Covid 19 - Contacts
Contents
Problem definition
The global Covid 19 pandemic is impacting everyone's lives. To contain the pandemic, mass events have been banned in Germany since 2020 and masks must be worn daily on public transport and in stores. These measures are increasingly criticized and disregarded by some parts of the population.
This simulation is used to illustrate the impact of bans on mass gatherings on infection rates and the extent to which wearing masks protects all members of society.
Method
NetLogo is used for the simulation. This allows the representation of autonomous agents.Thus, pandemic behavior can be well represented in a situation where people/agents move differently in the daily routine. Hence, reality can be suitably represented in an abstracted model to show the specifics of a pandemic spread.
Model
The model shows the abstracted version of a village. The houses of the inhabitants and points of interest (office, shops...) are randomly distributed through the village. The model simulates the daily routine of the inhabitants. The day is determined by a fixed number of ticks. At the start of a day the inhabitants are in their permanently assigned houses. Around 8 a.m. all residents leave their houses and go to one of the different points of interest. In the afternoon, residents return to their homes.
In this village, the spread of Covid 19 is simulated. Residents can become infected by being close enough to infected residents for a sufficient amount of time. If the contact is long and close enough for an infection, the person turns orange. If an infection has occurred, the chain of infection is represented by a link The person now infected also become contagious after an incubation period, turns red, and can infect other persons at home, on routes, or at one of the points of interest. Infection lasts between 7 and 10 days, after which time the person may die from the infection (triangle) or become immune and turn purple.
World
The world consists of a 64x64 patches standard Netlogo world. We assume one day as 240 ticks.
Static Elements of the World
At the beginning of each run the world is filled with its static elements, namely the points of interest and houses, each of which takes a random position. Houses are permanently assigned to agents. The number of houses is a quarter of the number of people to be generated, which is set at the start. A group of agents assigned to a house is called a family. One family lives per house.
Points of interest (pois) are stores, offices, schools etc. Which will be repeatedly visited by groups of people.
Dynamic Elements of the world
In the following, a given number of inhabitants is generated. When generated each person is assigned a random home (one-of houses) and a random point of interest (one-of pois). All people follow the same day structure: at around 8 am (80 ticks) each person decides with a given probability (home-prob) if he stays at home at this day. If he decides to leave the house he goes to his assigned point of interest with a given probability (1-pois-var-prob) or goes to a random point of interest. After eight hours (80 ticks) each person heads back home where he stays till the next morning.
Covid 19 Infection Mechanism
At the start a fixed number of infected and contagious people is given. The infection is indicated by setting the color of the person to red. For each healthy person is checked in each tick if there are any contagious persons within a certain radius. If infected persons remain within this radius for a sufficient time, the healthy person can become infected with a certain probability (inf-prob) per tick. If a person is infected he enters the incubation period indicated by changing its color to orange. After infection, a directed link is drawn from a randomly selected infected person present within the radius to the infected person. The incubation period length is derived from the log-normal distribution for each person. At the end of the incubation period the person becomes contagious for a given amount of time, derived from a moral distribution. After which the person recovers and becomes dies or becomes immune with a given probability. Death is indicated by a triangle. Immunity is indicated by a purple color.
Parameter
We differentiate between three types of parameters. The world parameters which describe the given situation in the village (number of people, number of pois, ...). Secondly, the behavioral parameters which determine the actions of the people and can be influenced by the anti-pandemic measures. And finally, infection mechanic parameters which describe how long a person is contagious. The parameters of the first two groups can be adjusted using sliders. The last group of infection mechanic parameters is derived from scientific findings about the Covid 19 pandemic.
World Parameters
persons - initial number of inhabitants of the village
infected-int - initial number of infected and already contagious people
cnt-pois - initial number of points of interest
Behavioral Parameters
inf-prob - the probability of infection per tick for healthy people surrounded by contagious people after a given time and can be influenced by ant-pandemic measures as wearing masks, banning mass events and reducing contacts
home-prob - the probability of a person of staying home and not leaving in the morning to any point of interest
pois-var-prob - the probability of a person to go to random point of interest instead of the one initially assigned (simulates shopping, meeting other people, staying at other points of the village, ...)
mass-event - switch to allow or ban mass events (on/off)
masks - switch to force people to wear masks or not (on/off)
Infection Mechanic Parameters
time-to-contagious - incubation time in days (in which the person is not contagious); drawn for each person from a log normal distribution with mean 5.8 and sigma of -1.98 [6]
time-contagious - contagious time of an infected person after the time-to-contagious in days; drawn from a normal distribution with mean 8.5 and standard deviation 0.75 [4]
death-rate - percentage of people who die after the contagious time of 0.05 [2]
Preset Values
Values are set at the beginning that an R0 value between 3-5 is achieved. The R0 value is given in research for the infectivity of a virus in case no measures are taken [3]. It should be mentioned that the R value is a value that depends on the contact behavior and population density [5].
Inf-prob is set to 0.01
people - 500
infected-int - 10
cnt-pois - 30 --> in this case 500 people / 30 are 16-17 people per point of interest
home-prob - 0.1
pois-va-prob 0.1
Output
The results were monitored using monitors and plots.
Monitors
Day - number of passed days
Reproduction number (R) - average of people infected by one infected and contagious person
Not infected - number of not infected people in the village
Plots
Statistics - shows a graph of the percentage of (infected, immune, contagious, deceased) people over time
R - shows a graph of the R value over time
Mass Events Tracker - shows number of mass events over time
Results
Beispiel mit wenigen Personen um Infektionskette genau verfolgen zu können
Conclusion
Sources
Chu, D. K. (2020). Physical distancing, face masks, and eye protection to prevent person-to-person transmission of SARS-CoV-2 and COVID-19: A systematic review and meta-analysis. 395, 15. from [1]
Coronavirus (COVID-19) cases and deaths Germany 2021 | Statista. (n.d.). Retrieved January 20, 2021, from [2]
Estimate of the Basic Reproduction Number for COVID-19: A Systematic Review and Meta-analysis. (2020). Retrieved January 20, 2021, from [3]
Evidence summary for COVID-19 viral load over course of infection from Health Infomation and Quality Authority, Ireland (2020) Retrieved January 20, 2021, from [4]
RKI - Coronavirus SARS-CoV-2—Epidemiologischer Steckbrief zu SARS-CoV-2 und COVID-19. (2021). Retrieved January 20, 2021, from [5]
The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application | Annals of Internal Medicine. (2020). Retrieved January 20, 2021, from [6]
