SEIR (DT)

In the SEIR model [1], during the course of an epidemics, a node is allowed to change its status from Susceptible (S) to Exposed (E) to Infected (I), then to Removed (R).

The model is instantiated on a graph having a non-empty set of infected nodes.

SEIR assumes that if, during a generic iteration, a susceptible node comes into contact with an infected one, it becomes infected after an exposition period with probability beta, than it can switch to removed with probability gamma (the only transition allowed are S→E→I→R).

This implementation assumes discrete time dynamics for the E->I and I->R transitions.

Statuses

During the simulation a node can experience the following statuses:

Name Code
Susceptible 0
Infected 1
Exposed 2
Removed 3

Parameters

Name Type Value Type Default Mandatory Description
beta Model float in [0, 1]   True Infection probability
gamma Model float in [0, 1]   True Removal probability
alpha Model float in [0, 1]   True Latent period

The initial infection status can be defined via:

  • fraction_infected: Model Parameter, float in [0, 1]
  • Infected: Status Parameter, set of nodes

The two options are mutually exclusive and the latter takes precedence over the former.

Example

In the code below is shown an example of instantiation and execution of an SEIR simulation on a random graph: we set the initial set of infected nodes as % of the overall population, a probability of infection of 1%, a removal probability of 0.5% and an incubation period of 5% (e.g. 20 iterations).

import networkx as nx
import ndlib.models.ModelConfig as mc
import ndlib.models.epidemics as ep

# Network topology
g = nx.erdos_renyi_graph(1000, 0.1)

# Model selection
model = ep.SEIRModel(g)

# Model Configuration
cfg = mc.Configuration()
cfg.add_model_parameter('beta', 0.01)
cfg.add_model_parameter('gamma', 0.005)
cfg.add_model_parameter('alpha', 0.05)
cfg.add_model_parameter("fraction_infected", 0.05)
model.set_initial_status(cfg)

# Simulation execution
iterations = model.iteration_bunch(200)
[1]J.L. Aron and I.B. Schwartz. Seasonality and period-doubling bifurcations in an epidemic model. Journal Theoretical Biology, 110:665-679, 1984