Dynamic analysis and bifurcation control of a fractional-order cassava mosaic disease model

In this paper, a fractional-order model including healthy cassava, infected cassava, and infected vectors is proposed to study the transmission dynamics of cassava mosaic disease. Firstly, the non-negativity and boundedness of the solutions in the system and the stability of all feasible equilibrium points of the system are strictly discussed. Hopf bifurcation induced by the disease transmission rate from the vectors to the healthy cassava is studied for the proposed system. Secondly, a novel periodic pulse feedback controller is proposed to suppress the bifurcation phenomenon. The expression of the bifurcation point of the controlled system is given with the help of the linearized average system. It is shown that the stability performance is extremely excellent with the help of the proposed controller and that the control effect is independent of pulse width. Numerical simulations are performed to validate the theoretical results.