A Mathematical Model on the Transmission Dynamics of Tuberculosis
Keywords:
Mathematical Model, Transmission, Dynamics, TuberculosisAbstract
This study explores a mathematical model to analyze the transmission dynamics of tuberculosis (TB), focusing on Drug-Sensitive TB (DS-TB) and Drug-Resistant TB (DR-TB). The study adopted a deterministic (SEIR) model where each compartment represents a distinct stage of the epidemic and the population's members are assigned to them (the immunized, susceptible, latently infected, infectious, and recovered compartments). Parameters such as transmission rates, treatment efficiencies, and vaccination coverage are incorporated into the model. Equilibrium analysis identifies a Disease-Free Equilibrium (DFE), and solutions are shown to be biologically feasible, bounded, and unique. Findings indicate that improved treatment efficiency and higher vaccination coverage lower the basic reproduction number (R₀) and mitigate TB spread. It is recommended that the government strengthen vaccination programs to maintain high coverage, particularly for newborns, and enhance treatment strategies to improve recovery rates.
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