Modeling innovation diffusion with distributed time lag

Abstract A theoretical framework has been proposed which takes into account the effect of time lag between the knowledge of an innovation and its actual adoption. This delay feature has been captured in the models by employing a distributed time lag approach in which the contributions of time delay are expressed as a weighted response over a finite interval of past time through appropriately chosen memory kernels. The temporal evolution of the adoption process has been modeled in terms of integro-differential equations. Another significant departure from the models available so far is that the number of potential adopters at a time has been visualized not as a fixed numerical limit but rather as a ceiling set by available resources—something akin to the carrying capacity of an ecosystem. The process dynamics has been examined when the carrying capacity is considered to be time-independent as well as time-dependent in a deterministic framework. It is found that time lag can induce damped oscillations under certain conditions. The effect of environmental stochasticity on the evolution of the adoption process has also been studied.