Using an epidemiological model to explore the interplay between sharing and advertising in viral videos

Abstract

How to exploit social networks to make internet content spread rapidly and consistently is an interesting question in marketing management. Although epidemic models have been employed to comprehend the spread dynamics of internet content, such as viral videos, the effects of advertising and individual sharing on information dissemination are difficult to distinguish. This gap forbids us to evaluate the efficiency of marketing strategies. In this paper, we modify a classic mean-field SIR (susceptible-infected-recovered) model, incorporating the influences of sharing and advertising in viral videos. We mathematically analyze the global stability of the system and propose an agent-based modeling approach to evaluate the efficiency of sharing and advertising. We further provide a case study of music videos on YouTube to show the validity of our model.

Figure 1

Diagram of the epidemic model.

Figure 2

Dynamics of system (1) with $S_0=9900$, $I_0=100$, $\beta =0.4$, ${\beta }_1=0.1$, $\alpha =0.03$, $b=0.02$. We consider $\gamma =0.002$ in (a) and vary $\gamma$ from 0 to 0.02 in (b, c).

Figure 3

Schematic illustration of the generation of viewers.

Algorithm 1

Pseudo-code for a single realization of the stochastic model

Figure 4

Dynamics of the agent-based model. Initial conditions are $S_0=9900$, $I_0=100$, $\beta =0.4$, ${\beta }_1=0.1$, $\alpha =0.03$, $b=0.02$. Dashed curves in (a) are the averaged number of susceptible (blue), infected (red) and recovered (green) individuals in numerical simulations. Solid curves in (a) are the solutions of (1). The blue region in (b) shows the number of individuals with Type A. The green region in (b) shows the number of individuals with Type B.

Figure 5

Our epidemic model (1) fitted to daily viewing data for YouTube music videos.