worldwide. This is largely attributed to the rise of drug-resistant strains, notably Multidrug-Resistant Tuberculosis (MDR-TB) and Extensively Drug-Resistant Tuberculosis (XDR-TB). These resistant forms pose significant challenges, undermining the progress made against TB and necessitating innovative approaches for their management. This study enhances the Discrete VSEIT epidemiological model for TB by incorporating the dynamics of MDR/XDR-TB. The model incorporates distinct compartments for susceptible, exposed, infected, and resistant individuals receiving either first- or second-line treatments, in addition to those actively undergoing treatment. It considers natural population growth, the interactions among these groups, and the impact of treatment by chemoprophylaxis. The fundamental reproduction number ($\mathcal{R}_0 $) is determined by the mean of the next-generation matrix method. Investigation of the Stability of both the Disease-Free Equilibrium (DFE) and the Epidemic Equilibrium (EE) validate their global asymptotic stability. Model parameters are based on TB case data from India and Russia, two high-burden countries, from 2000 to 2022. The results indicate $\mathcal{R}_0 > 1$ for India and $\mathcal{R}_0 < 1$ for Russia. analyzing the sensitivity and numerical simulations show that increasing chemoprophylaxis treatment for exposed individuals decreases the advancement to multidrug-resistant, infectious, and extensively drug-resistant states. Additionally, BCG vaccination of children enhances immunity against TB and reduces disease transmission to healthy individuals, contributing to overall disease reduction. TB remains a more significant issue in India compared to Russia.
Keywords
discrete-time mode ; tuberculosi ; equilibrium ; global stability ; XDR ; MDR
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