An improved upper bound for critical value of the contact process on $\mathbb{Z}^d$ with $d\geq 3$

In this paper we give an improved upper bound for critical value $\lambda_c$ of the basic contact process on the lattice $\mathbb{Z}^d$ with $d\geq 3$. As a direct corollary of out result, $$\lambda_c\leq 0.384.$$ when $d=3$.