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

Abstract

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.

Effects of information-induced behavioural changes during the COVID-19 lockdowns: the case of Italy

“…In this paper, the change in social behaviour is described by employing the method of information-dependent models [ 23 , 24 ] which is based on the introduction of a suitable information index (see [ 23 , 24 ]). This method has been applied to vaccine-preventable childhood diseases [ 24 , 25 ] and is increasingly being used (see [ 26 , 27 ] for very recent contributions).…”

Effects of information-dependent vaccination behavior on coronavirus outbreak: insights from a SIRI model

“…The behavioral change of individuals is introduced by employing the method of information-dependent models [14,15,33] which is based on the introduction of a suitable information index. Such an approach has been applied to general infectious diseases [8,14,15,23,33] as well as specific ones, including childhood diseases like measles, mumps and rubella [14,33] and is currently under development (for very recent papers see [5,22,35]). Therefore, another goal of this manuscript is to provide an application of the information index to a simple model containing relevant features of a coronavirus disease.…”

A theoretical approach to understanding rumor propagation dynamics in a spatially heterogeneous environment

“…Based on the above discussion, and combining (47) and (48), the characteristic equation 45is equivalent to Consequently, the characteristic equation of the linearized system of (40) at (0, 0, 0) is offered as follows…”

“…By using mean-field equations, Wang et al [30] established the SIRaRu rumor propagation model in complex networks and analyzed its dynamic characteristics. These studies above provided theoretical support for us to control rumor propagation more effectively [45,46,5,47,48].…”