Modules for Stochastic Network Models

Stochastic network models of infectious disease in EpiModel require statistical modeling of networks, simulation of those networks forward through time, and simulation of epidemic dynamics on top of those evolving networks. The netsim function handles both the network and epidemic simulation tasks. Within this function are a series of modules that initialize the simulation and then simulate new infections, recoveries, and demographics on the network. Modules also handle the resimulation of the network and some bookkeeping calculations for disease prevalence.

Writing original network models that expand upon our "base" model set will require modifying the existing modules or adding new modules to the workflow in netsim. The existing modules may be used as a template for replacement or new modules.

This help page provides an orientation to these module functions, in the order in which they are used within netsim, to help guide users in writing their own functions. These module functions are not shown on the help index since they are not called directly by the end-user. To understand these functions in more detail, review the separate help pages listed below.

Initialization Module

This function sets up nodal attributes, like disease status, on the network at the starting time step of disease simulation, \(t_1\). For multiple-simulation function calls, these are reset at the beginning of each individual simulation.

• initialize.net: sets up the main netsim_dat data structure used in the simulation, initializes which nodes are infected (via the initial conditions passed in init.net), and simulates a first time step of the networks given the network model fit from netest.

Disease Status Modification Modules

The main disease simulation occurs at each time step given the current state of the network at that step. Infection of nodes is simulated as a function of attributes of the nodes and the edges. Recovery of nodes is likewise simulated as a function of nodal attributes of those infected nodes. These functions also calculate summary flow measures such as disease incidence.

• infection.net: simulates disease transmission given an edgelist of discordant partnerships by calculating the relevant transmission and act rates for each edge, and then updating the nodal attributes and summary statistics.

• recovery.net: simulates recovery from infection either to a lifelong immune state (for SIR models) or back to the susceptible state (for SIS models), as a function of the recovery rate parameters specified in param.net.

Demographic Modules

Demographics such as arrival and departure processes are simulated at each time step to update entries into and exits from the network. These are used in epidemic models with network feedback, in which the network is resimulated at each time step to account for the nodal changes affecting the edges.

• departures.net: randomly simulates departure for nodes given their disease status (susceptible, infected, recovered), and their group-specific departure rates specified in param.net. Departures involve deactivating nodes.

• arrivals.net: randomly simulates new arrivals into the network given the current population size and the arrival rate specified in the a.rate parameters. This involves adding new nodes into the network.

Network Resimulation Module

In dependent network models, the network object is resimulated at each time step to account for changes in the size of the network (changed through entries and exits), and the disease status of the nodes.

• resim_nets: resimulates the network object one time step forward given the set of formation and dissolution coefficients estimated in netest.

Bookkeeping Module

Network simulations require bookkeeping at each time step to calculate the summary epidemiological statistics used in the model output analysis.

• prevalence.net: calculates the number in each disease state (susceptible, infected, recovered) at each time step for those active nodes in the network. If the epi.by control is used, it calculates these statistics by a set of specified nodal attributes.

• verbose.net: summarizes the current state of the simulation and prints this to the console.

One- & Two-Group Modules

If epidemic type is supplied within control.net, EpiModel defaults each of the base epidemic and demographic modules described above (arrivals.FUN, departures.FUN, infection.FUN, recovery.FUN) to the correct .net function based on variables passed to param.net (e.g. num.g2, denoting population size of group two, would select the two-group variants of the aforementioned modules). Two-group modules are denoted by a .2g affix (e.g., recovery.2g.net)