Optimal Control of an Age-structured Tuberculosis Model

Abstract

This dissertation highlights the importance of age-structured mathematical models in studying the transmission dynamics of tuberculosis, as an infectious disease characterized by alatency period and the possibility of relapse after recovery. In this work, we study an agestructured SEIR epidemic model that describes the evolution of the disease by introducing the latency age a and the infection age b, while taking relapse into account through the rate δ. The mathematical analysis of the model aims to study the well-posedness of the problem, determine the disease-free equilibrium

, and derive the basic reproduction number ,which represents a fundamental epidemiological threshold for understanding the behavio of the disease within the population. The local and global stability properties of the model are also studied. Optimal control theory is used to propose effective strategies to reduce the spread of tuberculosis, based on vaccination and relapse reduction while taking intervention costs into account. The results confirm the importance of mathematical modeling and optimal control in supporting scientifically based public health decisions.