Adaptive Sliding Mode Control Analysis of Non-Linear TB Epidemic Model

Abstract

Designing appropriate control intervention programs for handling infectious diseases such as tuberculosis (TB) involves elongated engagement with complex and challenging tasks. Several researchers used mathematical models and control system theory as a valuable tool in studying infectious disease dynamics and control. However, the majority of the previous studies for TB control are based on open-loop optimal control theory. In the design of the conventional optimal control approach, system parameters are assumed to be prior known and accurate. However, if the system contains uncertain parameters, the conventional control techniques may not provide the desired results. Therefore, in this study a robust adaptive sliding mode control (ASMC) strategy is applied to a non-linear TB model to handle the parameter uncertainties. The control objective is to decrease the population of individuals that are exposed and infected to zero by tracking a predefined reference trajectory. Adaption law is defined to update the parameter values to ensure the robustness of the control system against uncertainties. The stability of the closed-loop system is proved using the Lyapunov Function Theory, and the result is validated through numerical simulations. The study identifies alternative solutions in finding practically useful control strategies and illustrates the essential applications of closed-loop control systems. The work highlights a new methodology to inform realistic approaches towards realizing the United Nations (UN) 2030 plan for eradicating TB disease.