KONTROL SLIDING MODE ADAPTIF DENGAN VAKSINASI DAN TREATMENT PADA MODEL PENYEBARAN TUBERKULOSIS

• Published in: EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol. 18; no. 1; p. 54
• Main Author: Ayu, Regina Wahyudyah Sonata
• Format: Journal Article
• Language: English
• Published: 30.05.2024
• ISSN: 1978-4422; 2656-7660
• DOI: 10.20527/epsilon.v18i1.12326

This research examines the design of adaptive sliding mode control in a tuberculosis (TB) disease spread model, considering uncertainties within the model. The TB model involves five state variables (susceptible individuals, vaccinated individuals, individuals with latent TB infection, individuals with active TB infection, and individuals under treatment) and three control input variables consisting of vaccination and treatment. The objective of this control design is to reduce the number of susceptible individuals, individuals with active TB infection, and the number of individuals under treatment by tracking the given reference functions. Stability and convergence of tracking errors of the controlled system are proved using the Lyapunov Stability Theorem. Numerical simulations are conducted to evaluate the performance of the designed control under various parameter uncertainty conditions. Based on the simulation results, it is shown that the adaptive sliding mode controllers guarantee the convergence of tracking errors is achieved despite the presence of uncertainty in the model.