Global behavior of a two-stage contact process on complex networks

Wang, Yi; Cao, Jinde; Li, Mengqi; Li, Li

doi:10.1016/j.jfranklin.2019.02.020

Cited by 12 publications

(6 citation statements)

References 27 publications

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“…Proof It is easy to see that the vector field defined by the right-hand side of (5) is locally Lipschitz on R 4n + , so there admits a unique solution of system (5) for t ≥ 0. The proof of the nonnegativity of each state variable is similar to Lemma 2.1 in Wang et al [36], so it is omitted here.…”

Section: Degree-based Mean-field (Dbmf) Epidemic Dynamics Of Influenzamentioning

confidence: 99%

“…To compute the basic reproduction number R 0 for model (36), we employ the next-generation matrix approach involving only variables ϕ L , ϕ I and ϕ A . Lin-earizing the equations associated with these variables about the DFE (θ = 1, and…”

Section: Basic Reproduction Numbermentioning

confidence: 99%

“…Remark 2.5 Similar to the approach in [39], model (36) could be directly extended to influenza-like diseases in quenched networks with degree correlation. In particular, the probability θ(t) that a randomly chosen edge has never transmitted infection by time t should be associated with the degree k of a node, i.e., θ k (t).…”

Section: Letting G(1)mentioning

confidence: 99%

“…Similarly, for the model (36), if a population has a fixed contact structure, we may use the final size relation (46) to estimate the transmission rate τ and thus the basic reproduction number R 0 . The procedure proceeds as in annealed networks, though the calculations are more complex and cumbersome.…”

Section: Numerical Simulationsmentioning

confidence: 99%

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Epidemic dynamics of influenza-like diseases spreading in complex networks

2020

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Population contact pattern plays an important role in the spread of an infectious disease. This can be described in the framework of a complex network approach. In this paper network epidemic models for influenza-like diseases that may have infectious force in incubative or asymptomatic stage are formulated and studied. Two general types of network models are considered: the annealed and the quenched networks. The next-generation matrix approach is employed to compute the basic reproduction number of our networkbased models. The implicit equations for the final epidemic size are derived, and the existence and uniqueness of solutions for implicit equations are studied by rewriting implicit equations as suitable fixedpoint problems. In particular, for networks with no degree correlation, low-dimensional systems of nonlinear ordinary differential model are derived by employing an edge-based compartmental approach. Due to their low dimension, a gap between the parameter identification problem for influenza-like diseases or network inference and network epidemic models may be

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Section: Degree-based Mean-field (Dbmf) Epidemic Dynamics Of Influenzamentioning

confidence: 99%

Section: Basic Reproduction Numbermentioning

confidence: 99%

Section: Letting G(1)mentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

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Epidemic dynamics of influenza-like diseases spreading in complex networks

2020

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“…In addition, stochastic SIR model was adopted to study the influence of environmental noise [19], expert intervention [20], and network structure [21] on rumor propagation. Moreover, the studies on disease spread in complex network [22][23][24][25][26] and its control measures [27][28][29][30] can provide reference for the investigations on rumor propagation and control.…”

Section: Introductionmentioning

confidence: 99%

A 3SI3R model for the propagation of two rumors with mutual promotion

et al. 2020

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There are often many kinds of rumors spreading in new media after emergencies; however, the existing studies have focused on the rumors with competition, and little attention has been paid to those with mutual promotion. Therefore the mutual promotion between two rumors and the state transition rules between different groups are first analyzed. Then a 3SI3R model, extending the classical 2SI2R model, and mean-field equations of the proposed model are given. Further, the stability and influence of the mutual promotion on the final size of two rumors in the proposed model are derived. Finally, numerical simulations are carried out to investigate the influence of factors, that is, the mutual promotion, occurrence time differences, and the forgetting rate, on the propagation of two rumors. The results show that the enhancement of the mutual promotion can accelerate propagation of two rumors and enlarge their final size; the increase of forgetting rate helps to decrease the final size of two rumors; the decrease in occurrence time differences can result in a small increase in the final size of the later rumor, and the overall situation of two rumors becomes more difficult to control.

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