A multi-stage infectious disease model on the complete graph

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0，1C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 of λn(λ>0) was considered, its future trends under long-term effects was studied. And the critical value λc(λc>0) was explored, so that when λ>λc, the infectious disease survives with a high probability within the exponential time eCn; when λ<λc, the infectious disease extincts with a high probability within the logarithmic time Clnn.