UTLDR

The UTLDR model [1] describe a complex framework allowing to extend SEIR/SEIS to incorporate medical and non medical interventions. The acronym summarizes the five macro statuses an agent can be involved into:

  • U ndetected
  • T tested
  • L ocked
  • D ead
  • R ecovered

The U macro status follows the same rules of a classic SEIR(S) model and model the general epidemic evolution when no intervention is established.

The T macro status implements Testing (e.g., identification of exposed/infected agents) and model different classes of response (e.g., quarantine, hospitalization, ICU ospitalization).

The L macro status implements Lockdowns (that can be fine tuned on node attributes) and, as such, social contacts reduction.

Finally, the R and D statuses model the final outcome of an infection (either death or recovery) and are sensible to the various paths for reaching them.

Moreover, UTLDR allows also to include (effective/uneffective) vaccination effects.

UTLDR schema

UTLDR schema: U black statuses, T green statuses, L orange statuses.

Statuses

During the simulation a node can experience the following statuses:

Name Code
Susceptible 0
Infected 1
Exposed 2
Recovered 3
Identified Exposed 4
Hospitalized Mild conditions 5
Hospitalized in ICU 6
Hospitalized in Severe conditions (not ICU) 7
Lockdown Susceptible 8
Lockdown Exposed 9
Lockdown Infected 10
Dead 11
Vaccinated 12

Parameters

Name Type Value Type Default Mandatory Description
sigma Model float in [0, 1]   True Incubation rate
beta Model float in [0, 1]   True Infection rate
gamma Model float in [0, 1]   True Recovery rate (Mild, Asymtomatic, Paucisymtomatic)
gamma_t Model float in [0, 1] 0.6 False Recovery rate (Severe in ICU)
gamma_f Model float in [0, 1] 0.95 False Recovery rate (Severe not ICU)
omega Model float in [0, 1] 0 False Death probability (Mild, Asymtomatic, Paucisymtomatic)
omega_t Model float in [0, 1] 0 False Death probability (Severe in ICU)
omega_f Model float in [0, 1] 0 False Death probability (Severe not ICU)
phi_e Model float in [0, 1] 0 False Testing probability (if Exposed)
phi_i Model float in [0, 1] 0 False Testing probability (if Infected)
kappa_e Model float in [0, 1] 0.7 False 1 - False Negative probability (if Exposed)
kappa_i Model float in [0, 1] 0.9 False 1 - False Negative probability (if Infected)
epsilon_e Model float in [0, 1] 1 False Social restriction, percentage of pruned edges (Quarantine)
epsilon_l Model float in [0, 1] 1 False Social restriction, percentage of pruned edges (Lockdown)
lambda Model float in [0, 1] 1 False Lockdown effectiveness
mu Model float in [0, 1] 1 False Lockdown duration (1/expected iterations)
p Model float in [0, 1] 0 False Probability of long range (random) interactions
p_l Model float in [0, 1] 0 False Probability of long range (random) interactions (Lockdown)
lsize Model float in [0, 1] 0.25 False Percentage of long range interactions w.r.t. short range ones
icu_b Model int in [0, inf] N False ICU beds availability
iota Model float in [0, 1] 1 False Severe case probability (requiring ICU)
z Model float in [0, 1] 0 False Probability of infection from corpses
s Model float in [0, 1] 0 False Probability of no immunization after recovery
v Model float in [0, 1] 0 False Vaccination probability (once per agent)
f Model float in [0, 1] 0 False Probability of vaccination nullification (1/temporal coverage)
activity Node float in [0, 1] 1 False Node’s interactions per iteration (percentage of neighbors)
segment Node str None False Node’s class (e.g., age, gender)

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.

Methods

The following class methods are made available to configure, describe and execute the simulation:

Configure

class ndlib.models.epidemics.UTLDRModel.UTLDRModel(graph, seed=None)
UTLDRModel.__init__(graph)

Model Constructor

Parameters:graph – A networkx graph object
UTLDRModel.set_initial_status(self, configuration)

Set the initial model configuration

Parameters:configuration – a `ndlib.models.ModelConfig.Configuration` object
UTLDRModel.reset(self)

Reset the simulation setting the actual status to the initial configuration.

Describe

UTLDRModel.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
UTLDRModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns:a dictionary (status->code)

Execute Simulation

UTLDRModel.iteration(self)
Parameters:node_status
Returns:
UTLDRModel.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}

Dynamically Update Policies

UTLDRModel.set_lockdown(self)

Impose the beginning of a lockdown

Parameters:households – (optional) dictionary specifying the households for each node <node_id -> list(nodes in household)>
Returns:
UTLDRModel.unset_lockdown(self)

Remove the lockdown social limitations

Returns:
UTLDRModel.add_ICU_beds(self, n)

Add/Subtract beds in intensive care

Parameters:n – number of beds to add/remove
Returns:

Example

In the code below is shown an example of instantiation and execution of an UTLDR simulation on a random graph.

import networkx as nx
import numpy as np
import ndlib.models.ModelConfig as mc
import ndlib.models.epidemics as epd

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

model = epd.UTLDRModel(g)
config = mc.Configuration()

# Undetected
config.add_model_parameter("sigma", 0.05)
config.add_model_parameter("beta", {"M": 0.25, "F": 0})
config.add_model_parameter("gamma", 0.05)
config.add_model_parameter("omega", 0.01)
config.add_model_parameter("p", 0.04)
config.add_model_parameter("lsize", 0.2)

# Testing
config.add_model_parameter("phi_e", 0.03)
config.add_model_parameter("phi_i", 0.1)
config.add_model_parameter("kappa_e", 0.03)
config.add_model_parameter("kappa_i", 0.1)
config.add_model_parameter("gamma_t", 0.08)
config.add_model_parameter("gamma_f", 0.1)
config.add_model_parameter("omega_t", 0.01)
config.add_model_parameter("omega_f", 0.08)
config.add_model_parameter("epsilon_e", 1)
config.add_model_parameter("icu_b", 10)
config.add_model_parameter("iota", 0.20)
config.add_model_parameter("z", 0.2)
config.add_model_parameter("s", 0.05)

# Lockdown
config.add_model_parameter("lambda", 0.8)
config.add_model_parameter("epsilon_l", 5)
config.add_model_parameter("mu", 0.05)
config.add_model_parameter("p_l", 0.04)

# Vaccination
config.add_model_parameter("v", 0.15)
config.add_model_parameter("f", 0.02)

nodes = g.nodes
ngender = ['M', 'F']
work = ['school', 'PA', 'hospital', 'none']
for i in nodes:
    config.add_node_configuration("activity", i, 1)
    config.add_node_configuration("work", i, np.random.choice(work, 2))
    config.add_node_configuration("segment", i, np.random.choice(ngender, 1)[0])

model.set_initial_status(config)
iterations = model.iteration_bunch(10)

households = {0: [1, 2, 3, 4], 5: [6, 7]}
model.set_lockdown(households, ['PA', 'school'])
iterations = model.iteration_bunch(10)

model.unset_lockdown(['PA'])
iterations = model.iteration_bunch(10)

model.set_lockdown(households)
iterations = model.iteration_bunch(10)

model.unset_lockdown(['school'])
iterations = model.iteration_bunch(10)

model.add_ICU_beds(5)
iterations = model.iteration_bunch(10)
[1]
  1. Rossetti, L. Milli, S. Citraro. UTLDR: an agent-based framework for modeling infectious diseases and public interventions. Working Paper, 2020