Transmission dynamics of a two-strain pairwise model with infection age

Zhang, Juping; Li, Dan; Jing, Wenjun; Zhou, Jin; Zhu, Huaiping

doi:10.1016/j.apm.2019.03.001

Cited by 7 publications

(12 citation statements)

References 28 publications

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“…The present paper extend the Röst SIR model [13] and the other literature [9,15,21] to establish a rumor pairwise model and analyze the effect of spreading age on the speed of the rumor transmission in complex network. The rest of this article is arranged as following.…”

Section: Introductionmentioning

confidence: 87%

“…The notations are similar to those notations given in the literature [21], the explanations of variables and parameters are shown in Table 1. Then we can obtain…”

Section: The Model Formulationmentioning

confidence: 99%

“…In many cases, we realize demography and infection age are important factors in the epidemic disease model [9,21]. However, in the literature [10], it found that the most of the researcher ignored the important effect of the spreading age on the spreading process of the rumor.…”

Section: Introductionmentioning

confidence: 99%

“…Obviously, these are not consistent with the reality [14,17]. To make the rumor model more accurate and truthful, after investigating the modern epidemic dynamics models and documents [9,14,21], we introduce the risk function instead of the recovery rate, where the recovery rate depend on the spreading age. Numerical simulations are used to verify the accuracy of the model and ensure the model in line with the reality.…”

Section: Introductionmentioning

confidence: 99%

“…Numerical simulations are used to verify the accuracy of the model and ensure the model in line with the reality. In numerical simulations, Jing et al [9] and Zhang et al [21] discovered that the different recovery time distributions could lead to different effects on the spreading process. Neil et al [14] studied the rumor models on scale-free network by performing Monte Carlo simulations and made numerical solutions of the mean-field equations.…”

Section: Introductionmentioning

confidence: 99%

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An SIR rumor pairwise model with spreading age

Liu¹,

Li²

2020

J. Nonlinear Sci. Appl.

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In this paper, we extend the classical rumor model with non-Markovian recovery process in a complex network. We follow the ideas from R\"{o}st to analyze the pairwise model; then, the hyperbolic system can be transformed into integro-differential equations. For the rumor model, the reproduction number is obtained. Next, we use numerical simulation to verify the accuracy of the result. In the end, we focus on how the three different distributions of recovery time with spreading age influence on rumor model. The result illustrates the significant effect of different distribution functions on the process of rumor spreading.

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Section: Introductionmentioning

confidence: 87%

“…The notations are similar to those notations given in the literature [21], the explanations of variables and parameters are shown in Table 1. Then we can obtain…”

Section: The Model Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An SIR rumor pairwise model with spreading age

Liu¹,

Li²

2020

J. Nonlinear Sci. Appl.

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Mathematical Analysis of Epidemic Models with Treatment in Heterogeneous Networks

et al. 2023

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In this paper, we formulate two different network-based epidemic models to investigate the effect of partly effective treatment on disease dynamics. The first network model represents the individuals with heterogeneous number of contacts in a population as choosing a new partner at each moment, whereas the second one assumes the individuals have fixed or stable neighbors. The basic reproduction number is computed for each model, using the next generation matrix method. In particular, the critical treatment rate is defined for the model, above which the disease can be eliminated through the treatment. The final epidemic size relations are derived, and the solvability of these implicit equations is studied. In particular, a unique solution of the implicit equation for the final epidemic size is determined, and by rewriting the implicit equation as a suitable fixed point problem, it is proved that the iteration of the fixed point problem converges to the unique solution. Stochastic simulations and numerical simulations, including in comparison with the model outputs and the joint influence of network topology and treatment on the final epidemic size, are conducted to illustrate the theoretical results.

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SIR dynamics with infection age in complex heterogeneous networks

Yan

Zhou

2023

Communications in Nonlinear Science and Numerical Simulation

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Transmission dynamics of a two-strain pairwise model with infection age

Cited by 7 publications

References 28 publications

An SIR rumor pairwise model with spreading age

An SIR rumor pairwise model with spreading age

Mathematical Analysis of Epidemic Models with Treatment in Heterogeneous Networks

SIR dynamics with infection age in complex heterogeneous networks

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