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The original Bass product growth model has been modified in this paper by incorporating a diffusion term and a delay. The imitation parameter β is assumed to be negative which represents the effect of "negative-word-of-mouth" (NWOM). The occurrence of Hopf bifurcation at the positive equilibrium of the remaining market growth u* was proved as β passes through a critical value. The analysis of the distribution of eigenvalues led to the following conclusion. The unstable positive equilibrium state at zero diffusion (d = 0) under NWOM becomes stable when d > 0 for a wide range of β. This observation suggests that when there is a critical NWOM, favorable conditions for the future stable state of u* could be achieved by promoting the product in space (new geographical areas).

We deal with the time delay model for the diffusion of innovation technologies proposed by Fanelli and Maddalena [2012]. For this model, the stability switches and the occurrence of Hopf bifurcations are still largely undetermined, and in the present paper we perform some analysis on these topics. In particular, by applying the theory of delay differential equations and the analytical-geometrical approach developed by Beretta and Kuang [2002], we show that the equilibrium may lose stability and Hopf bifurcations may occur. Moreover, using the normal form theory and the center manifold theorem, we derive closed-form expressions that allow us to determine the direction of the Hopf bifurcations and the stability of the periodic solutions. Numerical results are presented which confirm and illustrate the theoretical predictions obtained.

This paper describes the application of a combination of TRIZ and Bass modeling to forecast the technology growth projections for one of the wearable devices, fitness trackers. For the TRIZ modeling, the fitness tracking system was divided into three subsystems and each was analyzed as per the technology trends from current literature. The subsystems’ combined assessment was then visualized via a radar plot. The analysis showed the technology to be in an emergent state with primary growth in the hardware and software subsystem areas. The Bass model showed the market peaking at eight and saturating in 15 years.

Mobile applications (apps) have grown drastically since their birth in 2008. Acquiring more app users as quickly as possible after the app is released in the app stores is one of the key rules for app developers to survive in this emerging and competitive digital market. This paper uses cumulative weekly downloading data from the US Apple App Store during a two-year period of 2015 and 2016 to study the early expansion curves and diffusion patterns of mobile apps in the app market. Downloading payment methods (free or paid to download an app) and hedonic or utilitarian value-orientated app types (games and productivity apps) are considered when we study the diffusion pattern of mobile apps. The Bass model is used as the baseline model, and the logistic model and Gompertz model are used to conduct a robustness check. Nonlinear least squares (NLS) is the measurement to obtain parameters of diffusion models. The results show that the Bass model is the best-fitting model compared with the other two models, and the diffusion pattern of mobile apps is S-shaped at the market level. The first 35 weeks are essential for the app developers to attract app users’ downloads. More app data from different app stores and more diffusion models can be tested for mobile app diffusion and early expansion patterns in future research.

Although the literature has recognised short time to market and early entry as relevant factors, they are not enough alone to ensure success. In fact, an early entrant may successfully serve early adopters, but then fail in developing products suitable for those who adopt later (i.e., the early majority), dissipating the first-mover advantages previously gained. This paper argues that the likelihood of being successful in the early majority segment depends also on the rethinking time, defined as the time available to firms serving early adopters for planning and developing products that will be offered to the upcoming early majority segment. The rethinking time is here analytically defined through the Bass model and its relationship with product success is investigated. The paper shows that the market leader in the early majority segment is expected to be the incumbent when rapid diffusion occurs and, conversely, new entrants when rethinking time is longer.

In this work, the spread of a contagious disease on a society where the individuals may take precautions is modeled. The primary assumption is that the infected individuals transmit the infection to the susceptible members of the community through direct contact interactions. In the meantime, the susceptibles gather information from the adjacent sites which may lead to taking precautions. The SIR model is used for the diffusion of infection while the Bass equation models the information diffusion. The sociological classification of the individuals indicates that a small percentage of the population takes action immediately after being informed, while the majority expects to see some real advantage of taking action. The individuals are assumed to take two different precautions. The precursory measures are getting vaccinated or trying to avoid direct contact with the neighbors. A weighted average of states of the neighbors leads to the choice of action.

The fully connected and scale-free Networks are employed as the underlying network of interactions. The comparison between the simple contagion diffusion and the diffusion of infection in a responsive society showed that a very limited precaution makes a considerable difference in the speed and the size of the spread of illness. Particularly, highly connected hub nodes play an essential role in the reduction of the spread of disease.

Proper forecast of product market diffusion enables optimal planning of resources, investments, revenue, marketing and sales. Quantitative forecasting methods for this purpose rely on sigmoidal growth models such as logistic growth and Bass model, which are acceptable for the first adoption interval of product life cycle (PLC). Modelling of other PLC segments requires complex models that need large set of input data that limits their application for the forecasting purposes.

This paper presents extensions of the logistic growth model that combine the principle of sigmoidal growth and the concept of interpolation splines. In addition, adaptation of the logistic model is shown to be congruent with Bass model. Applications of developed models for the forecasting of PLC segments are analysed and examined, together with possible ways of interaction between different products. Developed models and interaction types enable forecasting of entire PLC with minimum set of input data, or assessment of qualitative forecasting results.