Modeling decline dynamics of a Teaching Material Sharing Network in lack of perceived new innovations

Teaching material sharing networks (TMSNs) are a class of co-creating social networks (CSNets) which have made significant impacts on human civilization, where a network member is both content user and contributor. To understand and manage a TMSN, Chen and Chang, 2013, has developed a generalized Bass diffusion model (GBDM) embedded Discrete Time Markov chain (DTMC) to describe its growth dynamics of membership and content volume from the introduction to saturation stage. This paper is focused on modeling the dynamics of decline, which has two root causes of member leaving in lack of new teacher material (TM) uploads, defined as perceived innovations (PIs), and no retention once a member leaves. Our novel modeling methodology extends GBDM to describing the growth of leaving probability with the lack of new PIs and adds to DTMC a sink state to capture the no retention phenomenon. Key innovation of the GBDM extension lies in the embedding in its innovation coefficient term with an auto-regression (AR) model of PIs with time-discounting coefficients on new TM upload quantities over a number of recent time periods. Continuously low PI values over a few periods will lead to a high coefficient value of GBDM and hence high leaving probability. Simulation study verifies that teacher's leaving probability is high with small time-discounting coefficients of AR model which means small PI. The AR model captures the small PI will lead to the network decline. Furthermore, sustained monthly TM upload above a threshold is a critical to decline mitigation. To increase TM uploads per month, incentives design to attract member sharing are discussed, and it is helpful for application to co-creation network management.