This example feataures an information diffusion model based on an SI (susceptible-infected) contagion process in EpiModel. This model may represent dissemination of new ideas across a social network. In contrast to a typical epidemic model transmission process in which transmission requires only two discordant nodes, social difficusion may require more complex network connectivity, such as:
Scenario 1: A minimum threshold of degree (e.g., current friendships) who have the new idea/meme; in this case, the probability of disseminating an idea may require a deterministic minimum treshold of current contacts that have the idea.
Scenario 2: The probability of transmission may instead be a continuous function of degree of idea-discordant contacts. This continuous probability could be expressed on the log odds scale (to constrain the marginal probability between 0 and 1). Parameters for this scenario would be log odds coefficients for the intercept and slope (see examples below).
The infection module (function = infect_mod) includes the following changes from the base EpiModel infection module (infection.net):
- Querying the degree of discordant edges for susceptible nodes.
- The infection probability is only assigned to susceptible nodes with more than the minimum degree of discordant edges, otherwise it is set to 0.
The infection module (function = infect_mod2) includes the following changes from the base EpiModel infection module (infection.net):
- Querying the degree of discordant edges for susceptible nodes
- The infection probability is a logistic function of degree of discordant edges for susceptible nodes with user specified paramters.
The new or altered epidemic model parameters are as follows.
min.degree: the minimum degree of information-discordant contacts for the diffusion to occur
beta0: the baseline log odds of diffusion when susceptible individuals have 0 degree of discordant contacts; usually negative as transmission probability is usually 0 when one has 0 degree of discordant contacts (a suggested coefficient may be-3).beta1: the increase of log odds with 1 degree increase of discordant contacts; usually positive as an increase of degree would increase the diffusion probability.
In Example 1 in model.R, we consider a situation in which people are densely connected and susceptible individuals only aquire new ideas if they have more than 3 partnerships with infected individuals (min.degree = 3). Similar to an SI epidemic model, the diffusion process is slow initially and increases as more people become infected with the idea. However, the si.flow is lower than normal SI model and not as smooth as infectious probability jumps at minimum degree.
In Example 2 in model.R, this model specifies the baseline transmission probability at almost 0 when susceptible individuals have 0 discordant contacts (beta0 = -7), and transmission probability increases relatively fast with the increase of the degree (beta1 = 0.5). The process is similar to infection process in normal SI model, incidence increases initially as more people are infected then decreases as the susceptible population decreases.
Yuan Zhao, Emory University