A fractional-order mathematical model based on vaccinated and infected compartments of SARS-CoV-2 with a real case study during the last stages of the epidemiological event
Özet
In 2020 the world faced with a pandemic spread that affected almost everything of
humans’ social and health life. Regulations to decrease the epidemiological spread and
studies to produce the vaccine of SARS-CoV-2 were on one side a hope to return back
to the regular life, but on the other side there were also notable criticism about the
vaccines itself. In this study, we established a fractional order differential equations
system incorporating the vaccinated and re-infected compartments to a SIR frame to
consider the expanded and detailed form as an SVIIvR model. We considered in the model
some essential parameters, such as the protection rate of the vaccines, the vaccination
rate, and the vaccine’s lost efficacy after a certain period. We obtained the local stability
of the disease-free and co-existing equilibrium points under specific conditions using the
Routh–Hurwitz Criterion and the global stability in using a suitable Lyapunov function.
For the numerical solutions we applied the Euler’s method. The data for the simulations
were taken from the World Health Organization (WHO) to illustrate numerically some
scenarios that happened
