CAJ | 학술논문

研究一类具有积分时滞的SIRS传染病动力学模型在脉冲免疫接种条件下的动力学行为。运用离散动力系统的频闪映射，获得一个“无病”周期解，证明该“无病”周期解是渐近稳定的。当模型的参数在适当条件下，该“无病”周期解是全局吸引的。运用脉冲时滞泛函微分方程理论获得带时滞系统持久性的充分条件，也得到该模型的全局吸引性条件。
연구일류구유적분시체적SIRS전염병동역학모형재맥충면역접충조건하적동역학행위。운용리산동력계통적빈섬영사，획득일개“무병”주기해，증명해“무병”주기해시점근은정적。당모형적삼수재괄당조건하，해“무병”주기해시전국흡인적。운용맥충시체범함미분방정이론획득대시체계통지구성적충분조건，야득도해모형적전국흡인성조건。
An SIRS epidemic disease model with pulse vaccination and integral delays was considered, and dynamics behaiors of the model under pulse vaccination were analyzed. By use of the discrete dynam-ical system determined by the stroboscopic map, an“infection-free” periodic solution was obtained and it iwas shown that the‘infection-free’ periodic solution was asymptotic stability. Then, it was proved that when some parameters of the model were in appropriate condictions, the ‘infection-free’ periodic sollu-tion was globally attractive. Futher, with the theory on delay functional and impulsive differential equa-tion, sufficient condiction with time delay for permanence of the system was given. At the same time, the condition of the global attractivity of the model was obtained.