| Abstract: |
| We consider the dynamical behavior of an SEIS model with delay denoting an incubation time. In Paulhus, Wang (2015), global stability of equilibria is investigated by constructing suitable Lyapunov functionals. They mention that a disease-free equilibrium $E_0$ is globally asymptotically stable if $R_0 \leq 1$, and the endemic equilibrium $E_*$ is global asymptotically stable if $R_0 > 1$, where $R_0$ is the basic reproductive ratio. However, in the proof of global stability of $E_0$, an additional condition is required to construct Lyapunov functional in Paulhus, Wang (2015). We prove stability of $E_0$ under an another condition by constructing a new Lyapunov functional. Combining with their results, we claim that any conditions are not necessary under $R_0 \leq 1$ to prove global asymptotic stability of $E_0$. |
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