Analysis of an SIR epidemic model with the effects of disease awareness
SUN Yanan1， XUE Yakui1， SUN Song2
(1.Department of Mathematics， North University of China， Taiyuan 030051， China； 2.Department of Civil Engineering， Hebei University of Architecture， Zhangjiakou， Hebei 075000， China)
Abstract：In this paper， in order to control the spread of infectious diseases， an epidemic model affected by the disease awareness was established. The basic reproduction number R0was calculated by using the next generation matrix. Two kinds of equilibria were solved. By using an algebraic method of Lyapunov function， it was proved that when R0〈1， the disease-free equilibrium was globally asymptotically stable， when R0〉1， the endemic equilibrium was globally asymptotically stable and disease-free equilibrium was unstable. In addition， the sensitivity analysis of R0 was carried out， and the effects of raising awareness on the sensitivity of R0 was also considered. It was found that raising awareness could reduce the basic reproduction number and effectively control the spread of epidemics. Our theoretical results were verified by numerical simulation， which provides theoretical basis for analysis of infectious diseases.
孙雅楠,薛亚奎,孙 松. 受疾病意识影响的SIR传染病模型分析[J]. 华中师范大学学报(自然科学版), 2021, 55(3): 337-342.
SUN Yanan,XUE Yakui,SUN Song. Analysis of an SIR epidemic model with the effects of disease awareness. journal1, 2021, 55(3): 337-342.
2021, Vol. 55 
