Simulation of pandemic spread

Title: Simulation of pandemic spread

Author: Daniel Kopecký

Method: Agent-based model

Tool: NetLogo

Introduction and problem definition

Not so long ago we had the COVID-19 pandemic, which showed us the shortcomings in dealing with this type of problem. Pandemic propagation simulation can be a key tool to model, analyse and predict the evolution of a pandemic. This model deals specifically with viral diseases. The aim of this simulation is to be able to predict the spread of a pandemic virus, whereby using appropriate values, it can simulate the approximate development of a pandemic in the Czechia.

Method

An agent-based model in NetLogo is used to simulate the spread of the pandemic. This allows us to code our own scenario using different variables and helps us to get closer to the real pandemic evolution.

Model

The model contains a map of the Czechia, where the selected population is randomly scattered at the beginning of the simulation. The inhabitants can move freely within the entire rendered territory. The selected population is already infected and by running the simulation they can infect other uninfected citizens. The model offers to create a custom scenario where the user sets their own variable values. It is also possible to choose from preset viruses that set the variables for the user.

Environment

The model is reserved for the Czechia. This was achieved using a silhouette of the Czech Republic that was uploaded to NetLogo using this code: ‎import-pcolors "cesko.png"‎.

Agents

People are represented by agents who have three different colors. People who are healthy, but not immune, are green. These people can also be infected by infected individuals. The red colour is used for people who are infected. So these people can spread the virus, get better or die from the virus. Individuals who have had the virus and are now immune to the virus are blue.

Movement

People move randomly around the territory of the Czechia. During their movement they may meet other individuals from whom they could potentially be infected.

Spread of infection

The original infected individuals can infect any individual that comes into their vicinity. The variables qurantine.effort, trasmission.rate, and the number of infected around an uninfected individual affect whether an individual becomes infected. If an individual has already been infected but has recovered, this means that it has immunity and therefore cannot be re-infected. Immunity can be turned off when setting up the model.

Recovery from infection

Individuals who are infected have a chance to recover, which is set by the recovery.rate variable. If they recover and immunity is on, the individual's color will change to blue. If immunity is off, the color of the individual will change to green.

Death

If an individual is infected, there is a chance that they will die. This is affected by two variables, namely healthcare.capacity and infected-mortality. Healthcare.capacity is the spare capacity of healthcare facilities. The value ranges from 0 to 1 and represents the maximum % of the population that can be hospitalized at one time. If the % of infected in the population exceeds the capacity limit of the healthcare facilities, the probability of an individual dying rises.

End of the simulation

The simulation ends when the virus stops spreading and the number of infected drops to zero, or when the number of infected equals the population size, or when the virus kills off the entire population.

Predefined viruses

The model offers the possibility to choose a predefined virus or to choose a custom scenario where the user defines their own variable values. Once a virus is selected, its transmission rate and mortality rate are set.

Covid-19

Covid-19, caused by the novel coronavirus SARS-CoV-2, emerged in late 2019 and quickly developed into a global pandemic. It primarily spreads through respiratory droplets, causing a range of symptoms from mild respiratory issues to severe pneumonia, with a heightened risk for older adults and those with underlying health conditions.
R0 = 0.71
Fatality rate = 0.0004
Recovery rate = 9
Immunity = True

Spanish Influenza

The Spanish Influenza, which occurred in 1918, was an exceptionally deadly H1N1 influenza A virus that caused a devastating pandemic.
R0 = 1.2 - 3.0
Fatality rate = 0.03
Recovery rate = 7-30 (cannot be exactly found)
Immunity = CANNOT BE FOUND

Seasonal Influenza

Seasonal Influenza, or the flu, is an annual respiratory illness caused by influenza viruses. It typically circulates during the colder months and can lead to fever, cough, and muscle aches.
RO = 0.9 - 2.1
Fatality rate = 0.000005
Recovery rate = 7
Immunity = False (own experience :-) )

Measles

Measles is a highly contagious viral infection, primarily affecting children, characterized by a distinctive rash and fever.
R0 = 12-18
Fatality rate = 0.001
Recovery rate = 7-18
Immunity = True

SARS

SARS (Severe Acute Respiratory Syndrome) emerged in 2002, caused by a coronavirus (SARS-CoV), resulting in severe respiratory distress.
R0 = 2.7
Fatality rate = 0.096
Recovery rate = 10-14
Immunity = True

Ebola

Ebola, a severe and often fatal viral hemorrhagic fever, gained global attention during outbreaks in Africa. It causes internal bleeding and multiple organ failure, with a high mortality rate.
R0 = 1.95
Fatality rate = 0.5
Recovery rate = 10-14 
Immunity = True 

Variables

• init-population - Population at the beginning of the simulation

• init-infected - Number of infected at the start of the simulation

• recovery.rate - Rate of recovery of infected individuals

• init-immune - Number of immune individuals at the beginning of the simulation

• quarantine.effort - Quarantine effort (affects the chance of infecting an individual)

• transmission.rate - Rate of virus transmission between individuals

• infected-mortality - Virus mortality rate

• healthcare.capacity - Capacity of health facilities (affects the rate of death of individuals)

• immunity? - Turns immunity on or off

UI

The user interface consists of setup and go buttons. These are used to prepare all necessary data and values before starting the simulation and to start or pause the simulation itself.
A switch that enables/disables immunity, which affects whether individuals in the simulation can be immune to the virus after they have recovered from it.
Also from various sliders that set the values of variables that are then used within the simulation run.
The population slider sets the initial number of individuals that appear in the simulation. We can choose from values 1-1000.
Slider to set the initial infected individuals.
A slider to set the rate at which individuals heal.
Slider to set the initial state of immune individuals.
Quarantine effort, which tells us how individuals are trying to comply with the quarantine.
The transmission rate of the virus between individuals.
The mortality rate of the virus when an individual is infected with it.
And the capacity of health facilities, which is reflected in the rate of spread of the virus if it is exceeded.

Results

Here we can see on the graph the results for the individual diseases that are selected, with the quarantine effort set to 0.2 and the capacity of the health facilities also set to 0.2.

• 

  (Covid19)

• 

  (Measles)

• 

  (Ebola)

For all simulation results shown above, the default settings for the selected virus were used. The population was set to 501, the number of infected individuals to 19, and the number of individuals with immunity to 0.

Conclusion

The model in this simplified version can simulate the development of various pandemics within the Czech Republic. Its main advantage is the limitation of the territory that follows the borders of the Czech Republic and also the preset values for different viruses, which are based on real data. We must also not forget the customization option, thanks to which the user can create tailor-made virus simulations. Creating the model itself was not as challenging as searching for all the background information for each virus. As part of the extension, it would be possible to add additional predefined viruses or to add additional refinement parameters that would affect the course of the entire simulation for a given virus.

NetLogo File

Below I attach the source file together with the map of the Czech Republic, which must be in the same directory as the NetLogo source file.
File:Virus sim.nlogo