一类具有饱和传染率且带有潜伏期和接种期的SVEIR模型的研究

摘要

In this paper, we consider an epidemic model with latent and vaccination period, and establish the SVEIR epidemic model with saturated infection rate. Then, we find the basic reproduction number which determines whether the disease exists. By applying the suitable Lyapunov functional and LaSalle invariant principle, we prove that when the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable; when the basic reproduction number is greater than unity, the unique endemic equilibrium exists and is the globally asymptotically stable of the endemic equilibrium. Finally, the numerical simulations indicate the theoretical analysis is correct.%本文研究了带有潜伏期和接种期的传染病，建立一类具有饱和发生率且带有潜伏期和接种期的SVEIR模型，找到了决定疾病绝灭或持续生存的阀值-基本再生数。通过构造合适的Lyapunov函数，运用LaSalle不变集原理，证明了当基本再生数小于1时，无病平衡点是全局渐近稳定的；当基本再生数大于1时，存在唯一的感染平衡点，并且得到了该平衡点的全局稳定性。最后，数值模拟验证了理论的正确性。