Abstract
We introduce the fractional-order derivatives into an HIV infection model with nonlinear incidence and show that the established model in this paper possesses nonnegative solution, as desired in any population dynamics. We also deal with the stability of the infection-free equilibrium, the immune-absence equilibrium, and the immune-presence equilibrium. Numerical simulations are carried out to illustrate the results.
Highlights
Fractional differential equations have garnered a lot of attention and appreciation due to their ability to provide an exact description of different nonlinear phenomena
We introduced a fractional-order HIV infection model with nonlinear incidence and dealt with the mathematical behaviors of the model
We found that the stability of the infection-free equilibrium and the immune-absence equilibrium of system (5) is the same as that of system (4)
Summary
A large number of works on modeling the dynamics of viral infection have been done [16,17,18,19,20], it has been restricted to integer-order (delay) differential equations. It has turned out that many phenomena in virus infection can be described very successfully by the models using fractional-order differential equations [21, 22]. Motivated by these references, in this paper, we will consider a fractionalorder HIV model.
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