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An SEIV epidemic model for childhood diseases with partial permanent immunity. (English) Zbl 1344.92151
Summary: 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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##### References:
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