School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.
The Alan Turing Institute, 96 Euston Road, London NW1 2DB, United Kingdom.
Phys Rev E. 2020 Sep;102(3-1):032305. doi: 10.1103/PhysRevE.102.032305.
We propose a tractable epidemic model that includes containment measures. In the absence of containment measures, the epidemics spread exponentially fast whenever the infectivity rate is positive λ>0. The containment measures are modeled by considering a time-dependent modulation of the bare infectivity λ leading to effective infectivity that decays in time for each infected individual, mimicking, for instance, the combined effect of the asymptomatic onset of the disease, testing policies, and quarantine. We consider a wide range of temporal kernels for effective infectivity, and we investigate the effect of the considered containment measures. We find that not all kernels are able to push the epidemic dynamics below the epidemic threshold with some containment measures only able to reduce the rate of the exponential growth of newly infected individuals. We also propose a pandemic model caused by a growing number of separated foci.
我们提出了一个包含遏制措施的传染病模型。在没有遏制措施的情况下，只要感染率为正 λ>0，传染病就会呈指数级快速传播。通过考虑对基本感染率 λ 的时间相关调制来模拟遏制措施，从而导致每个感染者的有效感染率随时间衰减，例如，模拟疾病无症状发作、检测策略和隔离的综合影响。我们考虑了广泛的有效感染率的时间核，并研究了所考虑的遏制措施的效果。我们发现并非所有的核都能够将传染病动力学推到传染病阈值以下，因为某些遏制措施只能降低新感染个体的指数增长速度。我们还提出了一个由不断增加的分离焦点引起的大流行模型。
