Structure of the modified SIR rumor spreading model for the rumor-spread process.

<p>R1 represents the stiflers who do not know the truth or falsehood of the rumor and simply lose interest in spreading the rumor, and R2 represents stiflers who see the falsity of the rumor and oppose its spread. The sub-script line label indicates the interaction partner, the super-script line label indicates the rate of state transition.</p

Nodes immunization effects on the prevention and control of rumors-spread.

<p>A) Changes in the density of R1 stiflers over time (<i>t</i>) as a function of the immunization rate <i>p</i>. B) Changes in the density of R2 stiflers over time (<i>t</i>) as a function of the immunization rate <i>p</i>. C) Changes in the final value of the R1 and R2 stiflers, and the final size of the rumor (<i>R</i>) as a function of the proportion of the population that is immunized <i>p</i>. The values of the model parameters are <i>λ</i> = 0.45, <i>β</i> = 0.02, <i>γ</i> = 0.53, <i>α</i> = 0.45, <i>θ</i> = 0.50, <i>δ</i> = 0.35, and <math><mrow><mi>k</mi><mo>¯</mo><mo>=</mo><mn>10</mn></mrow></math>.</p

Densities of the four groups in the rumor model over time(<i>t</i>).

<p>The parameters are <i>λ</i> = 0.85, <i>β</i> = 0.03, <i>γ</i> = 0.12, <i>α</i> = <i>θ</i> = 0.25, <i>δ</i> = 0.35, and <math><mrow><mi>k</mi><mo>¯</mo><mo>=</mo><mn>10</mn></mrow></math>.</p

Immunization against the Spread of Rumors in Homogenous Networks

<div><p>Since most rumors are harmful, how to control the spread of such rumors is important. In this paper, we studied the process of "immunization" against rumors by modeling the process of rumor spreading and changing the termination mechanism for the spread of rumors to make the model more realistic. We derived mean-field equations to describe the dynamics of the rumor spread. By carrying out steady-state analysis, we derived the spreading threshold value that must be exceeded for the rumor to spread. We further discuss a possible strategy for immunization against rumors and obtain an immunization threshold value that represents the minimum level required to stop the rumor from spreading. Numerical simulations revealed that the average degree of the network and parameters of transformation probability significantly influence the spread of rumors. More importantly, the simulations revealed that immunizing a higher proportion of individuals is not necessarily better because of the waste of resources and the generation of unnecessary information. So the optimal immunization rate should be the immunization threshold.</p></div

The relationship between the spread threshold (<i>λ</i>_<i>c</i>) and the immunization threshold (<i>p</i>_<i>c</i>).

<p>The parameters are <i>λ</i> = 0.85, <i>θ</i> = 0.45, <i>α</i> = 0.25.</p

Shape of the function <i>g</i>(<i>R</i>).

<p>The parameters are <math><mrow><mi>β</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>03</mn><mo>,</mo><mi>γ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>15</mn><mo>,</mo><mi>θ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>45</mn><mo>,</mo><mi>α</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn><mo>,</mo><mi>δ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>35</mn><mo>,</mo><mi>k</mi><mo>¯</mo><mo>=</mo><mn>10</mn><mo>,</mo></mrow></math> and <i>p</i> = 0.2.</p

Shape of the function <i>f</i>(<i>R</i>).

<p>The parameters are <i>β</i> = 0.03, <i>γ</i> = 0.15, <i>θ</i> = 0.45, <i>α</i> = 0.25, <i>δ</i> = 0.35, and <math><mrow><mi>k</mi><mo>¯</mo><mo>=</mo><mn>10</mn></mrow></math>.</p

Sample means and 95% confidence intervals of 30 ratios of .

<p>Sample means and 95% confidence intervals of 30 ratios of .</p

Distributions of degrees in a Watts-Strogatz network and degrees estimated by Eq (6).

<p>The WS network was generated with parameters of (<i>n</i> = 1,000, <i>K</i> = 8, <i>p</i> = 0.04).</p

Estimated values of <i>p</i>, <i>CC</i> and <i>DS</i>.

<p>For each case of (a) <i>n</i> = 10,000 and (b) <i>n</i> = 20,000, 100 WS networks were generated with <i>K</i> = 80 and a randomly chosen <i>p</i> ∈ [0.005, 0.05]. From each network, <i>s</i> = 100 nodes were randomly sampled along with their degrees to calculate from Algorithm 1. All estimated values were normalized between 0 and 1.</p