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To understand the interaction between the insects and the plants, a system of delay differential equations is proposed and studied. We prove that if , the disease-free equilibrium is globally asymptotically stable for any length of time delays by constructing a Lyapunov functional, and the system admits a unique endemic equilibrium if . We establish the sufficient conditions for the stability of the endemic equilibrium and existence of Hopf bifurcation. Using the normal form theory and center manifold theorem, the explicit formulae which determine the stability, direction, and other properties of bifurcating periodic solutions are derived. Some numerical simulations are given to confirm our analytic results.

Stability and Hopf Bifurcation Analysis of a Plant Virus Propagation Model with Two Delays