Theoretical and Computational Study of Fractional-order Mathematical Models for Infectious Diseases

Epidemiology is the study of how diseases spread and the factors that contribute to their transmission. It uses mathematical models to comprehend disease patterns and control measures. Fractional and fractal-fractional order operators are mathematical tools that can more effectively model complex real-world problems than integer-order tools. This research aims to address gaps in current knowledge by utilizing these operators to analyze the impact of isolation and transmission modes on COVID-19. It also applies these tools to examine the COVID-19 situation in Wuhan, China. The research develops mathematical models and conducts qualitative and quantitative analyses to explore the existence theory, stability, and dynamics of these models. Numerical simulations are performed using real data to validate the accuracy of the models.