An SEIV epidemic model for childhood diseases with partial permanent immunity.

*(English)*Zbl 1344.92151Summary: An SEIV epidemic model for childhood disease with partial permanent immunity is studied. The basic reproduction number \(R_0\) has been worked out. The local and global asymptotical stability analysis of the equilibria are performed, respectively. Furthermore, if we take the treated rate \(\tau\) as the bifurcation parameter, periodic orbits will bifurcate from endemic equilibrium when \(\tau\) passes through a critical value. Finally, some numerical simulations are given to support our analytic results.

##### MSC:

92D30 | Epidemiology |

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\textit{M. Bai} and \textit{L. Ren}, Comput. Math. Methods Med. 2015, Article ID 420952, 13 p. (2015; Zbl 1344.92151)

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