24  Experimenting with Population Heterogeneity in Network Models

In this lab, you will work to simulate a network-based epidemic model with population heterogeneity. This will use the special group attribute so that you can explore variations in both network structure and epidemic parmaeterization. The specific learning objectives for this lab are to:

  1. Practice initializing and parameterizing a two-group network model and epidemic model;
  2. Identify solutions in network model parameterization under conditions of poor diagnostics;
  3. Understand the relationship between heterogeneity in degree versus assortative mixing on epidemic outcomes.

24.1 Setup

Once you are ready, start out by clearing your R object environment, to make sure that you do not have any objects lingering from the tutorial. This can be accomplished with:

rm(list = ls())

24.2 Lab Steps

The model in Session 5 used a nodematch term with a target statistic value of 0 to parameterize a model in which none of the relations were within group.

  • Run that same model but change the epidemic parameters so that women (group 1) have twice the probability of infection (40% versus 20%) of males (Group 2). Inspect the group-specific prevalence and incidence plots, and calculate the raw (not standardized) cumulative incidence in these models and compare against the cumulative incidence in the tutorial. Try it again with a 4-fold higher probability for women (80% versus 20%).

  • Relax that assumption but keep everything else constant and allow for 50% of relationships to be within group and 50% to be across group. We will call this a proportional mixing model. The degree terms and target statistics may be kept unchanged, but update the nodematch target statistic accordingly. After you fit the model, diagnose it. Does the edges statistic look good? If not, how can you update the model fit with netest? Try refitting the model accordingly (this might take a couple minutes).

  • Next run the an SIR epidemic model with the proportional mixing model, and with the two inf.prob parameters set to 0.2 (the same as the original tutorial model). Inspect the group-specific prevalence and incidence plots, and calculate the raw (not standardized) cumulative incidence in these models and compare against the cumulative incidence in the tutorial.

24.3 Lab Questions

After you have completed running the models above, please answer the following questions and discuss in your work group.

  1. What is the general relationship between the per-act infection probability and the epidemic outcomes (cumulative incidence) in your model with purely disortative mixing? What are a couple reasons why increasing the infection probability parameter 2- or 4-fold does not result in a similar relative increase in the cumulative incidence? What happens when mixing moves from disortative to proportional?

  2. With the proportional mixing model, we didn’t change the degree-related target statistics. But would it be possible to do so? Conceptually, what would happen if we changed the degree(1) statistic for males (group 2) from 77.5 to some larger value (say, 100) in a proportional mixing model? Would the same balancing considerations apply as with the purely disortative mixing model? Where would those excess relations for males go?