中北大学学报（自然科学版）2025，Vol.46Issue(4)：525-531,7.DOI:10.62756/jnuc.issn.1673-3193.2024.12.0005
考虑社会行为影响的离散传染病模型的建立及分析
Establishment and Analysis of a Discrete Infectious Disease Model Considering the Effects of Social Behavior
摘要
Abstract
During the outbreak of infectious diseases,how to effectively control the disease transmission and small social cost losses,is a major challenge for governments and public health decision-makers.In this paper,we introduced a utility function with information delay,which was described the social behaviors such as the expected cost and risk of infection,established and analyzed a discrete infectious disease model with contact rate that was affected by social behaviors.By calculating,the basic reproductive number of the model was obtained when the information was not delayed,and the existence conditions of the disease-free and positive equilibria were given.Using the method of constructing Lyapunov functions,we proved that the disease-free equilibrium was globally asymptotically stable,and the positive equilibrium was locally asymptotically stable by the Jury criterion.Furthermore,we simulated the behavior of system with the different time delay,and found that the system exhibits complex dynamic behaviors,such as monotonic stability,oscillation stability,periodicity,and even multiple peaks and spikes over a longer period of time with the increase of time delay,which means that time delay may lead to uncertainty of behaviors for the system.关键词
时间延迟/离散模型/社会行为/效用函数/稳定性Key words
time delay/discrete model/social behavior/utility function/stability分类
数理科学引用本文复制引用
韩婧,李桂花..考虑社会行为影响的离散传染病模型的建立及分析[J].中北大学学报（自然科学版）,2025,46(4):525-531,7.基金项目
山西省自然科学基金资助项目(201901D111179,202203021212130) （201901D111179,202203021212130）
