"Life simulation" of a SEIR inspired model to better understand pandemic using python.
pip install pandemic-simulation # Last stable version
# or
apt-get install python3-venv gcc python3-dev
python3 -m venv ./venv
source ./venv/bin/activate
pip install -r requirements.txt
### To plot new daily cases
python -m simulator.run --draw new --show-plot
### To plot daily state with 150 days and other parameters kept default
python -m simulator.run --nday 150 --draw pop --show-plot
### To plot hospitalization state with 5000 individuals
python -m simulator.run --nday 200 --nind 5000 --draw hos --show-plot
### To plot a summary of the pandemic (with short immunity time)
python -m simulator.run --nday 500 --nind 5000 --immunity-bounds 120 150 --draw sum new --show-plot35k individuals (--nind), 20 simulations (--nrun). Add --show-plot if you want plots to be displayed in a pop-up instead of written to images/output folder
Scenario -1 : It is just a flu (using 3 cpu in parallel)
python -m scenario.run --nrun 20 --nday 180 --nind 35000 --scenario -1 --draw exa pop summ R0 --ncpu 3Scenario 0 : Eradicate
python -m scenario.run --nrun 40 --nday 90 --nind 35000 --scenario 0 --p-house 0.5 --p-work 0.01 --p-transport 0.01 --p-store 0.001 --draw exa pop summ R0Scenario 1 : One shot lockdown removal
python -m scenario.run --nrun 20 --nday 360 --nind 35000 --scenario 1 --extra 14 --draw exa pop summ lock hos new R0Scenario 2 : Yo-yo lockdown removal
python -m scenario.run --nrun 20 --nday 360 --nind 35000 --scenario 2 --extra 7 1 2 --draw exa pop summ lock hos new R0Scenario 3 : Herd immunity
python -m scenario.run --nrun 20 --nday 360 --nind 35000 --scenario 3 --extra 0 --draw exa pop summ lock hos new R0Scenario 4 : Rogue citizen
python -m scenario.run --nrun 20 --nday 180 --nind 35000 --scenario 4 --extra 1 10 --draw exa pop summ lock hos new R0Scenario 5 : Rogue neighborhood
python -m scenario.run --nrun 20 --nday 180 --nind 35000 --scenario 5 --extra 4 10 --draw exa pop summ lock hos new R0Scenario 6 : Infected travelers
python -m scenario.run --nrun 20 --nday 180 --nind 35000 --scenario 6 --p-store 0.001 --extra 5 --draw exa pop summ lock hos new R0Scenario 7 : Temporal immunity
python -m scenario.run --nrun 20 --nday 720 --nind 35000 --scenario -1 --imm 30 60 --draw exa pop summ R0More scenarios are available in the scenario package.
usage: run_benchmark.py [-h] [--nrun NRUN] [--random-seed RANDOM_SEED]
[--ncpu NUM_CPU] [--nind N_INDIVIDUALS]
[--nday N_DAYS] [--sto-house NB_STORE_PER_HOUSE]
[--nblock NB_1D_GRID_BLOCK]
[--remote-work REMOTE_WORK_PERCENT]
[--sto-pref PROB_PREFERENCE_STORE]
[--sto-nb STORE_NB_CHOICE_KEY]
[--inn-infec INITIAL_INNOCULATION_NB]
[--p-house PROB_HOUSE_INFECTION]
[--p-store PROB_STORE_INFECTION]
[--p-work PROB_WORK_INFECTION]
[--p-transport PROB_TRANSPORT_INFECTION]
[--transport-contact-cap TRANSPORT_CONTACT_CAP]
[--contagion-bounds CONTAGION_BOUNDS CONTAGION_BOUNDS]
[--hospitalization-bounds HOSPITALIZATION_BOUNDS HOSPITALIZATION_BOUNDS]
[--death-bounds DEATH_BOUNDS DEATH_BOUNDS]
[--immunity-bounds IMMUNITY_BOUNDS IMMUNITY_BOUNDS]
[--nbeds-icu ICU_BED_PER_1K_INDIV]
[--scenario-id SCENARIO_ID]
[--draw [DRAW_GRAPH [DRAW_GRAPH ...]]]
[--extra-scenario-params [ADDITIONAL_SCENARIO_PARAMETERS [ADDITIONAL_SCENARIO_PARAMETERS ...]]]
Please feed model parameters
optional arguments:
-h, --help show this help message and exit
--nrun NRUN Number of simulations
--random-seed RANDOM_SEED
Random seed
--ncpu NUM_CPU Number of cpus to use (-1 is all but one)
--nind N_INDIVIDUALS Number of individuals
--nday N_DAYS Number of days
--nvariant N_VARIANT Number of variants
--sto-house NB_STORE_PER_HOUSE
Number of store per house
--nblock NB_1D_GRID_BLOCK
Number of blocks in the grid
--remote-work REMOTE_WORK_PERCENT
Percentage of people remote working
--sto-pref PROB_PREFERENCE_STORE
Probability going to nearest store
--sto-nb STORE_NB_CHOICE_KEY
Number of nearest stores to consider
--inn-infec INITIAL_INNOCULATION_NB
Initial innoculation percentage
--p-house PROB_HOUSE_INFECTION
Probability of house infection
--p-store PROB_STORE_INFECTION
Probability of store infection
--p-work PROB_WORK_INFECTION
Probability of workplace infection
--p-transport PROB_TRANSPORT_INFECTION
Probability of public transportation infection
--transport-contact-cap TRANSPORT_CONTACT_CAP
Number of people an individual is close when commuting
--contagion-bounds CONTAGION_BOUNDS CONTAGION_BOUNDS
Contagion bounds
--hospitalization-bounds HOSPITALIZATION_BOUNDS HOSPITALIZATION_BOUNDS
Hospitalization bounds
--death-bounds DEATH_BOUNDS DEATH_BOUNDS
Death bounds
--immunity-bounds IMMUNITY_BOUNDS IMMUNITY_BOUNDS
Immunity bounds
--nbeds-icu ICU_BED_PER_1K_INDIV
Number of ICU beds per thousand population
--scenario-id SCENARIO_ID, --sce SCENARIO_ID
Immunity bounds
--draw [DRAW_GRAPH [DRAW_GRAPH ...]]
Draw a kind of graph by specifying at least the first
3 letters of its keys. Choose from "example",
"hospital", "new", "summary", "population", "lockdown"
and more
--show-plot Show the plots instead of persistings them to files
--extra-scenario-params [ADDITIONAL_SCENARIO_PARAMETERS [ADDITIONAL_SCENARIO_PARAMETERS ...]]
Additional scenario parametersI wanted to recreate the SEIR model results without having to use the differentials equations like in [1]. This means going down the individual level and simulating each person life.
So what is "life" in a pandemic lockdown situation (where almost all nations are now) ?
- You are an individual with an age (important factor here)
- You have a house where you live along family members, probably with children
- If you haven't been authorized to do remote work, you will have to go to your workplace every day
- You or one of the adults living in your house has to go to the grocerie store every day
- In every place (house, store, work or transport), you get to interact with other individuals who can be infected. So there is a probability you will get infected too
- If you are infected, you become contagious after few days and start to spread the disease
- If you are infected, you will die or recover from the disease after a period of time, based on your age (and health issues but let's forget about those for now)
- If hospitals are full, mortality rates raises
- Death or immunity will not make you anymore contagious for other individual, obviously
- You are isolated if one of your family members has been hospitalized
Each house and workplace is being assigned a geolocation in a grid. This grid can be cut into blocks (defined by a parameter). When a worker goes from his house to his workplace, he goes through blocks that are shared by other workers. We maintain a dictionnary of this transportation relationship between workers to propagate the pandemic.
With default parameters.
Placement of houses, stores and workplaces in a grid :
Evolution of the number of healthy, infected, dead and immune people :
It is nice to see the famous 70% herd immunity
Evolution of the number of new cases :
Check the long tail, new cases can emerge days after been to 0
With a temporary immunity, we see waves slowly eaten by dead people :
Temporary immunity of 60 to 90 days can prevent the pandemic from dying
With a summary of a strange non-wave pandemic evolution using :
python -m simulator.run --nday 500 --nind 5000 --immunity-bounds 120 150 --draw summary
The lockdown beats the immunity decreasing. I had to launch the simulation with those models many times to get it.
Here are multiple runs plot against each other :
python -m simulator.run --nrun 20 --nday 180 --nind 1000 --immunity-bounds 60 90 --draw exa
Using a quick and dirty kmeans, we only display the most "different" run distributions to illustrate the butterfly effect of a pandemic
- Simulate a population density and allow people to go to other houses in very dense place (in poor neighborhood)
- Build a new kind of individuals who do not work in workplaces but can go in every house or store (policemen for example)
- Add a delay between test and isolation (PCR tests can take one day)
- Self-isolation of individuals based on symptoms probability of appearance
- Add a tqdm progress bar to ray parallelized code execution
- parallelize the runs (using for example N_proc-1 processors multithreading)
- Build a moving average R0 instead of the daily R0 currently used
- Add a moroccan age pyramid
- Get rid of FN_K: get_infection_params and use a python class
- FAILED : Switch from dictionaries and list to numpy array (may be way more efficient, probably enabling some nice vectorization but huge refactors to come. Turns out it was a bad idea for performance -> lonely branch)
- More tests, there are never enough tests
- Get rid of params as a global variable and use a function (probably a bad pattern)
- Plot the R0 of the pandemic ? (with linear and logarithmic scale)
- Fix transport propagation performance issue
- Add a test-isolation stratey. Since at the end of the confinement, we assume that a part of the people will be tested and positive persons will be isolated.
- When hospitals are full, mortality rates raises
- Make contagion probability slowly raises as I assume people will get tired of the lockdown and start to be lazy at wearing masks and staying home ... (Handled in a scenario)
- Contagion parameters depend on geographic blocks (using individual model, we achieve this)
- Use a contagion probability model for each individual (e.g. probability of contagion is obtained with a model)
- Reviewing the distribution model of individuals over households, probably it can be modeled with a truncated normal distribution, we can set parameters using information from this website https://www.hcp.ma/Les-projections-de-la-population-et-des-menages-entre-2014-et-2050_a1920.html.
- Infection can and often occurs on public transportation. We need to build a basic transport model with infection probabilities
- You probably won't go to the grocerie store every day, but probably twice in week day and once on the weekend (that could be a random variable)
- Extract more parameters from the code
- Model temporary immunity
- Handle multiple runs and add error bars to result plots
- Work is only on week days, weekend need to be removed
- You may go to the second nearest grocerie store instead of the closest one (as implemented)
- You probably won't go to the grocerie store every day, but probably twice in week day and once on the weekend (that could be a random variable)
- Add a model for hospitalized people (since hospitals can be saturated)
- Handle multiple runs and add error bars to result plots
https://issam.ma/jekyll/update/2020/04/11/covid-pandemic-simulation.html (French) https://issam.ma/jekyll/update/2020/05/01/pandemic-lockdown-scenarios.html (French) https://issam.ma/jekyll/update/2020/07/04/macro-economic-immunity.html (French) https://issam.ma/jekyll/update/2021/03/10/mutation-mortalite.html (French)
[1] https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SEIR_model