A multi-stage SIR model for rumor spreading

Abstract

We propose a multi-stage structured rumor spreading model that consists of ignorant, new spreader, old spreader, and stifler. We derive a mean field equation to obtain the multi-stage structured model on homogeneous networks. Since rumors spread from a few people, we consider a large population by setting the number of initial spread to one in total population n and limiting n to ∞. We investigate a threshold phenomenon of rumor outbreak in the sense of the large population limit by studying the driven multi-stage structured model. The main conclusion of this paper is that the proposed model has a threshold phenomenon in terms of a basic reproduction number which is similar to the SIR epidemic model. We present numerical simulations to show the developed theory numerically.

Logistic equation and COVID-19

“…In more complex models, people are divided into different groups: (S) The susceptible class: those individuals who are capable of contracting the disease and becoming infected, (I) The infected class: those individuals who are capable of transmitting the disease to others, and (R) The removed class: infected individuals who are deceased, or have recovered and are either permanently immune or isolated, so the mathematical model called SIR model and its generalizations, includes a higher-order ODE system. The dynamics of such systems has not yet been sufficiently studied, and stochastic oscillations are possible in it [18], [19], [20], [21], [22], [23], [24], [25], [26]. However, models of this level can be comparatively easily implemented, they have shown their effectiveness and are actively used to model the distribution of COVID-19 [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38].…”

Analysis and Control of Malware Mutation Model in Wireless Rechargeable Sensor Network with Charging Delay

“…Thus, the endemic equilibrium is E * = (3.6501, 39.0175, 11.6384, 25.5761, 20.1179). The parameters are set to satisfy the Hopf condition, and the initial values of the nodes are set as (S, I 1 , I 2 , R, L) = (20,35,10,20,15). We can obtain ω 02 = 0.4706 and the critical value τ 30 = 4.9049.…”

“…A SEIR model is proposed by Zhu et al [13], and the authors analyzed the threshold, time delay, and global stability of a rumor spreading on social networks. Then, authors [14,15] also studied the spread of rumors in complex networks. Huang et al [16] proposed spreading dynamics of social behaviors in multiplex networks.…”

Dynamics of a stochastic epidemic-like rumor propagation model with generalized nonlinear incidence and time delay

“…Yao et al [22] proposed a rumor propagation model with dangerous state, studied the phenomenon of repeated rumor propagation on social media, and analyzed its local and global asymptotic stability. Choi et al [23] constructed a multi-stage structured rumor propagation model and discussed the threshold phenomenon of rumors outbreak under the restriction of large population. Generally speaking, most of the above studies study the dynamic behavior of rumor propagation from a certain perspective or factor, and rarely analyze the dynamic rules of rumor propagation from multiple perspectives.…”

“…(1) Extended the previous rumor spreading models. The idea of rumor propagation models presented on social networks in most literatures is mainly based on ODEs [21][22][23][36][37][38]. These models only deal with collective behavior, but do not take into account the effects of social network noises.…”