Confidential Customized for Lorem Ipsum LLC Beyond the
Confidential Customized for Lorem Ipsum LLC Beyond the Degree Distribution Section 10. 5 from Network Science by Albert Laszlo Barabasi Ruofan Liu Version 1. 0
Content 1. Concept Review 2. Factors that can affect the spread of a pathogen a. Temporal Networks b. Bursty Contact Patterns c. Degree Correlations d. Link Weights and Communities 3. Conclusion
Content 1. Concept Review 2. Factors that can affect the spread of a pathogen a. Temporal Networks b. Bursty Contact Patterns c. Degree Correlations d. Link Weights and Communities 3. Conclusion
SIS Model - Susceptible - infectious - Susceptible Appropriate for diseases that commonly have repeat infections �� controls the rate of spread �� is the recovery rate - �� = 1/D where D is the average duration of infection https: //institutefordiseasemodeling. github. io/Documentation/general/model-si. html
SIR - SIRS Model - - Susceptible - Infectious - Recovered (Susceptible) Appropriate for diseases with lifelong immunity upon recovery �� controls the rate of spread �� is the recovery rate - �� = 1/D where D is the average duration of infection ξ is the rate which recovered individuals return to the susceptible state https: //institutefordiseasemodeling. github. io/Documentation/general/model-sir. html? search. Text=SIR
Epidemic threshold “The critical number or density of susceptible hosts required for an epidemic to occur. ” In a large scale-free network τ=0, which means that a virus can instantaneously reach most nodes. Where τ is the characteristic time In a large scale-free network λc=0 (threshold vanish), which means that even viruses with small spreading rate can persist in the population. Where λc is the epidemic threshold
Content 1. Concept Review 2. Factors that can affect the spread of a pathogen a. Temporal Networks b. Bursty Contact Patterns c. Degree Correlations d. Link Weights and Communities 3. Conclusion
Content 1. Concept Review 2. Factors that can affect the spread of a pathogen a. Temporal Networks b. Bursty Contact Patterns c. Degree Correlations d. Link Weights and Communities 3. Conclusion
Temporal Network - Timing and durations are needed to make the model more accurate Ignoring timing can sometimes lead to wrong results http: //networksciencebook. com/chapter/10#degree-distribution-10 -5
Content 1. Concept Review 2. Factors that can affect the spread of a pathogen a. Temporal Networks b. Bursty Contact Patterns c. Degree Correlations d. Link Weights and Communities 3. Conclusion
Bursty Contact Patterns The interevent times in most social systems follow a power law distribution, not an exponential distribution as assumed before. the sequence of contacts between two individuals is characterized by periods of frequent interactions
Bursty Contact Patterns the power law also implies that occasionally there a very long time gaps between two contacts. Therefore the contact pattern have an uneven, “bursty” character in time
Content 1. Concept Review 2. Factors that can affect the spread of a pathogen a. Temporal Networks b. Bursty Contact Patterns c. Degree Correlations d. Link Weights and Communities 3. Conclusion
Degree Correlations - Many social networks are assortative. Meaning that high degree nodes tends to connect to other high degree nodes This degree correlation alter the speed with which a pathogen spreads in a network
Degree Correlations 1. Assortative correlations decrease the epidemic threshold ƛ and disassortative correlations increasee it 2. Epidemic threshold has nothing to do with degree correlations as it vanishes for scale-free network 3. Given that hubs are the first to be infected in a network, assortativity accelerates the spread of a pathogen, and disassortativity slows the spreading process. 4. In the SIR model, assortative correlations lower the prevalence but increase the average lifetime of an epidemic outbreak
Content 1. Concept Review 2. Factors that can affect the spread of a pathogen a. Temporal Networks b. Bursty Contact Patterns c. Degree Correlations d. Link Weights and Communities 3. Conclusion
Link Weights and Communities - Tie strengths vary considerably. They are not equal! Tie strengths affects the accuracy strong ties tend to be within communities while weak ties are between them http: //networksciencebook. com/chapter/10#degree-distribution-10 -5
Content 1. Concept Review 2. Factors that can affect the spread of a pathogen a. Temporal Networks b. Bursty Contact Patterns c. Degree Correlations d. Link Weights and Communities 3. Conclusion
Conclusion Simple Contagion vs. Complex Contagion - Communities have multiple consequences for spreading. (I. e. Pathogens and memes on twitter may follow different spreading patterns. ) Prompting us to distinguish simple from complex contagion
Conclusion
Conclusion In summary, several network characteristics can affect the spread of a pathogen in a network, from degree correlations to link weights and the bursty nature of the contact pattern. As we discussed in this section, some network characteristics slow a pathogen, others aid their spread. These effects must therefore be accounted for if we wish to predict the spread of a real pathogen. While these patterns are of obvious relevance for infectious diseases, they also influence the spread of such non-infectious diseases as obesity http: //networksciencebook. com/chapter/10#degree-distribution-10 -5
Thank you.
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