A propagation model with defensive measures for PLC-PC worms in industrial networks

•A novel mathematical model for worms spreading in a two-layered PLC-PC coupled network is proposed.•The disease-free and endemic equilibriums of the model are acquired.•The numerical and simulation experiments of the model are performed.•The effectiveness of different defensive measures on the security of PLC-PC coupled networks is discussed.•The effectiveness of extending the connection surface on the security of PLC-PC coupled networks is discussed.