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

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

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

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

Data_Sheet_1_Optimizing national border reopening policies in the COVID-19 pandemic: A modeling study.docx

ObjectiveAfter emergence of the COVID-19 pandemic and subsequent restrictions, countries worldwide have sought to reopen as quickly as possible. However, reopening involves the risk of epidemic rebound. In this study, we investigated the effective policy combination to ensure safe reopen.MethodsOn the basis of the classical SEIR epidemic model, we constructed a COVID-19 system dynamics model, incorporating vaccination, border screening, and fever clinic unit monitoring policies. The case of China was used to validate the model and then to test policy combinations for safe reopening.FindingsVaccination was found to be crucial for safe reopening. When the vaccination rate reached 60%, the daily number of newly confirmed COVID-19 cases began to drop significantly and stabilized around 1,400 [1/1,000,000]. The border screening policy alone only delayed epidemic spread for 8 days but did not reduce the number of infections. Fever clinic unit monitoring alone could reduce the peak of new confirmed cases by 44% when the case identification rate rose from 20 to 80%. When combining polices, once the vaccination rate reached 70%, daily new confirmed cases stabilized at 90 [0.64/1,000,000] with an 80% case identification rate at fever clinic units and border screening. For new variants, newly confirmed cases did not stabilize until the vaccination rate reached 90%.ConclusionHigh vaccination rate is the base for reopening. Vaccination passport is less effective compared with a strong primary care monitoring system for early detection and isolation of the infected cases.</p