The critical infection rate of the high-dimensional two-stage contact process

In this paper we are concerned with the two-stage contact process on the lattice ${\mathbb{Z}}^d$ introduced in \cite{Krone1999}. We gives a limit theorem of the critical infection rate of the process as the dimension $d$ of the lattice grows to infinity. A linear system and a two-stage SIR model are two main tools for the proof of our main result.