Analysis of a fractional mathematical model for Zika virus under the
framework of singular and nonsingular kernels
Abstract
In this paper, we investigate the dynamics of a fractional zika virus
model (ZIKV) with Caputo, Caputo-Fabrizio-Caputo (CFC) and
Atangana-Baleanu-Caputo (ABC) derivatives. Firstly the basic properties
of the classical integer order model are furnished followed by the
equilibrium points and basic reproduction number. Furthermore, with
respect to the Caputo, CFC and ABC derivatives, we establish via a fixed
point technique that under certain conditions the fractional ZIKV model
admits a unique system of solutions. The Adams-Bashforth numerical
scheme incorporating the fractional order parameter is then used to
obtain numerical schemes for the approximate solutions of the fractional
ZIKV model with respect to each of the considered fractional
differential operators. Finally, with a view to visualize the behaviour
of the approximate solutions to fractional ZIKV model with respect to
each of the fractional differential operators, we do some numerical
simulations for distinct values of the fractional order parameter.