Control and applications of dynamical systems

Abstract

The work presented in this thesis is a study two types of problems associated with the HIV/AIDS epidemic model: the equilibrium model’s stability analysis and the optimal con- trol problem within the frameworks of ODE and PDE senses. We analyzed the local and global stability using the theory of Volterra-Lyapunov stable matrices combined with the classical Lyapunov function method. For the optimal control problem, an optimal con- trol strategy was proposed that incorporates three key measures to combat the spread of HIV/AIDS: promoting condom use, screening individuals unaware of their infection status, and providing treatment to those infected. The objective functional was designed to mini- mize the total number of both susceptible and infected individuals. Then an optimal control is obtained which minimizes the objective functional. Numerical simulations were carried out to illustrate and validate the analytical findings.