Modeling of epidemics using the SEIR model
Project description
Python package for modeling epidemics using the SEIR model.
Installation
The package is available in the Python Package Index, and can be installed using pip
pip install seir
An up-to-date version can be found in the master branch of the repository at Github, and can be installed with pip like
pip install git+https://github.com/covid19-bh-biostats/seir
Command line simulation tool
The seir package includes a command line tool seir-model for a simulation of
a simple compartmentalized SEIR model. Basic use looks like the following
$ seir-model config
Here config is a configuration file containing information on the epidemic and the population. Examples of configuration files can be found in the example_configs/ directory of the Github repository.
Config-files
The configuration file should contain three sections, [simulation], [model], and [population]. Example files are provided in the example_configs/ directory at the root of the repository.
[simulation]
The [simulation] section defines parameters relating to the numerical simulation of the SEIR ordinary differential equation. Supported parameters are
[simulation] max_simulation_time = 300 method = DOP853 max_step = 0.5
Here the only required parameter is max_simulation_time, i.e., the
number of simulated days.
The parameter method can be used to change the numerical integration routine. For supported values, please check the documentation of scipy.integrate.solve_ivp.
max_step defines the maximum time-step used in the integration.
[model] (no compartmentalization)
The [model] section defines the parameters of the disease model. In its simplest form, where you wish to model the entire population and do not wish to compartmentalize it, the [model] section looks like
[model] population = 5e6 incubation_period = 3 infectious_period = 7 initial_R0 = 2.5 hospitalization_probability = 0.1 hospitalization_duration = 20 hospitalization_lag_from_onset = 7 icu_probability = 0.01 icu_duration = 10 icu_lag_from_onset = 11 death_probability = 0.1 death_lag_from_onset = 25
Here the parameters are
- incubation_period
Incubation period of the disease in days.
- infectious_period
How long a patient can infect others (in days) after the incubation period.
- initial_R0
Basic reproductive number of the disease
- hospitalization_probability
Probability that an infected person needs hospitalization
- hospitalization_duration
Average duration of a hospitalization in days.
- hospitalization_lag_from_onset
Average time (in days) from the onset of symptoms to admission to hospital
- icu_probability
Probability that an infected person needs hospitalization.
- icu_duration
Average duration of the need for intensive care in days.
- icu_lag_from_onset
Average time (in days) from the onset of symptoms to admission to ICU.
- death_probability
Probability that an infected person dies from the disease.
- death_lag_from_onset
Average time from the onset of symptoms to death (in days).
- population
The total population.
[model] (compartmentalization)
The [model] section defines the parameters of the disease model. When
you wish to separate your population into various compartments (e.g., age groups),
your [model] section becomes more involved.
As an example, consider the population of Finland, divided to three compartments by ages: 0…15, 16…65, and 65+
[model]
compartments =
0-15,
16-65,
65+
population =
871036,
3422996,
1231274
incubation_period = 3
infectious_period = 7
initial_R0 = 2.5
hospitalization_probability =
0.11,
0.17,
0.29
hospitalization_duration = 20
hospitalization_lag_from_onset = 7
icu_probability = 0.01
icu_duration = 10
icu_lag_from_onset = 11
death_probability = 0.1
death_lag_from_onset = 25
Here the parameters are
- compartments
A comma-separated list of the compartment names
- population
A comma-separated list of population of each compartment
- incubation_period
Incubation period of the disease in days. If a single number, the same number is used for all compartments. You can define a different incubation period for each compartment by supplying a comma-separated list.
- infectious_period
How long a patient can infect others (in days) after the incubation period. If a single number, the same number is used for all compartments. You can use a different value for each compartment by supplying a comma-separated list.
- initial_R0
Basic reproductive number of the disease. A single number.
- hospitalization_probability
Probability that an infected person needs hospitalization. If a single number, the same number is used for all compartments. You can use a different value for each compartment by supplying a comma-separated list.
- hospitalization_duration
Average duration of a hospitalization in days.
- hospitalization_lag_from_onset
Average time (in days) from the onset of symptoms to admission to hospital.
- icu_probability
Probability that an infected person needs hospitalization. If a single number, the same number is used for all compartments. You can use a different value for each compartment by supplying a comma-separated list.
- icu_duration
Average duration of the need for intensive care in days.
- icu_lag_from_onset
Average time (in days) from the onset of symptoms to admission to ICU.
- death_probability
Probability that an infected person dies from the disease. If a single number, the same number is used for all compartments. You can use a different value for each compartment by supplying a comma-separated list.
- death_lag_from_onset
Average time from the onset of symptoms to death (in days).
[initial state] (no compartmentalization)
When there are no compartments in the model, the [initial state]
section of the configuration file should look something like
[initial state] probabilities = True population_susceptible = 0.8 population_exposed = 0.15 population_infected = 0.05
Here the parameters are
- probabilities
If
true, the rest of the parameters in this section are considered as probabilities, and the total number of exposed/infected people is computed by multiplying the total population by the provided value.- population_exposed
The total number (or probability) of exposed people
- population_infected
The total number (or probability) of infected people
[initial state] (compartmentalized)
When there are compartments in the model, the [initial state]
section of the configuration file should look something like
[initial state]
probabilities = True
population_exposed =
0.001,
0.01,
0.005
population_infected =
0.001,
0.01,
0.005
Here the parameters are
- probabilities
If
true, the rest of the parameters in this section are considered as probabilities, and the total number of exposed/infected people is computed by multiplying the total population by the provided value.- population_exposed
The total number (or probability) of exposed people
- population_infected
The total number (or probability) of infected people
Contact patterns (compartmentalized models)
Sometimes we have the knowledge of how many different daily contacts a person
in compartment i has with persons from compartment j. This is
called the contacts matrix, C[i,j].
The contacts matrix can be supplied to the seir-model command line tool
with the flag -c
$ seir-model -c my_contacts_matrix.csv configfile
The contacts matrix should be a space or comma separated file with the same number of columns and rows as there are compartments defined in the configuration file. For an example, please try:
$ seir-model -c contacts_matrices/finland --visualize-compartments example_configs/finland
Example contact pattern matrix can be found in the contacts_matrices/ directory of the repository in Github.
Output file
The seir-model tool outputs the computed model in a file called outfile.csv (can be changed with the -o option).
The outputfile is a comma separated table containing the following simulation results:
timeArray of days from the beginning of the simulation
('susceptible', <compartment name>)Number of susceptible people of compartment
<compartment name>corresponding to each day in the ‘time’ array.susceptibleNumber of susceptible people in all compartments.
('exposed', <compartment name>)Number of exposed people of compartment
<compartment name>corresponding to each day in the ‘time’ array.exposedNumber of exposed people in all compartments.
('infected (active)', <compartment name>)Number of people with an active infection of compartment
<compartment name>corresponding to each day in the ‘time’ array.infected (active)Number of people with an active infection in all compartments.
('infected (total)', <compartment name>)Number of people who have an active infection (or have had one in the history) from compartment
<compartment name>corresponding to each day in the ‘time’ array.infected (total)Number of people who have an active infection (or have had one in the history) in all compartments.
('removed', <compartment name>)Number of removed of compartment
<compartment name>corresponding to each day in the ‘time’ array.removedNumber of removed people in all compartments.
('hospitalized (active)', <compartment name>)Number of people who need hospitalization from compartment
<compartment name>corresponding to each day in the ‘time’ array.hospitalized (active)Total number of people who need hospitalization.
('in ICU', <compartment name>)Number of people who (currently) need intensive care from compartment
<compartment name>corresponding to each day in the ‘time’ array.in ICU (active)Total number of people who currently need intensive care.
('deaths', <compartment name>)Number of people from compartment
<compartment name>who have died (cumulative sum).deathsTotal number of people who have died.
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