School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong, 030619, People's Republic of China.
School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, People's Republic of China.
Sci Rep. 2024 Nov 5;14(1):26765. doi: 10.1038/s41598-024-78218-4.
In the current study, we present a stochastic SAIS (unaware susceptible-aware susceptible-infectious-unaware susceptible) epidemic dynamic model on complex networks with multi-weights. The disease dynamic is influenced by random perturbations to the force of the infection rates, as well as awareness rates. To analyze the problem of extinction, we discuss both the stochastic asymptotic stability in the large and almost surely exponential stability of the trivial solution. Then, we get some sufficient conditions, which guarantee the stochastic persistence of infectious disease. Based on the Erdös-Réyni random graph, the numerical simulations are given. These not only validate our conclusions but also obtain else significative results. Both theoretical results and numerical simulations further reflect that improvement of risk awareness and reduction of decay in awareness are highly effective in preventing disease spread. And then, environmental noises play a significant role in disease transmission.
在当前的研究中，我们提出了一个具有多权重的复杂网络上的随机 SAIS（无意识易感染-有意识易感染-感染-无意识易感染）传染病动力学模型。疾病动态受到感染率和意识率的随机扰动的影响。为了分析灭绝问题，我们讨论了大随机渐近稳定性和平凡解的几乎必然指数稳定性。然后，我们得到了一些充分条件，这些条件保证了传染病的随机持久性。基于 Erdös-Réyni 随机图，给出了数值模拟。这些不仅验证了我们的结论，还获得了其他有意义的结果。理论结果和数值模拟进一步反映了提高风险意识和降低意识衰减在预防疾病传播方面非常有效。然后，环境噪声在疾病传播中起着重要作用。
