FRACTIONAL MATHEMATICAL MODEL FOR DYNAMICS OF INFECTIOUS DISEASES

Abstract

This thesis presents a comprehensive study of fractional-order differential models used for analysing the dynamics of infectious diseases. The fractional-order framework generalizes classical models with the inclusion of derivatives not being integer, thus capturing memory effects that describe long-term dependencies in disease spread and dynamics. We have also introduced time delays to account for incubation periods or delayed interventions seen in the real world delay between disease spread and treatment. Such delays have major impacts on both epidemic progress and the timing of control measures, such as quarantine, vaccination or therapeutic intervention. In this work, we developed and evaluated fractional-order models for infectious diseases, including delayed versions of SIR and SIQR models. We investigated the system's positiveness, boundedness, stability, bifurcation, and long-term behavior with various fractional orders and time delays. This study examined how these characteristics affect crucial epidemiological indicators including the basic reproduction number (𝑅0). Numerical simulations are used to describe the spread of diseases like COVID-19, demonstrating that time delays along with fractional dynamics provide a more accurate description of disease behaviour over time.