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[[File:Snipaste_2020-10-23_20-56-39.png|thumb|right|250px|Probability Pinf of infection for a susceptible individual after K contacts with infected individuals. (a) Independent interaction (e.g., SIR-type) model. (b) Stochastic threshold model. (c) Deterministic threshold model. Adapted from Dodds and Watts, 2004.]]  

[[File:Snipaste1.png|thumb|right|250px|Probability Pinf of infection for a susceptible individual after K contacts with infected individuals. (a) Independent interaction (e.g., SIR-type) model. (b) Stochastic threshold model. (c) Deterministic threshold model. Adapted from Dodds and Watts, 2004.]]  

For disease epidemics it is customary to assume that a susceptible individual has a constant probability to receive the infection from a peer upon every exposure, independently of whether other infected individuals are simultaneously in contact or other exposures have occurred in the past. While generally reasonable for the transmission of pathogens [although exceptions may occur <ref>Joh R I, Wang H, Weiss H, et al. Dynamics of indirectly transmitted infectious diseases with immunological threshold[J]. Bulletin of mathematical biology, 2009, 71(4): 845-862.</ref> ], this hypothesis is clearly unrealistic in most situations where a social meme is spreading: a piece of information is more credible if arriving from different sources; the push to adopt a technological innovation is stronger if neighboring nodes in the social network have already adopted it. These consid�erations lead naturally to the introduction of “threshold models” for spreading phenomena, where the effect of multiple exposures changes from low to high as a function of their number. Figure 14 displays the probability of infection (adoption) Pinf after K attempts in the different scenarios. In the case of SIR  each attempt has a fixed probability $p$ of success and $P_{inf}=1-(1-p)^K$.

For disease epidemics it is customary to assume that a susceptible individual has a constant probability to receive the infection from a peer upon every exposure, independently of whether other infected individuals are simultaneously in contact or other exposures have occurred in the past. While generally reasonable for the transmission of pathogens [although exceptions may occur <ref> Joh R I, Wang H, Weiss H, et al. Dynamics of indirectly transmitted infectious diseases with immunological threshold[J]. Bulletin of mathematical biology, 2009, 71(4): 845-862.</ref> ], this hypothesis is clearly unrealistic in most situations where a social meme is spreading: a piece of information is more credible if arriving from different sources; the push to adopt a technological innovation is stronger if neighboring nodes in the social network have already adopted it. These consid�erations lead naturally to the introduction of “threshold models” for spreading phenomena, where the effect of multiple exposures changes from low to high as a function of their number. Figure 14 displays the probability of infection (adoption) Pinf after K attempts in the different scenarios. In the case of SIR  each attempt has a fixed probability $p$ of success and $P_{inf}=1-(1-p)^K$.

疾病传播过程中，习惯上假定易感个体在每次接触已感染个体时以常数概率被感染，而与过去是否同时接触其他感染个体或发生其他接触暴露无关。 上述假定通常对于疾病传播是合理的（尽管可能会发生例外情况），但是在含有社会模因传播的多数情况下，这种假设显然是不真实的：在信息传播过程中，往往多渠道传播过来的信息会相对更加可靠；在某项技术创新的传播中，如果社会网络中某个节点的多个周围邻居已经接受该技术创新，则此节点接受该技术创新的动力会更强。综合以上考虑，则就很自然地会导致在针对信息扩散现象引入“阈值模型”，其中多次暴露的影响随其数量的增加从低到高变化。图14显示了感染（接受信息）的可能性$P_{inf}$在不同情况下进行$K$尝试后的结果。对于SIR（图(a)），每次尝试都有固定的成功概率$p$和$P_{inf}=1-(1-p)^K$。

疾病传播过程中，习惯上假定易感个体在每次接触已感染个体时以常数概率被感染，而与过去是否同时接触其他感染个体或发生其他接触暴露无关。 上述假定通常对于疾病传播是合理的（尽管可能会发生例外情况），但是在含有社会模因传播的多数情况下，这种假设显然是不真实的：在信息传播过程中，往往多渠道传播过来的信息会相对更加可靠；在某项技术创新的传播中，如果社会网络中某个节点的多个周围邻居已经接受该技术创新，则此节点接受该技术创新的动力会更强。综合以上考虑，则就很自然地会导致在针对信息扩散现象引入“阈值模型”，其中多次暴露的影响随其数量的增加从低到高变化。图14显示了感染（接受信息）的可能性$P_{inf}$在不同情况下进行$K$尝试后的结果。对于SIR（图(a)），每次尝试都有固定的成功概率$p$和$P_{inf}=1-(1-p)^K$。