Bifurcation Analysis of a Fractional-Order Simplicial SIRS System Induced by Double Delays

Abstract

In this paper, a fractional-order susceptible-infected-recovered-susceptible (SIRS) model is studied, focusing on delay effects and high-order interactions. Two types of time delays are considered to describe latent period and healing cycle, respectively. From the ecological point of view, we found that the increasing delays caused by either the latent period or the healing cycle lead to the periodic outbreak of disease. The finding provided us with an important implication to preventing periodic outbreaks of disease by reducing the time delay, like accelerating the healing process with effective medication and medical intervention. Specifically, taking the time delays as bifurcation parameters, the stability of endemic equilibria and the existence of Hopf bifurcation are studied by analyzing the characteristic equation of the SIRS model. From a general point of view, based on the establishment of a fractional-order SIRS model, we found that the order of the fractional order is critical for describing the dynamic behavior of the model. Typically, the decrease of the order appears to bring about the disappearance of the periodic phenomenon (i.e. the periodic oscillation) of the originally stable system.

Pattern formation in reaction-diffusion information propagation model on multiplex simplicial complexes

“…The results show that although rumors spread faster on scale-free networks than on ER networks, the propagation scale is diametrically opposite [18]. Additionally, delay as an influencing factor in dynamical models widely exists in social environments and is often introduced [7,[22][23][24][25]. For example, in the stage of rumor propagation, it takes a certain amount of time for susceptible individuals to become rumor spreaders, as well as for rumor-infected individuals to dispel their doubts about the rumor [26][27][28].…”

“…Although the research background is different, there are strong similarities between the spread of disease and the spread of information from a mathematical point of view. Therefore, some classical dynamic models, such as the Suspicious-Infected (SI), Susceptible-Infected-Recovered (SIR), Susceptible-Exposed-Infected-Recovered (SEIR), and Susceptible-Infected-Recovered-Susceptible (SIRS) models, which are used to describe the dynamic process of epidemic transmission [5][6][7][8][9][10], have been applied to rumor transmission. Specifically, these studies are mostly based on ordinary differential equation models to study the propagation thresholds, global dynamics, control strategies, and the possible occurrence of complex bifurcation phenomena, such as forward bifurcation, backward bifurcation, and Hopf bifurcation [11][12][13][14].…”