Epidemics on interconnected lattices

Epidemic remains one of the major threats to human society, which has attracted much attention for decades. Since real-world systems usually depend on each other, epidemics on interconnected networks have been studied recently. However, in most studies spatial constraints in these interconnected networks are neglected. Here we study the epidemics in a system composed of two interconnected lattices, which is compared with the epidemics in interconnected Erdös-Rényi (ER) networks. Our results show that the epidemic threshold in interconnected lattices decreases with increasing spatial length of interconnected links between networks. When the infection rate is small, the spatial constraints limit the transmission of the disease, where the infection density is lower in interconnected lattices than in interconnected ER networks. For large infection rate, however, the infection density is higher in interconnected lattices than in interconnected ER networks