A case study of fractional-order varicella virus model to nonlinear dynamics strategy for control and prevalence

Abstract The purpose of this work is to construct and evaluate a dynamical susceptible–vaccinated–infected–recovered model for the propagation of the varicella virus in Jordan using existing epidemiological data. We use the fractal–fractional derivative in the Caputo sense to investigate the dynamical aspects of the suggested model. We investigate the model’s equilibria and evaluate the threshold parameter known as the reproductive number. A sensitivity analysis is also performed to detect the uncertainty of infection. Fixed point theorems and Arzela–Ascoli concepts are used to prove positivity, boundedness, existence, and uniqueness. The stability of the fractal–fractional model is examined in terms of Ulam–Hyers and generalized Ulam–Hyers types. Finally, using a two-step Newton polynomial technique, numerical simulations of the effects of various parameters on infection are used to explore the impact of the fractional operator on different conditions and population data. Chaos analysis and error analysis revealed the accuracy and precessions of solutions in the viable range. Several findings have been discussed by considering various fractal dimensions and arbitrary order. Overall, this study advances our understanding of disease progression and recurrence by establishing a mathematical model that can be used to replicate and evaluate varicella virus model behavior.