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**Mathematical analysis of a cholera model with vaccination.**
*(English)*
Zbl 1406.92351

Summary: We consider a \(SVR-B\) cholera model with imperfect vaccination. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is established. We calculate the certain threshold known as the control reproduction number \(\mathscr{R}_v\). If \(\mathscr{R}_v<1\), we obtain sufficient conditions for the global asymptotic stability of the disease-free equilibrium; the diseases will be eliminated from the community. By comparison of arguments, it is proved that if \(\mathscr{R}_v>1\), the disease persists and the unique endemic equilibrium is globally asymptotically stable, which is obtained by the second compound matrix techniques and autonomous convergence theorems. We perform sensitivity analysis of \(\mathscr{R}_v\) on the parameters in order to determine their relative importance to disease transmission and show that an imperfect vaccine is always beneficial in reducing disease spread within the community.

### MSC:

92C60 | Medical epidemiology |