Zhang Rui, Zhang Yunhu
Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, People's Republic of China.
Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, People's Republic of China.
J Theor Biol. 2022 Jul 7;544:111134. doi: 10.1016/j.jtbi.2022.111134. Epub 2022 Apr 22.
As a common infectious disease, scarlet fever has exposed a tendency of slow fluctuating ups and downs in recent years with a certain periodicity. In this work, a novel differential equation epidemic model with freely transmitted viruses is introduced to investigate the transmission dynamics of scarlet fever in Northwest China. First, the correlation analysis reveals that the incidence rate of scarlet fever is significantly positively correlated with air pressure (r = 0.61), conversely negatively correlated with precipitation (r = -0.15). Furthermore, the basic reproduction number R is derived, and this paper proves that the unique disease-free periodic solution P is globally symptotically stable when R < 1, while the disease is uniformly persistent and at least one positive periodic solution exists when R > 1. Moreover, by studying the qualitative of correlation between the effective reproduction number and air pollutants or meteorological factors, the seasonal variation pattern of incidence is summarized. Our investigations suggest that the relevant epidemic prevention departments should pay close attention to changes in environmental factors of the five provinces of Northwest China to formulate timely prevention strategies before the arrival of the high-risk period.
猩红热作为一种常见的传染病，近年来呈现出缓慢波动起伏且具有一定周期性的趋势。在这项工作中，引入了一种具有自由传播病毒的新型微分方程流行病模型，以研究中国西北地区猩红热的传播动态。首先，相关性分析表明，猩红热发病率与气压显著正相关（r = 0.61），相反与降水量呈负相关（r = -0.15）。此外，推导了基本再生数R，本文证明当R < 1时，唯一的无病周期解P是全局渐近稳定的，而当R > 1时，疾病是一致持续的且至少存在一个正周期解。而且，通过研究有效再生数与空气污染物或气象因素之间相关性的定性特征，总结了发病率的季节变化模式。我们的研究表明，相关防疫部门应密切关注中国西北五省环境因素的变化，以便在高危期到来之前及时制定预防策略。
