SEIS
In the SEIS model, during the course of an epidemics, a node is allowed to change its status from Susceptible (S) to Exposed (E) to Infected (I), then again to Susceptible (S).
The model is instantiated on a graph having a non-empty set of infected nodes.
SEIS 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 back to susceptible with probability lambda (the only transition allowed are S→E→I→S).
Statuses
During the simulation a node can experience the following statuses:
Name |
Code |
Susceptible |
0 |
Infected |
1 |
Exposed |
2 |
Parameters
Name |
Type |
Value Type |
Default |
Mandatory |
Description |
beta |
Model |
float in [0, 1] |
|
True |
Infection probability |
lambda |
Model |
float in [0, 1] |
|
True |
Removal probability |
alpha |
Model |
float in [0, 1] |
|
True |
Incubation period |
The initial infection status can be defined via:
- percentage_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.
Methods
The following class methods are made available to configure, describe and execute the simulation:
Describe
SEISModel.
get_info
(self)
-
Describes the current model parameters (nodes, edges, status)
Returns: |
a dictionary containing for each parameter class the values specified during model configuration |
SEISModel.
get_status_map
(self)
-
Specify the statuses allowed by the model and their numeric code
Returns: |
a dictionary (status->code) |
Execute Simulation
SEISModel.
iteration
(self)
-
Execute a single model iteration
Returns: |
Iteration_id, Incremental node status (dictionary node->status) |
SEISModel.
iteration_bunch
(self, bunch_size)
-
Execute a bunch of model iterations
Parameters: |
- bunch_size – the number of iterations to execute
- node_status – if the incremental node status has to be returned.
|
Returns: |
a list containing for each iteration a dictionary {“iteration”: iteration_id, “status”: dictionary_node_to_status}
|
Example
In the code below is shown an example of instantiation and execution of an SEIS simulation on a random graph: we set the initial set of infected nodes as 5% 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.SEISModel as seis
# Network topology
g = nx.erdos_renyi_graph(1000, 0.1)
# Model selection
model = seis.SEISModel(g)
# Model Configuration
cfg = mc.Configuration()
cfg.add_model_parameter('beta', 0.01)
cfg.add_model_parameter('lambda', 0.005)
cfg.add_model_parameter('alpha', 0.05)
cfg.add_model_parameter("percentage_infected", 0.05)
model.set_initial_status(cfg)
# Simulation execution
iterations = model.iteration_bunch(200)