【摘要】 建立了一类具有变化潜伏期的水源性疾病数学模型,得到了水源性疾病流行的阈值R0(基本再生数)。利用LaSalle不变集原理,通过构造新的Liapunov函数证明了平衡点的全局稳定性:当R0≤1时,系统的无病平衡点p0是全局渐近稳定的;当R0>1时,系统的地方病平衡点p*是全局渐近稳定的。最后利用数值模拟说明结论的正确性。更多还原

【Abstract】 The mathematical model of waterborne diseases with variable latent periods should be established in order to find out the epidemic threshold of waterborne diseases R0(basic reproductive number).By LaSalle Invariance Principle,the global stability of the equilibrium is proved by means of defining a new Liapunov function:when R0 ≤ 1,the disease-free equilibrium of the systemp0 is globally asymptotically stable;when R0 >1,the endemic equilibrium of the system p*is globally asymptotically stable.Some numerical simulations are also carried out to prove the correctness of the conclusion.更多还原