CAJ | 학술논문

研究了一类含有潜伏时滞和非线性发生率的 SEIR 流行病模型。给出了疾病流行的阈值条件，并且得到了无病平衡点和流行病平衡点的局部稳定性条件。通过构造适当的 Lyapunov 泛函，结合 LaSalle 不变集原理，证明了当基本再生数 R01时，无病平衡点是全局渐近稳定的；但当 R0＞1时，流行病平衡点是全局渐近稳定的，同时利用数值模拟验证了分析的结果。
연구료일류함유잠복시체화비선성발생솔적 SEIR 류행병모형。급출료질병류행적역치조건，병차득도료무병평형점화류행병평형점적국부은정성조건。통과구조괄당적 Lyapunov 범함，결합 LaSalle 불변집원리，증명료당기본재생수 R01시，무병평형점시전국점근은정적；단당 R0＞1시，류행병평형점시전국점근은정적，동시이용수치모의험증료분석적결과。
A mathematical model describing the transmission dynamics of disease with nonlinear inci-dence rate and delay is constructed.The local stability of the disease-free equilibrium and epidemic equi-librium is established by analyzing the corresponding characteristic equation.Using suitable Lyapunov function and LaSalle's invariance principle,it is proved that if R0  1 then the disease-free equilibrium is globally asymptotically stable,but if R0 >1 then the epidemic equilibrium is globally asymptotically sta-ble.Some numerical simulations are also given to explain the conclusions.