一种完全图上的多阶段传染病模型

A multi-stage infectious disease model on the complete graph

经典接触过程是一种建立在n个点的完全图C_(n)上的相互作用粒子系统模型.这是一个具有状态空间{0,1}^(C_(n))的连续时间马尔可夫过程,探究的是图上以一定速率传播的两阶段疾病的存活情况.然而模型中的粒子可能不止有“健康”和“全感染”两种状态.为此,考虑传播速率为λn(λ>0)的多阶段传染病模型,研究其在长时间效应下未来趋势的变化.探索λ的相变临界值λ_(c)(λ_(c)>0),使得当λ>λ_(c)时,传染病在指数时间e^(C_(n))内以高概率存活;当λ<λ_(c)时,传染病在对数时间Clnn内以高概率灭绝.

The classical contact process is an interactive particle system model based on the complete graph C_(n) of n points.This is a continuous-time Markov process with state space{0,1}^(C_(n)),which explores the survival of two-stage disease spread at a certain rate on the graph.However,particles in the model may have more than two states.To this end,a multi-stage infectious disease model with a propagation rate ofλ_(n)(λ>0)was considered,its future trends under long-term effects was studied.And the critical valueλ_(c)(λ_(c)>0)was explored,so that whenλ>λ_(c),the infectious disease survives with a high probability within the exponential time e^(C_(n));whenλ<λ_(c),the infectious disease extincts with a high probability within the logarithmic time Clnn.