Effects of memory on spreading processes in non-Markovian temporal networks

Many biological, social and man-made systems are better described in terms of temporal networks, i.e. networks whose links are only present at certain points in time, rather than by static ones. In particular, it has been found that non-Markovianity is a necessary ingredient to capture the non-trivial temporal patterns of real-world networks. However, our understanding of how memory can affect the properties of dynamical processes taking place over temporal networks is still very limited, being especially constrained to the case of short-term memory. Here, by introducing a model for temporal networks in which we can precisely control the link density and the strength and length of memory for each link, we unveil the role played by memory on the dynamics of epidemic spreading processes. Surprisingly, we find that the average spreading time in our temporal networks is often non- monotonically dependent on the length of the memory, and that the optimal value of the memory length which maximizes the spreading time depends on the strength of the memory and on the density of links in the network. Through analytical arguments we then explore the effect that changing the number and length of network paths connecting any two nodes has on the value of optimal memory.