Dynamical analysis of a fractional SVEIHRP mathematical model for COVID-19 transmission in the perspective of Bangladesh

In this study, we establish a sophisticated compartmental Caputo fractional-order Susceptible-Vaccinated-Exposed-Infected-Hospitalized-Recovered Pathogens mathematical model for analyzing the dynamical behavior of COVID-19 transmission in the perspective of COVID-19 pandemic situation of Bangladesh considering the data up to 2nd dose vaccination. The frame of Caputo fractional-order derivative has been used to fractionalize the model’s equations. A total of 10 distinct compartments have been used to represent the dynamics of human and novel coronavirus. The Next-generation matrix approach has been used for finding the basic reproduction number of considered model. For establishing the existence and uniqueness of the model’s solutions, here we apply Banach fixed point theorem. Routh–Hurwitz, Ulam–Hyers and generalized Ulam–Hyers stability criteria have been applied for stability analysis. We execute a sensitivity analysis to check the comparative prominence of the model’s parameters. For the numerical simulation, data have been accumulated from the COVID-19 dashboard of Directorate general of health services of Bangladesh. The Fractional Adams–Bashforth–Moulton method along with MATLAB code fde12.m has also been applied to perform the numerical simulation. Furthermore, here we use some Maple codes for finding the model’s equilibrium points, basic reproduction number and sensitivity indices. Finally, we include a discussion on the influence of new rate of infections through environment and interaction with infected persons as well as the effect of 1st and 2nd dose vaccinations.