Analysis of Caputo Fractional-Order Co-Infection COVID-19 and Influenza SEIR Epidemiology by Laplace Adomian Decomposition Method

Around the world, the people are simultaneously susceptible to or infected with several infections. This work aims at the analysis of the dynamics of transmission of two deadly viruses, COVID-19 and Influenza, using a co-infection epidemiological model by applying the Caputo fractional derivative. Fractional differential equations are currently used worldwide to model physical and biological phenomena. Our comprehension of complicated phenomena is improved when fractional-order derivatives are used to model systems with memory effects and long-range interactions. Mathematical depictions of infectious disease dynamics and dissemination across communities are provided by epidemiological models, which are essential resources for understanding and controlling infectious diseases. These models support informed decision making to prevent outbreaks, evaluate intervention measures, and help researchers and policymakers understand how diseases spread. A subclass of epidemiological models called co-infection models focuses on studying the dynamics of several infectious illnesses that occur in the same population at the same time. They are especially useful in situations where people are simultaneously susceptible to or infected with several infections. Co-infection models provide information on the development of effective control techniques, the progression of disease, and the interactions between several pathogens. The qualitative study via stability analysis is discussed at equilibrium, the reproduction number R0 is computed, and the results are simulated using the Laplace Adomian Decomposition Method (LADM) for Fractional Differential Equations. We employ MATLAB R2023a for graphical presentations and numerical simulations.