Departament d'Informàtica, Matemàtica Aplicada i Estadística, Universitat de Girona, Girona 17003, Catalonia, Spain.
Phys Rev E. 2020 Nov;102(5-1):052301. doi: 10.1103/PhysRevE.102.052301.
This paper is concerned with the robustness of the sustained oscillations predicted by an epidemic ODE model defined on contact networks. The model incorporates the spread of awareness among individuals and, moreover, a small inflow of imported cases. These cases prevent stochastic extinctions when we simulate the epidemics and, hence, they allow to check whether the average dynamics for the fraction of infected individuals are accurately predicted by the ODE model. Stochastic simulations confirm the existence of sustained oscillations for different types of random networks, with a sharp transition from a nonoscillatory asymptotic regime to a periodic one as the alerting rate of susceptible individuals increases from very small values. This abrupt transition to periodic epidemics of high amplitude is quite accurately predicted by the Hopf-bifurcation curve computed from the ODE model using the alerting rate and the infection transmission rate for aware individuals as tuning parameters.
本文关注的是在接触网络上定义的传染病微分方程模型所预测的持续振荡的鲁棒性。该模型包含了个体意识的传播，此外，还有少量的输入病例。当我们模拟流行病时，这些病例可以防止随机灭绝，因此，它们可以检查感染个体的比例的平均动力学是否可以通过 ODE 模型准确预测。随机模拟证实了不同类型的随机网络中存在持续振荡，随着易感个体的警报率从非常小的值增加，从非振荡渐近状态到周期性状态的急剧转变。这种对高幅度周期性流行病的突然转变，通过使用警报率和有意识个体的感染传播率作为调谐参数，从 ODE 模型计算出的 Hopf 分岔曲线可以非常准确地预测。
