Stability, Hopf bifurcation and control of a fractional order delay cervical cancer model with HPV infection

This paper presents a basic model for the therapeutic effect of two drugs on patients with early cervical cancer. Two cases are considered: with constant control and with optimal control. For case one, the system is proved to have a unique non-negativity solution if the initial values are positive; then the sufficient conditions for the existence and stability of the equilibriums are derived; and Hopf bifurcation is also considered. For case two, by using the Pontryagin's Maximum Principle, we get the optimal control solution. Some examples and numerical simulations are presented. Discussions and conclusions are listed at the end.