SEITRNet

Network-based SEITR epidemic modeling in R

A reproducible framework for simulating the spread of infectious disease over heterogeneous contact networks, with a coupled mean-field ODE benchmark and built-in network observables.

Overview · Model · Install · Quick start · API · Outputs · Cite

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Overview

SEITRNet implements a five-compartment Susceptible–Exposed–Infected–Treated–Recovered (SEITR) epidemic process on top of an explicit contact network. It is designed for studies in which who is connected to whom materially affects transmission dynamics — a setting in which the classical well-mixed ODE model is known to misestimate peaks, timing, and final epidemic size.

The package provides:

• A stochastic, discrete-time SEITR process simulated on a user-specified random graph,
• A coupled deterministic ODE solver for the mean-field analogue,
• Five canonical random-graph generators (Erdős–Rényi, Barabási–Albert, Watts–Strogatz, regular lattice, random regular),
• Demographic turnover (births, natural and disease-attributable deaths) with a hybrid integer-plus-Bernoulli rounding scheme,
• A panel of standard network observables (degree distribution, global clustering, mean path length, largest connected component) computed at every time step,
• Replication and aggregation utilities for multi-experiment comparisons.

The intended audience is researchers in mathematical epidemiology, network science, and computational biology who need a transparent, scriptable baseline for network-mediated SEITR dynamics.

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Mathematical Model

Compartmental flow

flowchart LR
    L((birth)) -->|Λ| S
    S -->|β₁ S I / N| E
    E -->|β₂| I
    I -->|β₃| R
    I -->|α₁| T
    T -->|α₂| R
    S -.->|μ| X((deceased))
    E -.->|μ| X
    I -.->|μ + δ_I| X
    T -.->|μ + δ_T| X
    R -.->|μ| X

Loading

Mean-field ODE system

Let $S(t), E(t), I(t), T(t), R(t)$ denote compartment sizes and $N(t) = S+E+I+T+R$. The deterministic SEITR system is

$$ \begin{aligned} \frac{dS}{dt} &= \Lambda - \frac{\beta_1 S I}{N} - \mu S, \\ \frac{dE}{dt} &= \frac{\beta_1 S I}{N} - (\beta_2 + \mu),E, \\ \frac{dI}{dt} &= \beta_2 E - (\beta_3 + \alpha_1 + \delta_I + \mu),I, \\ \frac{dT}{dt} &= \alpha_1 I - (\alpha_2 + \delta_T + \mu),T, \\ \frac{dR}{dt} &= \beta_3 I + \alpha_2 T - \mu R, \\ \frac{dN}{dt} &= \Lambda - \mu N - \delta_I I - \delta_T T. \end{aligned} $$

The ODE is solved with deSolve::ode and serves as the well-mixed reference against which network simulations are benchmarked.

Basic reproduction number

The disease-free equilibrium is $(S^{*}, E^{*}, I^{*}, T^{*}, R^{*}) = (\Lambda / \mu, 0, 0, 0, 0)$. Applying the next-generation matrix construction to the $(E, I, T)$ subsystem yields a closed-form expression for $\mathcal{R}_0$ in terms of the model parameters; the package returns this quantity together with the simulation output for convenience in parameter sweeps.

Network process

At each integer time step $t \to t+1$:

1. Demographic events. Expected counts of disease deaths ($\delta_I |I_t|$), treatment deaths ($\delta_T |T_t|$), natural deaths ($\mu |V_t|$), and births ($\Lambda$) are decomposed as floor + Bernoulli(fractional_part). Selected nodes are deleted; new nodes are appended in compartment $S$ and connected according to the topology's attachment rule.
2. Status transitions. Each surviving node draws an independent uniform $u \sim U(0,1)$ and updates its state according to the per-step probabilities induced by the rate parameters above (e.g., $S \to E$ with probability $\beta_1 I_t / N_t$, $E \to I$ with probability $\beta_2$, etc.).
3. Bookkeeping. Compartment counts and graph observables are recorded.

Independent replicates (num_exp) are aggregated into per-time-step means and dispersion bands.

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Installation

Prerequisites

install.packages(c("igraph", "deSolve", "ggplot2", "dplyr", "tidyr"))

R $\geq$ 4.2 is recommended.

From GitHub

install.packages("devtools")
devtools::install_github("skaraoglu/SEITRNet")
library(SEITRNet)

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Quick Start

library(SEITRNet)
set.seed(2026)

# Three replicates on a Watts–Strogatz small-world network
result <- SEITR_network(
  network_type = "WS",
  n            = 200,
  n_par1       = 0.10,   # rewiring probability
  n_par2       = 20,     # lattice neighborhood size
  t            = 150,
  num_exp      = 3,
  verbose      = FALSE
)

The returned object contains compartment trajectories (network and ODE), per-step network observables, and metadata for each replicate.

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API Reference

SEITR_network()

Top-level entry point. Generates a random graph of the requested topology, initializes compartment labels, and runs num_exp replicate stochastic simulations alongside the matched ODE.

SEITR_network(
  network_type = "ER",
  n = 100, n_par1 = 0.9, n_par2 = 10,
  Lambda = 1.1,
  beta1 = 0.8, beta2 = 0.18, beta3 = 0.02,
  alpha1 = 0.1, alpha2 = 0.055,
  delta_I = 0.03, delta_T = 0.03, mu = 0.01,
  S = 85, E = 5, I = 10, Tt = 0, R = 0, N = 100,
  t = 100, num_exp = 10,
  verbose = FALSE,
  state = NULL, parameters = NULL
)

Network topologies

Code	Topology	Generator (igraph)	n_par1	n_par2
ER	Erdős–Rényi	sample_gnp	edge probability $p$	—
BA	Barabási–Albert	sample_pa	scaling factor: $m = n \cdot n_\text{par1}$	—
WS	Watts–Strogatz	sample_smallworld	rewiring probability $p$	neighborhood $k$
LN	Regular lattice	make_lattice	neighborhood $k$	—
RR	Random regular	sample_k_regular	degree $k$	—

Epidemiological parameters

Argument	Symbol	Default	Description
Lambda	$\Lambda$	1.1	Birth rate (inflow into $S$)
beta1	$\beta_1$	0.80	Transmission rate, $S \to E$
beta2	$\beta_2$	0.18	Progression rate, $E \to I$
beta3	$\beta_3$	0.02	Spontaneous recovery rate, $I \to R$
alpha1	$\alpha_1$	0.10	Treatment uptake rate, $I \to T$
alpha2	$\alpha_2$	0.055	Recovery rate from treatment, $T \to R$
delta_I	$\delta_I$	0.03	Disease-induced mortality (from $I$)
delta_T	$\delta_T$	0.03	Treatment-associated mortality (from $T$)
mu	$\mu$	0.01	Natural mortality (acts on all compartments)

Initial conditions and simulation controls

Argument	Default	Description
n, N	100	Initial population size
S, E, I, Tt, R	85, 5, 10, 0, 0	Initial compartment sizes
t	100	Simulation horizon (time steps)
num_exp	10	Number of stochastic replicates
verbose	FALSE	Per-event logging
state, parameters	NULL	Optional pre-built deSolve inputs

Note. Initial compartment sizes must satisfy $S + E + I + T + R = n$. The package validates this on entry and raises an informative error on mismatch.

compare_experiment_sets()

compare_experiment_sets(list(ws_p.1_k20, er_p.2, ba_m.75))

Aligns trajectories from multiple SEITR_network() calls onto a common time axis and produces faceted comparison plots. Currently inactive — scheduled for the next release.

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Examples

Single topology

ba_m.75 <- SEITR_network("BA", n_par1 = 0.75, num_exp = 5)

Topology sweep

ws_p.1_k20 <- SEITR_network("WS", n_par1 = 0.10, n_par2 = 20, num_exp = 3)
er_p.2     <- SEITR_network("ER", n_par1 = 0.20,              num_exp = 3)
ba_m.75    <- SEITR_network("BA", n_par1 = 0.75,              num_exp = 3)

compare_experiment_sets(list(ws_p.1_k20, er_p.2, ba_m.75))

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Outputs

Each call to SEITR_network() returns a list containing:

• Trajectories — per-replicate, per-time-step counts for $S, E, I, T, R, N$ from both the network simulation and the matched ODE.
• Network observables — per-time-step degree distribution, global clustering coefficient (transitivity), mean shortest-path length, and largest-connected-component size.
• Visualizations — initial graph layout colored by status; periodic snapshots of the evolving network; ODE-vs-network compartment overlays with peak annotations; faceted observable panels.
• Metadata — replicate seeds, topology specification, parameter vector, and computed $\mathcal{R}_0$.

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Reproducibility

All stochastic primitives (graph generation, demographic events, status transitions) are mediated through R's RNG. To make a run bit-reproducible, set the seed before invocation:

set.seed(2026)
result <- SEITR_network("WS", n_par1 = 0.1, n_par2 = 20, num_exp = 3)

Per-replicate seeds are returned in the output metadata so individual realizations can be regenerated in isolation.

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Citation

If this software contributes to a publication, please cite: Karaoglu S, Imran M, McKinney BA. Network-based SEITR epidemiological model with contact heterogeneity: comparison with homogeneous models for random, scale-free and small-world networks. The European Physical Journal Plus. 2025 Jun 18;140(6):551, https://doi.org/10.1140/epjp/s13360-025-06481-z.

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