Author: Ruixia Yuan; Zhidong Teng; Jinhui Li
Title: Complex dynamics in an SIS epidemic model induced by nonlinear incidence Document date: 2018_5_25
ID: 396rgxno_51
Snippet: In this subsection, we will study the Hopf bifurcation of system (3) for (i) R * < R 0 < 1 and Λ > (1 − σ)/a; (ii) R 0 > 1. From the discussion in Section 2, it can be seen that Hopf bifurcation may occur at E 3 , E 5 . As the expressions of equilibria E 3 and E 5 are same, no considering the values of every parameters. Based on Theorem 4, Theorem 5 and Theorem 6, we know that the stability of E 3 and E 5 are similar and when ψ k = 0, E k (k.....
Document: In this subsection, we will study the Hopf bifurcation of system (3) for (i) R * < R 0 < 1 and Λ > (1 − σ)/a; (ii) R 0 > 1. From the discussion in Section 2, it can be seen that Hopf bifurcation may occur at E 3 , E 5 . As the expressions of equilibria E 3 and E 5 are same, no considering the values of every parameters. Based on Theorem 4, Theorem 5 and Theorem 6, we know that the stability of E 3 and E 5 are similar and when ψ k = 0, E k (k = 3, 5) is a weak focus or center. Thus, we show the existence of Hopf bifurcation around E k (k = 3, 5).
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