Modeling and investigating the spread of COVID-19 dynamics with Atangana-Baleanu fractional derivative: a numerical prospective

Abstract

Fractional-order models have been used in the study of COVID-19 to incorporate memory and hereditary properties into the systems Moira and Xu (2003) Respirology 8 S9â14. These models have been applied to analyze the dynamics and behavior of the novel coronavirus. Various fractional-order models have been proposed, including the SIR and SEIR models, with the addition of compartments such as asymptomatic classes and virus repositories. Overall, fractional-order models have proven to be effective in studying the dynamics and spread of COVID-19. In this paper, we propose a nonlinear fractional model employing the Atangana-Baleanu derivative to describe COVID-19. To offer a clearer perspective, our investigation incorporates two distinct quarantine stages within the population. The first quarantine class consists of individuals who have not yet contracted the virus but have chosen to self-isolate at home. The second quarantine class encompasses individuals who are infected and are undergoing quarantine in hospitals. Additionally, we introduce a vaccination class, consisting of the portion of the population that has received the COVID-19 vaccination and is now at a reduced risk of infection. Fixed point theorems are employed to prove the existence and uniqueness of the solutions. The model’s threshold parameter R0 is calculated to investigate the pandemic’s future dynamics. The Toufik-Atangana scheme is applied to obtain numerical solutions for the fractional model. Further, we analyzed the data to assess how vaccination impacts the spread of the virus.The model includes two novel parameters to determine the speed and effectiveness of vaccination measures. To evaluate the accuracy of our model, we simulate the graphical results of this stage and compared them with integer-order derivative. The mathematical model for COVID-19 shows that both equilibrium points are locally stable. Moreover, to gain a deeper understanding of the disease, we conduct a sensitivity analysis to examine the effect of parameters on R0 . The study recommends continuing hospitalization and home isolation for infected individuals until virus transmission reduces sufficiently after vaccination. The given model provides useful insights into the pandemic’s dynamics and suggests measures for controlling its spread.