论文标题
分析SIR-与全球和局部感染的模型
Analysis of an SIR--model with global and local infections
论文作者
论文摘要
一种流行病模型，可以考虑通过全球接触或通过局部，最近的邻居相互作用进行疾病传播。通过在不同流行病状态下局部对密度添加其他方程，可以扩展描述全局相互作用的经典sir-模型。 [0,1] $中的局部性参数$ p \是全球或局部感染的概率。分析了所得模型的平衡，以依赖于位置参数的依赖性和病原体的传递速率。根据位置参数和疾病参数的繁殖数的明确表达。瞬态模拟证实了这些发现。相邻的一对被感染和一个易感性可以被视为活跃对，因为该疾病的局部传播只能在这种情况下发生。我们的分析表明，活动对的比例对于位置参数的中间值最小。
An epidemic model where disease transmission can occur either through global contacts or through local, nearest neighbor interactions is considered. The classical SIR--model describing the global interactions is extended by adding additional equations for the density of local pairs in different epidemic states. A locality parameter $p\in [0,1]$ characterizes the probability of global or local infections. The equilibria of the resulting model are analyzed in dependence of the locality parameter and the transmission rate of the pathogen. An explicit expression for the reproduction number in terms of the locality parameter and the disease parameters is obtained. Transient simulations confirm these findings. Neighboring pairs of one infected and one susceptible can be considered as active pairs, since local transmission of the disease can only occur in that situation. Our analysis shows, that the fraction of active pairs is minimal for intermediate values of the locality parameter.
