Stability and bifurcation analysis on a delayed epidemic model with information-dependent vaccination

• Published in: Physica scripta Vol. 94; no. 12; pp. 125202 - 125216
• Main Authors: Zhu, Linhe, Zhou, Xiao, Li, Yimin, Zhu, Yuxun
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.12.2019
• Subjects: epidemic model; global stability; Hopf bifurcation; information-dependent vaccination; optimal control
• ISSN: 0031-8949; 1402-4896
• DOI: 10.1088/1402-4896/ab2f04

The propagation of vaccine information plays an important role in the spread of infectious diseases. Scholars have researched in-depth the spread of infectious diseases or focused on the differential model that only considers the characteristics of infectious diseases themselves. Little attempt has been given on the dynamic analysis of infectious diseases based on the vaccination rate depending on information. This paper primarily explores a delayed epidemic model with information-dependent vaccination, which addresses increasing the concept of propagation delay on the basis of the model in Alberto et al (2007 Theor. Population Biol. 71 301-17). Theoretical analysis reveals the local stability and Hopf bifurcation, the global stability and the optimal control of our epidemic model. Finally, numerical simulations verify the theoretical results and analyze the influence of time delay on the transmission characteristics of our model.