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Numerical results on non-Poissonian epidemics in networks are relatively scarce. Simple event-driven approaches rely on a time ordered sequence of events (tickets) that represent actions to be taken (recovery or infection) at given fixed times, which are computed from the interevent distributions <math>P_i(\tau_i)</math> and <math>P_a(\tau_a)</math>. These approaches are quite demanding, so only small system sizes can be considered. For example, Van Mieghem and van de Bovenkamp (2013)<ref name="Van2013">Van Mieghem P, Van de Bovenkamp R. Non-Markovian infection spread dramatically alters the susceptible-infected-susceptible epidemic threshold in networks[J]. Physical review letters, 2013, 110(10): 108701.</ref> reported results for the SIS model with Poissonian recovery, with rate <math>\mu</math>, while infection happens with a nonexponential distribution following the Weibull form <math>P_a(\tau_a)~(x/b)^{\alpha-1}e^{-(x/b)^\alpha}</math>. In this case, strong variations in the value of the prevalence and of the epidemic threshold are found when varying the parameter <math>\alpha</math>. A promising approach is provided by the general simulation framework proposed by <math>\mathrm{Bogu\tilde{n}\acute{a}}</math> et al. (2014)<ref name="Boguna2014">Boguná M, Lafuerza L F, Toral R, et al. Simulating non-Markovian stochastic processes[J]. Physical Review E, 2014, 90(4): 042108.</ref>, based on the extension of the Gillespie algorithm for Poissonian processes <ref name="Gillespie1977">Gillespie D T. Exact stochastic simulation of coupled chemical reactions[J]. The journal of physical chemistry, 1977, 81(25): 2340-2361.</ref>. This algorithm allows the simulation of much larger network sizes.

Numerical results on non-Poissonian epidemics in networks are relatively scarce. Simple event-driven approaches rely on a time ordered sequence of events (tickets) that represent actions to be taken (recovery or infection) at given fixed times, which are computed from the interevent distributions <math>P_i(\tau_i)</math> and <math>P_a(\tau_a)</math>. These approaches are quite demanding, so only small system sizes can be considered. For example, Van Mieghem and van de Bovenkamp (2013)<ref name="Van2013">Van Mieghem P, Van de Bovenkamp R. Non-Markovian infection spread dramatically alters the susceptible-infected-susceptible epidemic threshold in networks[J]. Physical review letters, 2013, 110(10): 108701.</ref> reported results for the SIS model with Poissonian recovery, with rate <math>\mu</math>, while infection happens with a nonexponential distribution following the Weibull form <math>P_a(\tau_a)~(x/b)^{\alpha-1}e^{-(x/b)^\alpha}</math>. In this case, strong variations in the value of the prevalence and of the epidemic threshold are found when varying the parameter <math>\alpha</math>. A promising approach is provided by the general simulation framework proposed by <math>\mathrm{Bogu\tilde{n}\acute{a}}</math> et al. (2014)<ref name="Boguna2014"></ref>, based on the extension of the Gillespie algorithm for Poissonian processes <ref name="Gillespie1977"></ref>. This algorithm allows the simulation of much larger network sizes.

复杂网络中关于非泊松流行病的数值结果相对较少。简单的事件驱动方法依赖于发生事件的时间顺序，这些事件表示的是在给定固定的时刻某些行为会发生，例如恢复或感染，而发生所需要的时间是由事件发生时间间隔分布<math>P_i(\tau_i)</math>和<math>P_a(\tau_a)</math>计算得出。这些方法的要求很高，因此只能考虑较小的系统来研究。例如，Van Mieghem和van de Bovenkamp在2013年研究了恢复过程为泊松过程，而感染过程是非泊松的且感染事件发生时间间隔服从韦布尔分布<math>P_a(\tau_a)~(x/b)^{\alpha-1}e^{-(x/b)^\alpha}</math>时，SIS模型传播的结果。在这种传播过程情况下，当改变参数<math>\alpha</math>时，发现疾病传播范围和传播阈值的有非常明显的差异性。在2014年，<math>\mathrm{Bogu\tilde{n}\acute{a}}</math>等人提出的通用仿真框架提供了一种不错的方法，基于用于泊松过程的Gillespie算法的延伸算法，该算法可以适用于模拟更大的网络规模下的结果。

复杂网络中关于非泊松流行病的数值结果相对较少。简单的事件驱动方法依赖于发生事件的时间顺序，这些事件表示的是在给定固定的时刻某些行为会发生，例如恢复或感染，而发生所需要的时间是由事件发生时间间隔分布<math>P_i(\tau_i)</math>和<math>P_a(\tau_a)</math>计算得出。这些方法的要求很高，因此只能考虑较小的系统来研究。例如，Van Mieghem和van de Bovenkamp（2013年）对SIS模型传播的研究结论是，恢复过程为泊松过程，速率为<math>\mu</math>，而感染过程是非泊松的，发生时间间隔服从韦布尔分布<math>P_a(\tau_a)~(x/b)^{\alpha-1}e^{-(x/b)^\alpha}</math>。在这种传播过程情况下，当改变参数<math>\alpha</math>时，发现疾病传播力和传播阈值的有非常明显的差异性。在2014年，<math>\mathrm{Bogu\tilde{n}\acute{a}}</math>等人<ref name="Boguna2014">Boguná M, Lafuerza L F, Toral R, et al. Simulating non-Markovian stochastic processes[J]. Physical Review E, 2014, 90(4): 042108.</ref>提出的通用仿真框架提供了一种不错的方法，基于用于泊松过程的Gillespie算法的延伸算法<ref name="Gillespie1977">Gillespie D T. Exact stochastic simulation of coupled chemical reactions[J]. The journal of physical chemistry, 1977, 81(25): 2340-2361.</ref>，该算法可以适用于模拟更大的网络规模下的结果。