TY - JOUR
T1 - A Detailed Study of a Fractal-Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination
AU - Shah, Kamal
AU - Sinan, Muhammad
AU - Abdeljawad, Thabet
AU - El-Shorbagy, M. A.
AU - Abdalla, Bahaaeldin
AU - Abualrub, Marwan S.
N1 - Publisher Copyright:
© 2022 Kamal Shah et al.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85143056314&partnerID=8YFLogxK
U2 - 10.1155/2022/7236824
DO - 10.1155/2022/7236824
M3 - Article
AN - SCOPUS:85143056314
SN - 1076-2787
VL - 2022
JO - Complexity
JF - Complexity
M1 - 7236824
ER -