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: 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.

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]

7. Rossetti, L. Milli, S. Citraro. UTLDR: an agent-based framework for modeling infectious diseases and public interventions. Working Paper, 2020