Abstract
In this note, under the condition for the permanence used by [Beretta and Breda, An SEIR epidemic model with constant latency time and infectious period, Math. Biosci. Eng. 8 (2011) 931-952], applying modified monotone sequences, we establish the global asymptotic stability of the endemic equilibrium of this SEIR epidemic model, without any other additional conditions on the global stability.
Highlights
Motivated by the interesting contribution by Xu and Du [4] and Xu and Ma [6] to the stability analysis by means of iterative schemes and comparison principles, Beretta and Breda [1] recently investigated a two delayed SEIR epidemic model with a saturation incidence rate
One delay is a time taken by the infected individuals to become infectious, and the other delay is a time taken by an infectious individual to be removed from the infection
Muroya et al [3] investigated improvement on monotone iterative techniques in Xu and Ma [5] to obtain the global stability of the endemic equilibrium of a delayed SIRS epidemic model
Summary
Motivated by the interesting contribution by Xu and Du [4] and Xu and Ma [6] to the stability analysis by means of iterative schemes and comparison principles, Beretta and Breda [1] recently investigated a two delayed SEIR epidemic model with a saturation incidence rate. By applying iterative schemes as used for a delayed SIR epidemic model in Xu and Du [4] and the comparison principles, Beretta and Breda [1] established the following result: Theorem A (See Beretta and Breda [1]). Muroya et al [3] (see Muroya et al [2]) investigated improvement on monotone iterative techniques in Xu and Ma [5] to obtain the global stability of the endemic equilibrium of a delayed SIRS epidemic model. The following result is obtained in Beretta and Breda [1, Lemma 2.1]. The following results are obtaind in Beretta and Breda [1, Lemma 2.2 and Theorems 2.7-2.8]. If the condition (1.11) holds, system (1.1) is permanent
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