EpiModel uses separable-temporal exponential-family random graph models (STERGMs) to estimate and simulate complete networks based on individual-level, dyad-level, and network-level patterns of density, degree, assortivity, and other features influencing edge formation and dissolution. Building and simulating network-based epidemic models in EpiModel is a multi-step process, starting with estimation of a temporal ERGM and continuing with simulation of a dynamic network and epidemic processes on top of that network.

In this tutorial, we work through a model of a Susceptible-Infected-Susceptible (SIS) epidemic. One example of an SIS disease would be a bacterial sexually transmitted infection such as Gonorrhea, in which persons may acquire infection from sexual contact with an infected partner, and then recover from infection either through natural clearance or through antibiotic treatment.

We will use a simplifying assumption of a closed population, in which there are no entries or exits from the network; this may be justified by the short time span over which the epidemic will be simulated.

To get started, load the EpiModel library.

library(EpiModel)

Network Model Estimation

The first step in our network model is to specify a network structure, including features like size and nodal attributes. The network_initialize function creates an object of class network. Below we show an example of initializing a network of 500 nodes, with no edges between them at the start. Edges represent sexual partnerships (mutual person-to-person contact), so this is an undirected network.

nw <- network_initialize(n = 500)

The sizes of the networks represented in this workshop are smaller than what might be used for a research-level model, mostly for computational efficiency. Larger network sizes over longer time intervals are typically used for research purposes.

Model Parameterization

This example will start simple, with a formula that represents the network density and the level of concurrency (overlapping sexual partnerships) in the population. This is a dyad-dependent ERGM, since the probability of edge formation between any two nodes depends on the existence of edges between those nodes and other nodes. The concurrent term is defined as the number of nodes with at least two partners at any time. Following the notation of the tergm package, we specify this using a right-hand side (RHS) formula. In addition to concurrency, we will use a constraint on the degree distribution. This will cap the degree of any person at 3, with no nodes allowed to have 4 or more ongoing partnerships. This type of constraint could reflect a truncated sampling scheme for partnerships within a survey (e.g., persons only asked about their 3 most recent partners), or a model assumption about limits of human activity.

formation <- ~edges + concurrent + degrange(from = 4)

Target statistics will be the input mechanism for formation model terms. The edges term will be a function of mean degree, or the average number of ongoing partnerships. With an arbitrarily specified mean degree of 0.7, the corresponding target statistic is 175: \(edges = mean \ degree \times \frac{N}{2}\).

We will also specify that 22% of persons exhibit concurrency (this is slightly higher than the 16% expected in a Poisson model conditional on that mean degree). The target statistic for the number of persons with a momentary degree of 4 or more is 0, reflecting our assumed constraint.

target.stats <- c(175, 110, 0)

The dissolution model is parameterized from a mean partnership duration estimated from cross-sectional egocentric data. Dissolution models differ from formation models in two respects. First, the dissolution models are not estimated in an ERGM but instead passed in as a fixed coefficient conditional on which the formation model is to be estimated. The dissolution model terms are calculated analytically using the dissolution_coefs function, the output of which is passed into the netest model estimation function. Second, whereas formation models may be arbitrarily complex, dissolution models are limited to a set of dyad-independent models; these are listed in the dissolution_coefs function help page. The model we will use is an edges-only model, implying a homogeneous probability of dissolution for all partnerships in the network. The average duration of these partnerships will be specified at 50 time steps, which will be days in our model.

coef.diss <- dissolution_coefs(dissolution = ~offset(edges), duration = 50)
coef.diss
Dissolution Coefficients
=======================
Dissolution Model: ~offset(edges)
Target Statistics: 50
Crude Coefficient: 3.89182
Mortality/Exit Rate: 0
Adjusted Coefficient: 3.89182

The output from this function indicates both an adjusted and crude coefficient. In this case, they are equivalent. Upcoming workshop material will showcase when they differ as result of exits from the network.

Model Estimation and Diagnostics

In EpiModel, network model estimation is performed with the netest function, which is a wrapper around the estimation functions in the ergm and tergm packages. The function arguments are as follows:

function (nw, formation, target.stats, coef.diss, constraints, 
    coef.form = NULL, edapprox = TRUE, set.control.ergm, set.control.stergm, 
    set.control.tergm, verbose = FALSE, nested.edapprox = TRUE, 
    ...) 
NULL

The four arguments that must be specified with each function call are:

  • nw: an initialized empty network.
  • formation: a RHS formation formula..
  • target.stats: target statistics for the formation model.
  • coef.diss: output object from dissolution_coefs, containing the dissolution coefficients.

Other arguments that may be helpful to understand when getting started are:

  • constraints: this is another way of inputting model constraints (see help("ergm")).

  • coef.form: sets the coefficient values of any offset terms in the formation model (those that are not explicitly estimated but fixed).

  • edapprox: selects the dynamic estimation method. If TRUE, uses the direct method, otherwise the approximation method.

    • Direct method: uses the functionality of the tergm package to estimate the separable formation and dissolution models for the network. This is often not used because of computational time.
    • Approximation method: uses ergm estimation for a cross-sectional network (the prevalence of edges) with an analytic adjustment of the edges coefficient to account for dissolution (i.e., transformation from prevalence to incidence). This approximation method may introduce bias into estimation in certain cases (high density and short durations) but these are typically not a concern for the low density cases in epidemiologically relevant networks.

Estimation

Because we have a dyad-dependent model, MCMC will be used to estimate the coefficients of the model given the target statistics.

est <- netest(nw, formation, target.stats, coef.diss)

Diagnostics

There are two forms of model diagnostics for a dynamic ERGM fit with netest: static and dynamic diagnostics. When the approximation method has been used, static diagnostics check the fit of the cross-sectional model to target statistics. Dynamic diagnostics check the fit of the model adjusted to account for edge dissolution.

When running a dynamic network simulation, it is good to start with the dynamic diagnostics, and if there are fit problems, work back to the static diagnostics to determine if the problem is due to the cross-sectional fit itself or with the dynamic adjustment (i.e., the approximation method). A proper fitting ERGM using the approximation method does not guarantee well-performing dynamic simulations.

Here we will examine dynamic diagnostics only. These are run with the netdx function, which simulates from the model fit object returned by netest. One must specify the number of simulations from the dynamic model and the number of time steps per simulation. Choice of both simulation parameters depends on the stochasticity in the model, which is a function of network size, model complexity, and other factors. The nwstats.formula contains the network statistics to monitor in the diagnostics: it may contain statistics in the formation model and also others. By default, it is the formation model. Finally, we are keeping the “timed edgelist” with keep.tedgelist.

dx <- netdx(est, nsims = 10, nsteps = 1000,
            nwstats.formula = ~edges + meandeg + degree(0:4) + concurrent,
            keep.tedgelist = TRUE)

We have also built in parallelization into the EpiModel simulation functions, so it is also possible to run multiple simulations at the same time using your computer’s multi-core design. You can find the number of cores in your system with:

parallel::detectCores()

Then you can run the multi-core simulations by specifying ncores (EpiModel will prevent you from specifying more cores than you have available).

dx <- netdx(est, nsims = 10, nsteps = 1000, ncores = 4,
            nwstats.formula = ~edges + meandeg + degree(0:4) + concurrent,
            keep.tedgelist = TRUE)

Printing the object will show the object structure and diagnostics. Both formation and duration diagnostics show a good fit relative to their targets. For the formation diagnostics, the mean statistics are the mean of the cross sectional statistics at each time step across all simulations. The Pct Diff column shows the relative difference between the mean and targets. There are two forms of dissolution diagnostics. The edge duration row shows the mean duration of partnerships across the simulations; it tends to be lower than the target unless the diagnostic simulation interval is very long since its average includes a burn-in period where all edges start at a duration of zero (illustrated below in the plot). The next row shows the percent of current edges dissolving at each time step, and is not subject to bias related to burn-in. The percentage of edges dissolution is the inverse of the expected duration: if the duration is 50 days, then we expect that 1/50 (or 2%) to dissolve each day.

print(dx)
EpiModel Network Diagnostics
=======================
Diagnostic Method: Dynamic
Simulations: 10
Time Steps per Sim: 1000

Formation Diagnostics
----------------------- 
           Target Sim Mean Pct Diff Sim SD
edges         175  176.586    0.906 13.530
meandeg        NA    0.706       NA  0.054
degree0        NA  270.455       NA 15.182
degree1        NA  119.591       NA 10.146
degree2        NA   96.281       NA 10.718
degree3        NA   13.673       NA  3.750
degree4        NA    0.000       NA  0.000
concurrent    110  109.954   -0.042 11.841
deg4+           0       NA       NA     NA

Duration Diagnostics
----------------------- 
      Target Sim Mean Pct Diff Sim SD
edges     50    49.85   -0.299  1.275

Dissolution Diagnostics
----------------------- 
      Target Sim Mean Pct Diff Sim SD
edges   0.02     0.02    0.244      0

Plotting the diagnostics object will show the time series of the target statistics against any targets. The other options used here specify to smooth the mean lines, give them a thicker line width, and plot each statistic in a separate panel. The black dashed lines show the value of the target statistics for any terms in the model. Similar to the numeric summaries, the plots show a good fit over the time series.

plot(dx)

The simulated network statistics from diagnostic object may be extracted into a data.frame with get_nwstats.

nwstats1 <- get_nwstats(dx, sim = 1)
head(nwstats1, 20)
   time sim edges meandeg degree0 degree1 degree2 degree3 degree4 concurrent
1     1   1   170   0.680     281     114      89      16       0        105
2     2   1   172   0.688     278     117      88      17       0        105
3     3   1   170   0.680     278     120      86      16       0        102
4     4   1   171   0.684     278     119      86      17       0        103
5     5   1   169   0.676     282     114      88      16       0        104
6     6   1   170   0.680     280     116      88      16       0        104
7     7   1   172   0.688     276     120      88      16       0        104
8     8   1   174   0.696     275     122      83      20       0        103
9     9   1   174   0.696     278     117      84      21       0        105
10   10   1   175   0.700     276     119      84      21       0        105
11   11   1   178   0.712     276     113      90      21       0        111
12   12   1   176   0.704     276     115      90      19       0        109
13   13   1   176   0.704     273     121      87      19       0        106
14   14   1   173   0.692     274     122      88      16       0        104
15   15   1   172   0.688     274     124      86      16       0        102
16   16   1   172   0.688     274     124      86      16       0        102
17   17   1   172   0.688     274     123      88      15       0        103
18   18   1   169   0.676     276     123      88      13       0        101
19   19   1   173   0.692     275     117      95      13       0        108
20   20   1   176   0.704     273     116      97      14       0        111

The dissolution model fit may also be assessed with plots by specifying either the duration or dissolution type, as defined above. The duration diagnostic is based on the average age of edges at each time step, up to that time step. An imputation algorithm is used for left-censored edges (i.e., those that exist at t1); you can turn off this imputation to see the effects of censoring with duration.imputed = FALSE. Both metrics show a good fit of the dissolution model to the target duration of 50 time steps.

par(mfrow = c(1, 2))
plot(dx, type = "duration")
plot(dx, type = "dissolution")

By inspecting the timed edgelist, we can see the burn-in period directly with censoring of onset times. The as.data.frame function is used to extract this edgelist object.

tel <- as.data.frame(dx, sim = 1)
head(tel, 20)
   onset terminus tail head onset.censored terminus.censored duration edge.id
1      0      197    1  101           TRUE             FALSE      197       1
2      0      145    2  142           TRUE             FALSE      145       2
3      0        3    5  356           TRUE             FALSE        3       3
4      0       19    5  454           TRUE             FALSE       19       4
5      0       22    6  132           TRUE             FALSE       22       5
6      0      148    6  387           TRUE             FALSE      148       6
7      0       28    8   26           TRUE             FALSE       28       7
8      0       30    8  316           TRUE             FALSE       30       8
9    541      568    8  316          FALSE             FALSE       27       8
10     0       45    9  100           TRUE             FALSE       45       9
11     0       16    9  386           TRUE             FALSE       16      10
12     0       34   14  121           TRUE             FALSE       34      11
13     0      131   14  474           TRUE             FALSE      131      12
14     0       29   20  409           TRUE             FALSE       29      13
15     0       62   26  464           TRUE             FALSE       62      14
16     0       80   28   60           TRUE             FALSE       80      15
17     0       65   28  366           TRUE             FALSE       65      16
18     0       29   30  146           TRUE             FALSE       29      17
19     0       13   30  214           TRUE             FALSE       13      18
20     0       81   32  115           TRUE             FALSE       81      19

If the model diagnostics had suggested a poor fit, then additional diagnostics and fitting would be necessary. If using the approximation method, one should first start by running the cross-sectional diagnostics (setting dynamic to FALSE in netdx). Note that the number of simulations may be very large here and there are no time steps specified because each simulation is a cross-sectional network.

dx.static <- netdx(est, nsims = 10000, dynamic = FALSE)
print(dx.static)

The plots now represent individual simulations from an MCMC chain, rather than time steps.

par(mfrow = c(1,1))
plot(dx.static, sim.lines = TRUE, sim.lwd = 0.1)

This lack of temporality is now evident when looking at the raw data.

nwstats2 <- get_nwstats(dx.static)
head(nwstats2, 20)
   sim edges concurrent deg4+
1    1   192        125     0
2    2   177        113     0
3    3   172         98     0
4    4   179        121     0
5    5   153         91     0
6    6   158         94     0
7    7   162         94     0
8    8   153         92     0
9    9   165         95     0
10  10   171         97     0
11  11   160         99     0
12  12   177        106     0
13  13   190        121     0
14  14   188        118     0
15  15   161         95     0
16  16   162        102     0
17  17   167        104     0
18  18   145         87     0
19  19   186        111     0
20  20   170        111     0

If the cross-sectional model fits well but the dynamic model does not, then a full STERGM estimation may be necessary (using edapprox = TRUE). If the cross-sectional model does not fit well, different control parameters for the ERGM estimation may be necessary (see the help file for netdx for instructions).

Epidemic Simulation

EpiModel simulates disease epidemics over dynamic networks by integrating dynamic model simulations with the simulation of other epidemiological processes such as disease transmission and recovery. Like the network model simulations, these processes are also simulated stochastically so that the range of potential outcomes under the model specifications is estimated.

The specification of epidemiological processes to model may be arbitrarily complex, but EpiModel includes a number of “built-in” model types within the software. Additional components will be programmed and plugged into the simulation API (just like any epidemic model); we will start to cover that tomorrow. Here, we will start simple with an SIS epidemic using this built-in functionality. This is starting point to what you can do in EpiModel!

Epidemic Model Parameters

Our SIS model will rely on three parameters. The act rate is the number of sexual acts that occur within a partnership each time unit. The overall frequency of acts per person per unit time is a function of the incidence rate of partnerships and this act rate parameter. The infection probability is the risk of transmission given contact with an infected person. The recovery rate for an SIS epidemic is the speed at which infected persons become susceptible again. For a bacterial STI like gonorrhea, this may be a function of biological attributes like sex or use of therapeutic agents like antibiotics.

EpiModel uses three helper functions to input epidemic parameters, initial conditions, and other control settings for the epidemic model. First, we use the param.net function to input the per-act transmission probability in inf.prob and the number of acts per partnership per unit time in act.rate. The recovery rate implies that the average duration of disease is 10 days (1/rec.rate).

param <- param.net(inf.prob = 0.4, act.rate = 2, rec.rate = 0.1)

For initial conditions in this model, we only need to specify the number of infected persons at the outset of the epidemic. The remaining persons in the network will be classified as disease susceptible.

init <- init.net(i.num = 10)

The control settings specify the structural elements of the model. These include the disease type, number of simulations, and number of time steps per simulation. (Here again we could use the model multi-core functionality by specifying an ncores value, but these models run so quickly that it’s not necessary.)

control <- control.net(type = "SIS", nsims = 5, nsteps = 500)

Simulating the Epidemic Model

Once the model has been parameterized, simulating the model is straightforward. One must pass the fitted network model object from netest along with the parameters, initial conditions, and control settings to the netsim function. With a no-feedback model like this (i.e., there are no vital dynamics parameters), the full dynamic network time series is simulated at the start of each epidemic simulation, and then the epidemiological processes are simulated over that structure.

sim <- netsim(est, param, init, control)

Printing the model output lists the inputs and outputs of the model. The output includes the sizes of the compartments (s.num is the number susceptible and i.num is the number infected) and flows (si.flow is the number of infections and is.flow is the number of recoveries). Methods for extracting this output is discussed below.

print(sim)
EpiModel Simulation
=======================
Model class: netsim

Simulation Summary
-----------------------
Model type: SIS
No. simulations: 5
No. time steps: 500
No. NW groups: 1

Fixed Parameters
---------------------------
inf.prob = 0.4
act.rate = 2
rec.rate = 0.1
groups = 1

Model Output
-----------------------
Variables: s.num i.num num si.flow is.flow
Networks: sim1 ... sim5
Transmissions: sim1 ... sim5

Formation Diagnostics
----------------------- 
           Target Sim Mean Pct Diff Sim SD
edges         175  173.513   -0.850 13.935
concurrent    110  108.208   -1.629 12.566
deg4+           0    0.000      NaN  0.000


Dissolution Diagnostics
----------------------- 
      Target Sim Mean Pct Diff Sim SD
edges   0.02      NaN      NaN     NA

Model Analysis

Now the the model has been simulated, the next step is to analyze the data. This includes plotting the epidemiological output, the networks over time, and extracting other raw data.

Epidemic Plots

Plotting the output from the epidemic model using the default arguments will display the size of the compartments in the model across simulations. The means across simulations at each time step are plotted with lines, and the polygon band shows the inter-quartile range across simulations.

par(mfrow = c(1, 1))
plot(sim)

Graphical elements may be toggled on and off. The popfrac argument specifies whether to use the absolute size of compartments versus proportions.

par(mfrow = c(1, 2))
plot(sim, sim.lines = TRUE, mean.line = FALSE, qnts = FALSE, popfrac = TRUE)
plot(sim, mean.smooth = FALSE, qnts = 1, qnts.smooth = FALSE, popfrac = TRUE)

Whereas the default will print the compartment proportions, other elements of the simulation may be plotted by name with the y argument. Here we plot both flow sizes using smoothed means, which converge at model equilibrium by the end of the time series.

par(mfrow = c(1,1))
plot(sim, y = c("si.flow", "is.flow"), qnts = FALSE, 
     ylim = c(0, 25), legend = TRUE, main = "Flow Sizes")

Network Plots

Another available plot type is a network plot to visualize the individual nodes and edges at a specific time point. Network plots are output by setting the type parameter to "network". To plot the disease infection status on the nodes, use the col.status argument: blue indicates susceptible and red infected. It is necessary to specify both a time step and a simulation number to plot these networks.

par(mfrow = c(1, 2), mar = c(0, 0, 0, 0))
plot(sim, type = "network", col.status = TRUE, at = 1, sims = 1)
plot(sim, type = "network", col.status = TRUE, at = 500, sims = 1)

Time-Specific Model Summaries

The summary function with the output of netsim will show the model statistics at a specific time step. Here we output the statistics at the final time step, where roughly two-thirds of the population are infected.

summary(sim, at = 500)

EpiModel Summary
=======================
Model class: netsim

Simulation Details
-----------------------
Model type: SIS
No. simulations: 5
No. time steps: 500
No. NW groups: 1

Model Statistics
------------------------------
Time: 500 
------------------------------ 
           mean      sd    pct
Suscept.  338.8  19.045  0.678
Infect.   161.2  19.045  0.322
Total     500.0   0.000  1.000
S -> I     16.2   4.207     NA
I -> S     15.2   3.493     NA
------------------------------ 

Data Extraction

The as.data.frame function may be used to extract the model output into a data frame object for easy analysis outside of the built-in EpiModel functions. The function default will output the raw data for all simulations for each time step.

df <- as.data.frame(sim)
head(df, 10)
   sim time s.num i.num num si.flow is.flow
1    1    1   490    10 500      NA      NA
2    1    2   487    13 500       4       1
3    1    3   487    13 500       2       2
4    1    4   488    12 500       1       2
5    1    5   489    11 500       0       1
6    1    6   487    13 500       2       0
7    1    7   487    13 500       3       3
8    1    8   485    15 500       3       1
9    1    9   483    17 500       3       1
10   1   10   483    17 500       3       3
tail(df, 10)
     sim time s.num i.num num si.flow is.flow
2491   5  491   355   145 500      16      16
2492   5  492   352   148 500      19      16
2493   5  493   357   143 500      18      23
2494   5  494   353   147 500      17      13
2495   5  495   358   142 500      12      17
2496   5  496   364   136 500      16      22
2497   5  497   365   135 500      19      20
2498   5  498   369   131 500      17      21
2499   5  499   367   133 500      19      17
2500   5  500   367   133 500      15      15

The out argument may be changed to specify the output of means across the models (with out = "mean"). The output below shows all compartment and flow sizes as integers, reinforcing this as an individual-level model.

df <- as.data.frame(sim, out = "mean")
head(df, 10)
   time s.num i.num num si.flow is.flow
1     1 490.0  10.0 500     NaN     NaN
2     2 486.8  13.2 500     4.6     1.4
3     3 485.0  15.0 500     2.8     1.0
4     4 484.6  15.4 500     3.0     2.6
5     5 484.0  16.0 500     1.6     1.0
6     6 483.6  16.4 500     1.8     1.4
7     7 481.8  18.2 500     3.2     1.4
8     8 481.2  18.8 500     2.2     1.6
9     9 480.0  20.0 500     3.2     2.0
10   10 479.8  20.2 500     3.2     3.0
tail(df, 10)
    time s.num i.num num si.flow is.flow
491  491 339.2 160.8 500    18.2    17.6
492  492 338.6 161.4 500    17.4    16.8
493  493 339.8 160.2 500    19.6    20.8
494  494 339.4 160.6 500    19.0    18.6
495  495 338.2 161.8 500    16.4    15.2
496  496 337.6 162.4 500    18.0    17.4
497  497 340.2 159.8 500    18.2    20.8
498  498 341.6 158.4 500    19.2    20.6
499  499 339.8 160.2 500    20.8    19.0
500  500 338.8 161.2 500    16.2    15.2

The networkDynamic objects are stored in the netsim object, and may be extracted with the get_network function. By default the dynamic networks are saved, and contain the full edge history for every node that has existed in the network, along with the disease status history of those nodes.

nw1 <- get_network(sim, sim = 1)
nw1
NetworkDynamic properties:
  distinct change times: 502 
  maximal time range: -Inf until  Inf 

 Dynamic (TEA) attributes:
  Vertex TEAs:    testatus.active 

Includes optional net.obs.period attribute:
 Network observation period info:
  Number of observation spells: 2 
  Maximal time range observed: 1 until 501 
  Temporal mode: discrete 
  Time unit: step 
  Suggested time increment: 1 

 Network attributes:
  vertices = 500 
  directed = FALSE 
  hyper = FALSE 
  loops = FALSE 
  multiple = FALSE 
  bipartite = FALSE 
  net.obs.period: (not shown)
  total edges= 1889 
    missing edges= 0 
    non-missing edges= 1889 

 Vertex attribute names: 
    active status testatus.active vertex.names 

 Edge attribute names not shown 

One thing you can do with that network dynamic object is to extract the timed edgelist of all ties that existed for that simulation.

nwdf <- as.data.frame(nw1)
head(nwdf, 25)
   onset terminus tail head onset.censored terminus.censored duration edge.id
1      1       44    1  293           TRUE             FALSE       43       1
2      1       72    3   87           TRUE             FALSE       71       2
3      1       16    5   71           TRUE             FALSE       15       3
4      1       53    5  133           TRUE             FALSE       52       4
5      1       47    7  184           TRUE             FALSE       46       5
6      1        2   10  126           TRUE             FALSE        1       6
7      1       24   10  214           TRUE             FALSE       23       7
8    129      138   10  214          FALSE             FALSE        9       7
9      1       38   13  420           TRUE             FALSE       37       8
10     1      175   16  244           TRUE             FALSE      174       9
11     1        6   16  420           TRUE             FALSE        5      10
12     1       30   22  391           TRUE             FALSE       29      12
13     1       46   22  406           TRUE             FALSE       45      13
14     1       71   25   60           TRUE             FALSE       70      14
15     1       64   28   81           TRUE             FALSE       63      15
16     1       87   31  346           TRUE             FALSE       86      17
17     1       32   32   69           TRUE             FALSE       31      18
18     1        9   36  189           TRUE             FALSE        8      19
19     1       55   38   58           TRUE             FALSE       54      20
20     1       32   39   64           TRUE             FALSE       31      21
21     1      100   44  241           TRUE             FALSE       99      22
22     1       43   44  336           TRUE             FALSE       42      23
23     1       21   46  361           TRUE             FALSE       20      24
24     1       20   47  298           TRUE             FALSE       19      25
25   288      290   47  298          FALSE             FALSE        2      25

A matrix is stored that records some key details about each transmission event that occurred. Shown below are the first 10 transmission events for simulation number 1. The sus column shows the unique ID of the previously susceptible, newly infected node in the event. The inf column shows the ID of the transmitting node. The other columns show the duration of the transmitting node’s infection at the time of transmission, the per-act transmission probability, act rate during the transmission, and final per-partnership transmission rate (which is the per-act probability raised to the number of acts).

tm1 <- get_transmat(sim, sim = 1)
head(tm1, 10)
   at sus inf infDur transProb actRate finalProb
1   2 198 251     28       0.4       2      0.64
2   2 325 321      2       0.4       2      0.64
3   2 490 352      3       0.4       2      0.64
4   2 462 447     10       0.4       2      0.64
5   3  90 447     11       0.4       2      0.64
6   3 325 321      3       0.4       2      0.64
7   4 447  90      1       0.4       2      0.64
8   6 106 490      4       0.4       2      0.64
9   6 447  90      3       0.4       2      0.64
10  7 123 342      5       0.4       2      0.64

Data Exporting and Plotting with ggplot

We built in plotting methods directly for netsim class objects so you can easily plot multiple types of summary statistics from the simulated model object. However, if you prefer an external plotting tool in R, such as ggplot, it is easy to extract the data in tidy format for analysis and plotting. Here is an example how to do so for out model above. See the help for the ggplot if you are unfamiliar with this syntax.

df <- as.data.frame(sim)
df.mean <- as.data.frame(sim, out = "mean")

library(ggplot2)

Attaching package: 'ggplot2'
The following object is masked from 'package:latticeExtra':

    layer
ggplot() +
  geom_line(data = df, mapping = aes(time, i.num, group = sim), alpha = 0.25,
            lwd = 0.25, color = "firebrick") +
  geom_bands(data = df, mapping = aes(time, i.num),
             lower = 0.1, upper = 0.9, fill = "firebrick") +
  geom_line(data = df.mean, mapping = aes(time, i.num)) +
  theme_minimal()



Last updated: 2022-07-07 with EpiModel v2.3.0