Stability analysis and control strategies for a new SIS epidemic model in heterogeneous networks.

•A new SIS epidemic model considering the infection rates of multiple edges interfere with each other on complex networks was proposed.•The basic reproduction number was found, and the local and global asymptotical stability of the disease-free equilibrium are studied.•The existence, uniqueness and the asymptotical stability of the equilibrium were studied and some disease control strategies are given.