A Detailed Study of a Fractal-Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination

This article is devoted to investigate a mathematical model consisting on susceptible, exposed, infected, quarantined, vaccinated, and recovered compartments of COVID-19. The concerned model describes the transmission mechanism of the disease dynamics with therapeutic measures of vaccination of susceptible people along with the cure of the infected population. In the said study, we use the fractal-fractional order derivative to understand the dynamics of all compartments of the proposed model in more detail. Therefore, the first model is formulated. Then, two equilibrium points disease-free (DF) and endemic are computed. Furthermore, the basic threshold number is also derived. Some sufficient conditions for global asymptotical stability are also established. By using the next-generation matrix method, local stability analysis is developed. We also attempt the sensitivity analysis of the parameters of the proposed model. Finally, for the numerical simulations, the Adams-Bashforth method is used. Using some available data, the results are displayed graphically using various fractal-fractional orders to understand the mechanism of the dynamics. In addition, we compare our numerical simulation with real data in the case of reported infected cases.

Automated summary

This article investigates a mathematical model for COVID-19, which consists of six compartments representing susceptible, exposed, infected, quarantined, vaccinated, and recovered individuals. The model describes the disease transmission mechanism and therapeutic measures, such as vaccination and treatment. The dynamics of the model are analyzed using fractal-fractional order derivatives, resulting in the formulation of the first model and computation of equilibrium points. Stability analysis and sensitivity analysis are performed, followed by numerical simulations using the Adams-Bashforth method. The results are graphically displayed and compared with real data on reported infected cases.