College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China.
Math Biosci Eng. 2020 Sep 8;17(5):5925-5943. doi: 10.3934/mbe.2020316.
In this paper, a stochastic SIRS epidemic model with saturating contact rate is constructed. First, for the deterministic system, the stability of the equilibria is discussed by using eigenvalue theory. Second, for the stochastic system, the threshold conditions of disease extinction and persistence are established. Our results indicate that a large environmental noise intensity can suppress the spread of disease. Conversely, if the intensity of environmental noise is small, the system has a stationary solution which indicates the disease is persistent. Eventually, we introduce some computer simulations to validate the theoretical results.
本文构建了一个带有饱和接触率的随机 SIRS 传染病模型。首先，针对确定性系统，利用特征值理论讨论了平衡点的稳定性。其次，针对随机系统，建立了疾病灭绝和持续的阈值条件。我们的结果表明，较大的环境噪声强度可以抑制疾病的传播。相反，如果环境噪声强度较小，系统存在一个稳定解，表明疾病持续存在。最后，我们引入了一些计算机模拟来验证理论结果。
