State Feedback and Synergetic controllers for tuberculosis in infected population.

Area of Science:

• Epidemiology
• Mathematical Modeling
• Control Theory

Background:

• Tuberculosis (TB) is a highly contagious disease with significant societal impact.
• Controlling TB spread requires effective interventions targeting both infected and susceptible populations.

Purpose of the Study:

• To design and analyze non-linear controllers for a Susceptible, Exposed, Infected, Recovered, and Resistant (SEIRs) mathematical model of TB.
• To evaluate the efficacy of State Feedback (SFB) and Synergetic controllers in TB prevention and control.

Main Methods:

• Development of a five-state SEIRs epidemiological mathematical model for TB.
• Design of State Feedback (SFB) and Synergetic non-linear controllers.
• Application of Lyapunov control theory to prove asymptotic stability.
• Simulation analysis using MATLAB/Simulink.

Main Results:

• Both SFB and Synergetic controllers demonstrated fast convergence of system states.
• Controllers effectively reduced infected individuals through treatment and prevented susceptible individuals via vaccination.
• The SFB controller exhibited superior performance compared to the Synergetic controller.

Conclusions:

• Non-linear control strategies, particularly SFB, offer a promising approach for managing and preventing TB outbreaks.
• Mathematical modeling combined with control theory provides a robust framework for epidemiological disease control.
• The SFB controller is recommended for its efficiency in reducing TB transmission and improving population health outcomes.