A B C Fractional Derivative for Varicella-Zoster Virus Using Two-Scale Fractal Dimension Approach with Vaccination

Abstract

Chickenpox or varicella is an infectious disease caused by the varicella-zoster virus $\left(\mathcal{V}\mathcal{Z}\mathcal{V}\right)$ . This virus is the cause of chickenpox (usually a primary infection in the nonimmune host) and herpes zoster. In this paper, a compartmental model for the dynamics of $\mathcal{V}\mathcal{Z}$ transmission with the effect of vaccination is solved using the $\mathcal{A}\mathcal{B}\mathcal{C}$ fractional derivative. The possibility of using the fractal dimension as a biomarker to identify different diseases is being investigated. The problem is investigated in two different levels of research using two scale dimensions. To ascertain the existence and uniqueness of the solution, we qualitatively evaluate the model. We have used the Euler method to compute the numerical solution for the system. At the end, we provide the graphical results showing the effectiveness of two-scale dimension and fractional calculus in the current model.