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An SEIV epidemic model for childhood disease with partial permanent immunity isstudied. The basic reproduction number R0 has been worked out. The local and global asymptoticalstability analysis of the equilibria are performed, respectively. Furthermore, if we take the treatedrate τ as the bifurcation parameter, periodic orbits will bifurcate from endemic equilibrium whenτ passes through a critical value. Finally, some numerical simulations are given to support ouranalytic results.

An SEIV Epidemic Model for Childhood Diseases with Partial Permanent Immunity