Feng Shanshan, Jin Zhen
1School of Data Science and Technology, North University of China, Taiyuan, China.
2Complex Systems Research Center, Shanxi University, Taiyuan, China.
Adv Differ Equ. 2018;2018(1):339. doi: 10.1186/s13662-018-1801-x. Epub 2018 Sep 24.
The global transmission of infectious diseases poses huge threats to human. Traditional heterogeneous mean-field models on metapopulation networks ignore the heterogeneity of individuals who are in different disease states in subpopulations with the same degree, resulting in inaccuracy in predicting the spread of disease. In this paper, we take heterogeneity of susceptible and infectious individuals in subpopulations with the same degree into account, and propose a deterministic unclosed general model according to Markov process on metapopulation networks to curve the global transmission of diseases precisely. Then we make the general model closed by putting forward two common assumptions: a two-dimensional constant distribution and a two-dimensional log-normal distribution, where the former is equivalent to the heterogeneous mean-field model, and the latter is a system of weighted ordinary differential equations. Further we make a stability analysis for two closed models and illustrate the results by numerical simulations. Next, we conduct a series of numerical simulations and stochastic simulations. Results indicate that our general model extends and optimizes the mean-field model. Finally, we investigate the impacts of total mobility rate on disease transmission and find that timely and comprehensive travel restriction in the early stage is an effective prevention and control of infectious diseases.
传染病的全球传播对人类构成了巨大威胁。传统的异质平均场模型在集合种群网络上忽略了处于相同度数子种群中不同疾病状态个体的异质性，导致在预测疾病传播时不准确。在本文中，我们考虑了相同度数子种群中易感个体和感染个体的异质性，并根据集合种群网络上的马尔可夫过程提出了一个确定性非封闭通用模型，以精确刻画疾病的全球传播。然后，我们通过提出两个常见假设使通用模型封闭：二维常数分布和二维对数正态分布，其中前者等同于异质平均场模型，后者是一个加权常微分方程组。进一步地，我们对两个封闭模型进行稳定性分析，并通过数值模拟来说明结果。接下来，我们进行了一系列数值模拟和随机模拟。结果表明，我们的通用模型扩展并优化了平均场模型。最后，我们研究了总流动率对疾病传播的影响，发现早期及时全面的旅行限制是防控传染病的有效措施。
