To investigate the diffusion of products in the market, this paper proposes a viral product diffusion model using an epidemiological approach. This model presents the process of product diffusion through the dynamics of human behaviors. Based on the stability theory of Ordinary Differential Equations, we demonstrate the conditions under which a product in the market persists or dies out eventually. Next, we use Google data to validate the model. Fitting results illustrate that the viral product diffusion model not only depicts the steady growth process of products, but also describes the whole diffusion process during which the products increase at the initial stage and then gradually decrease and sometimes even exhibit multiple peaks. This shows that the viral product diffusion model can be used to forecast the developing tendency of products in the market through early behavior of these products. Moreover, our model also provides useful insights on how to design effective marketing strategies via social contagions.
The promotion and diffusion of products in the market are a lasting and interesting research problem. To promote a new product which has just begun to occupy the market is very difficult, even if the product has more advantages than the existing products. However, a fraction of people who are the first users to accept a new product will take the role of a long fuse that can trigger the diffusion of the corresponding product throughout the market [
The most famous model for the study of product diffusion was the Bass model, which was proposed by Bass in 1969 [
Product diffusion is a process in which people communicate product information in the awareness stage and make a purchase decision during the decision-making stage. Whether in the awareness stage or in the decision-making stage, people’s behavior is highly contagious. This makes many similarities between the diffusion of products and the spread of infectious diseases. For this reason, scholars often use the epidemic model to study the diffusion of products [
The epidemic compartmental model was proposed in 1927 [
The contribution of this paper is that we propose a new product diffusion model, which forecasts the developing tendency of products in the market and offers some marketing advices. In contrast with classic models, our model adds to the analysis of dynamic behaviors of individuals before they become buyers and discusses the impact of these dynamic behaviors on the performance of products in the market. These analyses and discussions can be helpful to understand how a product occupies the market or disappears from the market and can help us to adjust marketing strategies more purposefully. In our model, the mechanism and process of product diffusion are better described and presented. Moreover, we also analyze the reasons for the formation of buyers. We believe that some of them are out of interest in the product, while others become buyers because of persuasive advertisement, or the influence of peers or others. We find that potential customers have different psychological characteristics and behavior patterns. For this reason, marketing strategies should also reflect the differences even if these strategies are all aimed at potential customers. This finding provides useful insights on designing more effective marketing strategies.
The rest of this paper is organized as follows. Section
The classical model for the study of new product diffusion was the Bass model (BM), which divided individuals into the innovators and imitators according to the decision behavior of individuals in a social system [
Based on this framework, Li and Jin [
In addition to the BM, econometric approach, grey theory, and complex network theory were also used to investigate the product diffusion. Elberse and Eliashberg [
Although the researches on the product diffusion had been very rich, little attention was paid to the dynamic changes of human behaviors. This study is to fill such a gap. We propose to model the diffusion of products via the dynamics of human behaviors and then investigate the influence of these behavior changes on product performance and marketing strategy.
Viral marketing was used as a term that started in 1997 [
Instead of broadcasting directly the existing advertising to a huge number of users [
As a marketing strategy, the success of viral marketing is because this strategy gives full play to the role of social contagions in product promotion. If opinion leaders were selected as the seed users, then evidence of contagion was an important driving force to trigger word of mouth chain-reaction [
Using the epidemiological approach to study a problem requires dividing the population into different classes. To pay respects to the heritage of the epidemic model, we use similar terms to define different classes in our model.
The diffusion of the product in the market is a complex process. It is not only reflected in the visible sales data. In effect, product diffusion should be evaluated with more metrics, such as the transmission of product information and product attention. This not only conforms to the cognitive law, but also can more accurately assess the performance of the product in the market. In such a broad sense of product diffusion, we explain how people are divided into different classes.
When a new product is introduced in the market, some people are very keen on the appearance of this new product. Those individuals who are exposed to and interested in a product at the first time constitute a class, which is called the “susceptible” class
In the Internet age, each individual is not isolated, and the behavior of the individual is likely to be affected by social contagions. When people talk about a product in social interaction, social contagions will lead to the repetitive behaviors that people pay attention to the product. In our model, we also introduce the second type of “susceptible” class. It is denoted by
One product can trigger people’s sustained interest, which is what we expect. However, due to the impact of many subjective and objective factors, people lose interest in the product when they know the basic product information. Thus, the last class is called the “recovered” class
By dividing the population into four classes, the transmission and diffusion of a product in the market can be abstracted as the following dynamic process.
In Figure
Flow chart of individual transfer among different classes.
Since class
In model (
Because the first three equations of model (
To solve the equilibria of model (
Based on the Ordinary Differential Equations (ODE) theory, we analyze the dynamic properties of model (
Consider model (
Let
Next, consider Jacobian matrix
Due to
The rapid development of Internet technology makes it possible to obtain the historical search data of a product. These historical data record the search behavior of a product and reflect the people’s attention to the product. To test our model, we collect Google search engine data, which are obtained from the Google Trends tool. Google search data began in 2004 and spaced at weekly intervals. These data report the relative number of search volume for a given product.
As the data provided by Google Trends are very rich, the selection of sample data is very flexible. Generally speaking, we only need to follow some major rules to determine the search strings. First, search strings are not confined to specific physical products. They can also be new applications in social networks or popular brands. Diverse choices can ensure the applicability of the model. Second, the selection of search strings should be relatively new because Google Trends provides search data since 2004. Finally, popular products are the best choice. For a given search string, we obtain the search data which are normalized by Google Trends. In a sense, if a product is more popular, then Google Trends can provide more effective product data. Based on the above criteria, we choose three search strings as sample data. They are Instagram, Nokia Lumia 920, and The North Face.
In order to test the validity of the model, we first need to estimate the unknown parameters in the model. In this section, we introduce the theory of parameter estimation and how to estimate those unknown parameters according to the sample data. Considering system (
Suppose that the observed values of system (
According to the Ordinary Least Squares (OLS), we can solve an estimator
To solve a best estimator, we can perform the following steps. First, we compute the numerical solutions of system (
According to the above calculation steps, the results of the parameter estimation for the three strings are shown in Table
Estimated parameter values.
Product | Parameter | |||||
---|---|---|---|---|---|---|
|
|
|
|
|
|
|
5.0 | 3.5 | 0.03 | 0.9 | 0.3 | 0.5 | |
Nokia Lumia 920 | 0.1 | 5.0 | 6.5 | 81.0 | 35.0 | 3.3 |
The North Face | 1.5 | 8.0 | 4.7 | 5.0 | 0.042 | 0.027 |
The first search string is “Instagram,” which is a very popular social networking service. Google Trends Data showed that the search volume of “Instagram” gradually increased since 2011. Up to now, the number of people who are concerned about Instagram is still in a stable growth state. Figure
Model fitting on “Instagram” from October 2011 to January 2016.
The second example is a digital product. The exact search string is “Nokia Lumia 920” to obtain sample data. The search volume of this product reached its peak in 2013 and then began to decline gradually. Google Trends Data showed that the search trend of “Nokia Lumia 920” presented an obvious peak. The fitted curve of the product can be seen in Figure
Model fitting on “Nokia Lumia 920” from August 2012 to January 2016.
The last search string is “The North Face,” which is a fashion brand. Unlike the above two examples, this brand existed prior to 2004 so that its search records began in 2004. The search volume of this brand showed multiple peaks in 2004–2016. That is to say, the performance of the brand in the market presents fluctuating changes. Figure
Model fitting on “The North Face” from January 2012 to January 2016.
The above fitting results illustrate that our model has shown good adaptability for the various performances of the product. The model not only depicts the steady growth process of products, but also describes the whole process that the products increase in the initial stage and then gradually decrease and even can handle multiple peaks of products. Hence, our model can be used to forecast the performance of products in the market.
From Figures
The basic form of the Bass model is
Bass model regression results.
Product | Period |
|
|
|
|
---|---|---|---|---|---|
Oct 23, 2011–Nov 30, 2013 | 3.4952 | 0.0367 | −8.2387 | 0.9644 | |
Oct 23, 2011–Jan 23, 2016 | 10.0414 | 0.0169 | −1.0801 | 0.9570 | |
Nokia Lumia 920 | Aug 05, 2012–Dec 22, 2012 | 21.9117 | 0.1306 | −59.1643 | 0.6064 |
Nokia Lumia 920 | Aug 05, 2012–May 11, 2013 | 28.1587 | 0.0952 | −39.6549 | 0.5729 |
Nokia Lumia 920 | Aug 05, 2012–Feb 15, 2014 | 45.2149 | 0.0278 | −9.2015 | 0.4596 |
Nokia Lumia 920 | Aug 05, 2012–Jan 23, 2016 | 51.7469 | 0.0134 | −5.1592 | 0.7815 |
Actual data and curves predicted by two models for “Instagram.”
Oct 23, 2011–Nov 30, 2013
Oct 23, 2011–Jan 23, 2016
Actual data and curves predicted by two models for “Nokia Lumia 920.”
Aug 05, 2012–Dec 22, 2012
Aug 05, 2012–May 11, 2013
Aug 05, 2012–Feb 15, 2014
Aug 05, 2012–Jan 23, 2016
Figures
To illustrate the general applicability of the model, we use three cases to validate our model. It is interesting to note from Figure
The solution of viral product diffusion model will tend to the equilibrium point.
By analyzing the dynamic properties of model (
The ideas to change these parameters are as follows. In view of the differences mentioned in the previous between
We have a brief explanation on parameters
In this paper we propose a viral product diffusion model via the epidemiological approach. Dynamic analysis of the model reveals the conditions for a product to persist or die out. The model has been verified according to Google Trends Data. Validation results show that our model describes the steady growth or a single peak of a product very well. Also, this model can reflect the fluctuation of a product. It is remarkable that the diffusion process of the product in the market can be modelled by such a simple viral model and the real data fit a theoretical curve so closely.
Our research provides a new approach to forecast the long-term performance of products through their early behaviors. Depending on accurate prediction of product performance, the company managers may adjust the production project and operation plan and update the products. The new approach provides a theoretical guarantee for the management to make the right decision. Furthermore, this study is also instructive to marketers. In order to achieve the expected sales, the design of marketing strategies should grasp the characteristics of customers, even if these customers are all potential customers. Specifically, marketing methods for individuals in class
There are still some limitations in this study. Parameters needed to be estimated in the three examples are assumed to be time-independent constants while they are likely to be time-varying. We will explore the product diffusion model with time-varying parameters in the future.
The authors declare that they have no conflicts of interest.
This work is supported by the National Natural Science Foundation of China (71531013 and 71490720).