Dynamics of a Fractional Order Htlv-1 Model with Both Cell-To-Cell Transmissions and Mitosis

Abstract

A fractional-order HTLV type -1 model with transmission from an infected cell to uninfected cell and also through mitosis is constructed and investigated. The requirements for the existence of equilibrium points are established. We have generalized the integer theorem introduced by LaSalle into the fractional system and given some adequate requirements for the infection-free equilibrium plus chronic equilibrium being globally asymptotically stable. We employed a numerical technique established for changing the fractional-order derivative to the integer-order derivative to work out the HTLV type- 1 model. Numerical simulations are given to illustrate our results. The fractional-order derivatives are defined using the Caputo definition.