THE STABILITY AND HOPF BIFURCATION OF THE DENGUE FEVER MODEL WITH TIME DELAY

Abstract

This paper studied the dengue fever model with time delay.  This paper divided the time delay into four cases: (1) τ₁ = τ₂ = 0, (2) τ₁ = τ, τ₂ = 0, (3) τ₁ = 0, τ₂ = τ , (4) τ₁ = τ, τ₂ = τ, and studied the stability and Hopf bifurcation of the model on these three cases.  At the end of this paper, we simulated the dengue model with time delay by using Matlab software, and gained the numerical condition of this model which appearing periodic solutions and Hopf bifurcation.  On the first case τ₁ = τ, τ₂ = 0, the time delay threshold is τ₀ = 0.6155; on the second case τ₁ = 0, τ₂ = τ , the time delay threshold is τ₀ = 0.0490; on the third case τ₁ = τ, τ₂ = τ , the time delay threshold is τ₀ = 3.5454.