Floyd William, Kay Leslie, Shapiro Michael
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA.
Bull Math Biol. 2008 Apr;70(3):713-27. doi: 10.1007/s11538-007-9275-0. Epub 2007 Dec 1.
We consider epidemics on social networks and address the question of whether administering a safe vaccine to one or more individuals can raise another individual's chances of becoming infected. Surprisingly, this can happen if transmission probabilities vary over time. If transmission probabilities do not vary with time, we show that in the discrete SIR model vaccination cannot cause collateral damage. We phrase this question in terms of monotonicity properties and answer it using bond percolation methods. By passing to a covering graph we are able to extend these results to models with more complicated latent and infective states.
我们考虑社交网络上的流行病，并探讨给一个或多个个体接种安全疫苗是否会增加另一个个体被感染的几率这一问题。令人惊讶的是，如果传播概率随时间变化，这种情况就可能发生。如果传播概率不随时间变化，我们证明在离散的SIR模型中，接种疫苗不会造成附带损害。我们用单调性性质来阐述这个问题，并使用键渗流方法来回答它。通过转换到一个覆盖图，我们能够将这些结果扩展到具有更复杂潜伏和感染状态的模型。
