Infectious disease models with proportional derivatives on time scales

The aim of this thesis is to formulate and solve the SI, SIR, and SIS infectious disease models on time scales, incorporating proportional derivatives. Initially, the fundamental principles of time scales and the details of proportional derivatives are explained to establish a foundational understanding. Following this, the history of infectious disease models and relevant studies in the literature are discussed. Problems involving the SI, SIR, and SIS models are solved in both classical and dynamic contexts. Finally, the SI, SIR, and SIS models on time scales are formulated using proportional derivatives and are solved with the aid of the properties of proportional derivatives and proportional integrals.