Impacts of memory-based and non-memory-based adoption in social contagion

In information diffusion within social networks, whether individuals adopt information often depends on the current and past information they receive. Some individuals adopt based on current information (i.e., no memory), while others rely on past information (i.e., with memory). Previous studies mainly focused on irreversible processes, such as the classic susceptible-infected and susceptible-infected-recovered threshold models, with less attention to reversible processes like the susceptible-infected-susceptible model. In this paper, we propose a susceptible-adopted-susceptible threshold model to study the competition between these two types of nodes and its impact on information diffusion. We also examine how memory length and differences in the adoption thresholds affect the diffusion process. First, we develop homogeneous and heterogeneous mean-field theories that accurately predict simulation results. Numerical simulations reveal that when node adoption thresholds are equal, increasing memory length raises the propagation threshold, thereby suppressing diffusion. When the adoption thresholds of the two node types differ, such as non-memory nodes having a lower threshold than memory-based nodes, increasing the memory length of the latter has little effect on the propagation threshold of the former. However, when the adoption threshold of the non-memory nodes is much higher than that of the memory-based nodes, increasing the memory length of the latter significantly suppresses the propagation threshold of the non-memory nodes. In heterogeneous networks, we find that as the degree of heterogeneity increases, the outbreak size of epidemic diffusion becomes smaller, while the propagation threshold also decreases. This work offers deeper insights into the impact of memory-based and non-memory-based adoption in social contagion.