A fractional order vaccination model for COVID-19 incorporating environmental transmission: a case study using Nigerian data

Abstract

In this work, a fractional-order vaccination model for the novel Coronavirus 2019 (COVID-19) incorporating environmental transmission is considered and analyzed using tools of fractional calculus. The Laplace transform technique and the fixed point theorem lay out the model solutions' existence and uniqueness. The solutions' positivity and boundedness are also demonstrated. Additionally, the stability of the model's equilibrium points is discussed using the fractional-order system stability theory. The model is fitted using the data sets for the Pfizer vaccination program in Nigeria from April 1, 2021, to June 10, 2021. In conclusion, simulation results for various fractional parameter values are presented. It has been observed that increasing fractional-order values has distinct effects on the various model compartments, for $R_0 < 1$ and $R_0 > 1$, respectively.