Several collected data representing the spread of some infectious disease have demonstrated
that the spread does not really exhibit homogeneous spread. Clear examples can include the spread
of Spanish u and Covid-19. Collected data depicting numbers of daily new infections in the case
of Covid-19 from countries like Turkey, Spain show three waves with different spread patterns.
A clear indication of crossover behaviors. While modelers have suggested many mathematical
models to depicting these behaviors, it becomes clear that their mathematical models cannot really
capture the crossover behaviors, especially passage from deterministic resetting to stochastics.
Very recently Atangana and Seda have suggested a concept of piecewise modeling consisting in
defining a differential operator piece-wisely, the idea was first in chaos and outstanding patterns
were captured. In this paper, we extend this concept to the field of epidemiology with the aim
to depict waves with different patterns. Due to the novelty of this concept, a different approach
to insure the existence and uniqueness of system solutions are presented. A piecewise numerical
approach is presented to derive numerical solutions of such models. An illustrative example is
presented and compared with collected data from 3 different countries including Turkey, Spain
and Czechia. The obtained results let no doubt for us to conclude that this concept is a new
window that will help mankind to better understand nature.
Keywords: Piecewise modeling, piecewise existence and uniqueness, piecewise numerical scheme,
Covid-19 model, fractional operators and stochastic approach.
ATANGANA–SEDA NUMERICAL SCHEME FOR LABYRINTH ATTRACTOR WITH NEW DIFFERENTIAL AND INTEGRAL OPERATORS
