The NEXT-NET (Next-reaction-based Epidemics eXtended to Temporal Networks) C++ library contains efficient algorithms for simulating epidemics with time-varying infectiousness (so-called "non-Markovian" epidemics) on complex networks. The main algorithm provided by NEXT-NET is based on the next reaction method and scales to networks with millions of nodes, see our preprint.

We recommend that users who are already familiar with Python or R use NEXT-Net through the packages NEXTNetR and NEXTNetPy which provide convenient and flexible access to the features of the C++ library. Currently, NEXTNetR is the most well-tested library and provides the most complete access to NEXTNet's features; however we aim to provide the same set of features in both packages eventually. For users not familiar with Python or R, the C++ library comes with a basic command-line tool called nextnet. This tool is less flexible than the Python and R packages when it comes to setting up and running simulations, but provides quick access to the main features of NEXT-Net. It also makes it easy to test custom modifications of the C++ code.

With NEXTNet-EmpiricalNetworks we also provide a database of empirical networks in a format compatible with NEXT-Net, compiled from the SNAP (Leskovec and Krevl, 2014), ICON (Clauset et al., 2016), and KONECT (Kunegis, 2013) and other publications (Rocha et al., 2010).

To download and install a prebuilt binary of the NEXT-NET command-line interface, go to Releases, select the latest release, download the binary release for your platform, and decompress; this should yield a binary called nextnet. Currently binary releases for Linux system (NEXTNet-v<VERSION>-linux-x86_64.tar.gz, supports most Linux systems) and Mac OS (NEXTNet-v<VERSION>-mac.tar.gz, supports Mac OS 10.13 and later) are provided. For other platforms, NEXT-Net must be built from source, see below for instructions.

To build NEXT-Net from source, and working C++ compiler with C++17 support, cmake and Boost are required. If git is installed, the latest version of NEXT-Net can be downloaded with

git clone --recurse-submodules --branch latest-release https://github.com/oist/NEXTNet.git

Otherwise, please got to Releases, select the latest release, download NEXTNet-v<VERSION>-source.tar.gz, decompress into a folder NEXTNet, and run the following commands to produce the command-line tool nextnet

cd NEXTNet
mkdir build
cd build
cmake -DCMAKE_BUILD_TYPE=Release ../
make

To simulate an epidemic starting until time t=250 from node 1 of a Watts-Strogatz network of size N=10.000 nodes with parameters K=6 and beta=0.1, gamma distributed infection times with mean 8 and variance 1, and log-normally distributed recovery times with mean 50 and variance 20 run

./nextnet -n 'watts_strogatz(10000, 4, 0.2)' -p 'gamma(8,1)' -r 'lognormal(30,20)' -i 1 -t 250 > trajectory.txt

To plot the resulting number of currently infected nodes over time using gnuplot, run

set key autotitle columnhead
set log y
plot 'trajectory.txt' using 1:9 with lines

The available network types and infection time distributions can be listed with

./nextnet --list-networks
./nextnet --list-times

The NEXT-NET library offers various epidemic models, static and dynamic networks, transmission time distributions, and simulation algorithms.

• SI (Susceptible Infected). Individuals start out susceptible and become infected upon transmission of the disease.
• SIS (Susceptible Infected Susceptible). Individuals start out susceptible, become infected upon transmission of the disease, and eventually recover and become susceptible again.
• SIR (Susceptible Infected Recovered). Individuals start out susceptible, become infected upon transmission of the disease, and eventually recover. Recovered individuals do not become susceptible agian (Currently only available through the R and Python packages).

NEXT-Net supports a range of synthetic and empirical networks, both static and dynamic. In the command-line simulator, the list of available networks can be queried with --list-networks, and a specific network is selected with option -n.

• Erdős–Rényi. Random networks in two nodes are connected by an edge with a certian probability. These networks exhibit no clustering or hubs. Command-line syntax erdos_renyi(size, avg_degree).
• Watts-Strogatz. Random small-world networks exhibiting clustering and hubs. Command-line syntax watts_strogatz(size, k, p).
• Barabási-Albert. Random preferential attachment networks exhibiting hubs and scale-free degree distributions. Command-line syntax barabasi_albert(size, m).
• Acyclic networks. Random tree-like networks with Poissonian distribution of number of offsprings. Command-line syntax acyclic(avg_degree) -i 1.
• Configuration model. Random networks with given degree distributions. Command-line syntax config_model(degrees).
• Clustered configuration model. Random networks with given degree distribution and clustering coefficients. Command-line syntax config_model_clustered(degrees, triangles, beta).
• Lattice. Regular spatial networks. Command-line syntax lattice_2d(edgelength), lattice_3d(edgelength)
• Empirical networks. Networks defined by an adjacency list, i.e. a list of neighbours of each node. See NEXTNet-EmpiricalNetworks for a list of empirical networks that can directly be loaded into NEXTNet. Command-line syntax empirical(file) for unweighted networks and weighted_empirical(file) for weighted networks. See the R package documentation for empirical_network and empirical_weighted_network for a description of the file format and optional parameters. Gzip-compressed files are supported if they end in ".gz".

• Temporal Erdös-Réyni. Temporal networks that at any instant resembles an Erdős–Rényi networks, but in which nodes randomly detach from a currently neighbour and reattach to a new, randomly chosen neighbour. Command-line syntax temporal_erdos_renyi(size, avg_degree), see the R package documentation for erdos_renyi_temporalnetwork for details.
• SIRX network. A network version of the SIRX model in nodes stochastically deactivate, i.e. remove their links, in response to an epidemic outbreak. Command-line syntax temporal_sirx(nw, kappa0, kappa), see the R package documentation for sirx_temporalnetwork for details.
• Activity-driven network. A temporal network in which nodes stochastically detatch from their current neighbour and reattach elsewhere. Command-line syntax activity_driven(activities = {1}, m, eta_sus, eta_inf, b_sus, b_inf), see the R package documentation for activity_driven_temporalnetwork for details.
• Brownian proximity network. A temporal network with spatial structure in which nodes move randomly in two dimensions and links represent spatial proximity between nodes. Command-line syntax brownian_proximity(size, avg_degree, radius = 1, D0 = 1, D1 = 1), see the R package documentation brownian_proximity_temporalnetwork for details.
• Epirical contact networks. Networks defined a list (t,i,j) of contact times t between individuals i and j. Command-line syntax empirical_contact(file, contact_kind = instantaneous, dt = 1), see the R package documentation for empirical_contact_temporalnetwork for a description of the file format. Gzip-compressed files are supported if they end in ".gz".

Time distributions define (a) the time it takes from the infection of a node until it transmits the disease across a specific link, and (b) the time it takes for a node to recover. NEXT-NET offers the following pre-defined distributions, and allows users to easily implement additional distributions. The list of avaible time distribution can be queried on the command-line with --list-times. Many of the common distributions listed below have an additional parameter pinf which specifies the probability of no infection. See the R package manual pages and time_functions for additional details. The distribution can be selected on the command-line with option -p for the transmission time and -r for the recovery time.

• Exponential. Exponential distribution with a given rate and optionally a given probability of no infection (i.e. an infinite transmission time). Command-line syntax exponential(lambda, pinf = 0).
• Gamma. Gamma distribution parametrized with mean and variance and optionally the probability of no infection. Command-line syntax gamma(mean, variance, pinf = 0).
• Lognormal. Log-normal distribution parametrized with mean and variance and optionally the probability of no infection. Command-line syntax lognormal(mean, variance, pinf = 0).
• Weibull. Weibull distribution parametrized with shape and scale and optionally the probability of no infection. Command-line syntax weibull(shape, scale, pinf = 0).
• Polynomial rate. Polynomial infectiousness function of arbitrary degree. Command-line syntax polynomial_rate(coeffs), where coeffs is a list {c0, c1, ...} of coefficients for x, x squared, etc.
• Infectiousness time-course. Arbitrary infectionsness function defined by a list of times and corresponding infection rates. Command-line syntax infectiousness(taus, lambdas), where taus and lambdas are lists {v0, v1, ...} of values describing time points and the corresponding lambda values.
• Deterministic. Fixed time of infection. Command-line syntax deterministic(tau).

The recommonded simulation algorithm for all user-cases is currently the NEXT-Net algorithm. The command-line simulator allows the algorithm to be selected from the following list by specifying option -a next|regir|nmga.

• Next reaction method. The most efficient algorithm available, in which the runtime to find the next infection depends only weakly on the number of infected nodes. Scales to networks with millions of nodes. Command-line syntax next.
• REGIR (Rejection Gillespie algorithm for non-Markovian Reactions *). Based on a similar approximation as nGMA, but removes the quadratic growth of the time it takes to find the next infection. Typically slower than the next reaction method but scales similarly with network size. Command-line syntax regir
• nMGA (non-Markovian Gillespie Algorithm). An approximate algorithms which works well on small networks. However, the runtime to find the next infection grows quadratically with the number of infected nodes, which limits the scalability to large networks. Command-line syntax ngma.