@article{Alshareef2024, 
author = {Abeer Alshareef},
title = {Quantitative analysis of a fractional order of the    S  E      I          c              I          η        V  R epidemic model with vaccination strategy},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {3},
pages = {6878-6903},
keywords = {global stability, fractional order, vaccination, infectious disease, the basic reproduction number},
url = {https://www.sciopen.com/article/10.3934/math.2024335},
doi = {10.3934/math.2024335},
abstract = {This work focused on studying the effect of vaccination rate    κ on reducing the outbreak of infectious diseases, especially if the infected individuals do not have any symptoms. We employed the fractional order derivative in this study since it has a high degree of accuracy. Recently, a lot of scientists have been interested in fractional-order models. It is considered a modern direction in the mathematical modeling of epidemiology systems. Therefore, a fractional order of the SEIR epidemic model with two types of infected groups and vaccination strategy was formulated and investigated in this paper. The proposed model includes the following classes: susceptible        S    (  t  ), exposed        E    (  t  ), asymptomatic infected              I              c              (  t  ), symptomatic infected              I              η              (  t  ), vaccinated        V    (  t  ), and recovered        R    (  t  ). We began our study by creating the existence, non-negativity, and boundedness of the solutions of the proposed model. Moreover, we established the basic reproduction number              R              0      , that was used to examine the existence and stability of the equilibrium points for the presented model. By creating appropriate Lyapunov functions, we proved the global stability of the free-disease equilibrium point and endemic equilibrium point. We concluded that the free-disease equilibrium point is globally asymptotically stable (GAS) when              R              0          ≤    1, while the endemic equilibrium point is GAS if              R              0        >  1. Therefore, we indicated the increasing vaccination rate    κ leads to reducing              R        0  . These findings confirm the important role of vaccination rate    κ in fighting the spread of infectious diseases. Moreover, the numerical simulations were introduced to validate theoretical results that are given in this work by applying the predictor-corrector PECE method of Adams-Bashforth-Moulton. Further more, the impact of the vaccination rate    κ was explored numerically and we found that, as    κ increases, the              R              0       is decreased. This means the vaccine can be useful in reducing the spread of infectious diseases.}
}