ClusterSim

Josh Herbeck

Overview

What biological or technical processes affect cluster size distributions?

This is a simple branching model of HIV transmission. There is no sexual network created, and there are no uninfected individuals; the model only includes infected individuals who can transmit, and then these newly infected recipients can transmit, and so forth into the future. The output is a transmission record (line list) that can be sampled and used to make phylogenies and identify clusters.

The branching process is kind of mechanistic, relative to other branching process process models: each individual has a probability of transmission per timestep (like a standard branching process model), but this probability is a combination of the partnership rate (number of sexual partners per timestep), the number of sex acts per day (per partner), and the per-act probability of transmission. Post-simulation there is an individual probability of sampling. (There is also an individual probability of removal/extinction from the population during a simulation. This could be akin to death or viral suppression or migration.)

First order goal: understand if high mean degree ("super-spreading", or the existence of a high risk core group/key population) results in more clustering and bigger clusters. Or, identify processes, either biological or technological, that produce the clustering patterns that we see in MSM and heterosexual data sets (testing the hypothesis that many processes can produce similar distributions).

Second order goal: identify general predictors of clustering patterns (i.e. make a simple, fast model with which I can vary offspring distribution, incidence/force of infection, sampling (sampling time after infection, sample fraction/coverage, and sampling bias), and cluster thresholds and build a function for predicting clustering patterns from those variables.

Model structure

The model is basically two data frames: population_summary and transmission_record, a run script "Run_script.R", and some functions that are called through a few scripts (see below).

A user should be able to just run the Run_script.R in order to get a line list of transmissions (extractable from the Population_summary).

Population_summary includes all individuals in the population and their individual data. These data include their transmission parameters, infection date, infection source, sampling/removal year, and cumulative partners and transmissions. This file structure is cribbed from Adam Akullian's agent-based vaccine trial model; the difference between Adam's model and this one is that the vaccine trial was interested in infections and this model is (mostly) interested in transmissions (and in recording each transmission for downstream use). So rather than assigning everyone some risks of acquisition, I am assigning everyone risks of transmission.

Transmission_record is a simple record of whether each individual is removed or transmits for each timestep.

The model includes some core functions:

• assign_heterogeneous_rates
• assign_homogeneous_rates
• assign_changing_rates
• assess_removal
• assess_transmission
• make_new_infections

How to run the model

Basically you just need to open up Run_script.R, modify the parameters listed below as you see fit, and source the Run script. The output will be the "population_summary" file. From this file you can extract the epidemic trajectory and summary statistics like transmissions per individual and generation time.

Initial input parameters:

samplesize
timestep
sim_time
mean_partner_parameter
acts_per_day_parameter
lambda_parameter (base infectivity; base per-act transmission rate) removal_rate_parameter

Things still to implement:

1. Allow for biased sampling (preferential sampling of individuals based on their individual characteristics, which would be their risk parameterization).

2. Allow for changes to individuals' risk parameterization over the course of a simulation (e.g. high to low partner number; high to low per-act risk).

3. Allow for per-act transmission rate to change based on time since infection?

4. Allow for importation of HIV, e.g. add infected individuals with no named source individual to the population at a certain rate. How to add those to the Newick files, though? Not sure.

5. Currently the transmission_risk_per_day parameter combines the risk across all partners; it doesn't allow an individual to transmit multiple times in the same timestep. Might need to fix that if and only if we use timesteps greater than 1 day.

Example run:

This is the parameterization of one example simulation. The output epidemic trajectory is the "ClusterSim.infections.example.jpeg"

samplesize <- 100 timestep <- 1
sim_time <- timestep5365 mean_partner_parameter <- 0.5
acts_per_day_parameter <- 0.3
lambda_parameter <- 0.002
removal_rate_parameter <- 0.001 sampling_delay <- 365 set.seed(40)