covid-simulation based on some graph method. Xuan Ma Introduction: Simulation of covid-19 spreading in our campus Since December 1, 2019, the New Coronavirus has started spreading globally. Nearly three years have passed since 2019. As a historically rare and highly infectious virus, the presence of the New Coronavirus has become integrated with each of our lives. Covid-19 has at least 5 variants so far which is Alpha found in Sep-2020, Beta found in may-2020, Gamma found in Nov-2020, Delta found in Oct-2020, and one of the most infectious viruses Omicron found in Nov-2021. Until today, we still live under the wave of COVID-19 on a daily basis. In a previous article we read during this semester, they were trying to simulate COVID-19 spreading in England and test some non-pharmaceutical factors effects on transmission process. The outcome of their simulation research pretty much duplicated the data from real life, and they took a bunch of non-pharmaceutical factors into account in their project. The purpose of my project here is to simulate the transmission process of COVID-19 of the community of Bard College with a user interactive control board to control some key factors that could infect the transmission and test the efficiency of vaccination in Bard. There are two specific types of data that have been collected carefully, transmission duration and the percentage of people that have not been infected, because they could represent the validity of vaccination.
Pilot study: For the purpose of simulating the community social network better, a pilot study which investigated the on-campus network of Bard students was conducted. The pilot study is a questionnaire based investigation, there are two questions in total on this questionnaire: the first question of the questionnaire is “how many close friends (having conversations at least 4 times per week) do you have within the Bard community?; the second question is “how many friends (not very close but having conversation at least 1 time per week) do you have within the Bard community?” There were 9 participants in total for this pilot study, none of them being excluded from the final data analysis. On average, each student from Bard has 3 close friends and 7 not very close friends. This data was collected and used in constructing the social network of Bard for the purpose of simulating COVID-19 transmission. Design & Methodology: The simulation of my project is based on Social Network Simulation from professor Anderson. By default, the original simulation is simulating COVID-19 transmission in a
randomly generated community where the relationship between individuals in the community is generated by createSmallWord method from JgraphT library, and non of residents in the community are vaccinated and the simulation does not take various of COVID-19 variants into account. In order to match the real life data as much as possible, there are three main changes from the original simulation: the user could determine whether members in the community have taken vaccinations or not, which COVID-19 variants are spreading among the community, and how many people are living in the community. The interface for the user to determine the factors in programming is through a Java GUI window designed by myself. By selecting the desired button before clicking the “enter ”button, the GUI could set up the value and pass it to the simulation class by itself. After hit the “enter” button on the keyboard, a button will appears on the right of size text box, after clicking the button the simulation will run it by itself, as long as there is no infected case in the simulational world, a graph representation of the community will pops up with white and green vertices (white vertex represents individual has not been infected throughout the complete simulation and green vertex represents individuals has been infected and then recovered). In addition, some important data
(number of people being infected, proportion of people being infected, number of people that are not being infected, and number of days the virus is spreading) will be printed out in the terminal window of this program. Users could rerun the simulation by clicking the “press to start simulation!” button and all the key factors could be resetted by clicking the desired button. Important data: To better match the simulation with real life, I grab the data mostly from cdc.gov which is a trustworthy government website for official pandemic data. According to the published data, vaccination efficiency for variant Alpha is around 93%, which means that fully vaccinated people have a 7% chance of being infected by Alpha variant if they are exposed to the virus; the efficiency of vaccination for Delta variant is 58%; the effectiveness of variant Omicron is 29.2%(cdc.gov). After a new booster that was designed for Omicron specifically was published, the effectiveness of resisting Omicron became 60%(cnn.com). Social networking structure: For the purpose of better simulating the social structure of Bard college within the graph, I took the data from pilot study and implemented it into the createSmallWorld method from JgraphT library. The createSmallWorld method requires 4 parameters in total, the first parameter is the square root of the size of the graph, the second
parameters represent the local connections to the nodes surround them (in social relationship, a connection to a close friend), the third parameter is distant connections which represent friends that are no very close, and the fourth parameter is the probability of distribution parameter which is not considered in this simulation. After calling the method of createSmallWorld, it initializes a graph that each of the nodes have their own id from 0 to the desired size-1. The way I determine which connection is pointing to close friends or friends is through calculating their ID difference. If the difference between two IDs is bigger than 2, then I define the node that the connection pointing to is friends, while the difference is smaller than 2, I count the connection as close friends’ relationship which have higher rate of transmission. For example, the 34 have a local connection to 35, the relationship between these two nodes will be counted as close friends. In the simulation, the rate of transmission between two friends is 7%, between two close friends is 12.1%, and there is no possibility that the virus could be transmitted to any strangers which doesn’t really match the real life data. Result: For the transmission duration, the average time for Alpha variant transmitted in a vaccinated community is 10.9 days, the average duration for Delta variant transmitted in a vaccinated community is 47.3 days, the average duration for Omicron transmitted in a vaccinated campus is 41.3 days, and the average durations for Omicron with updated booster is 48.4 days . My interpretation for these dataset is that while the vaccination for the virus is super effective, it could constrain the transmission in a short period of time, while the vaccination is not effective enough to variants, it will prolong the transmission duration and reduce the number of infection cases at the same time. The other datasets
also being collected along with the previous datasets are the duration of transmission of Alpha variant without vaccination (29.8 days), Delta variant without vaccination (29.4), and Omicron variant without transmission (28.9 days). According to the data presented before, the duration of transmission is pretty constant without the effect of vaccination. The effectiveness of vaccination is pretty similar to the real life data provided by CDC: vaccination effectiveness for Delta is “58% overall, without prior infection” (cdc.gov); vaccination effectiveness for Omicroon is “29.2%, 2 to 4 months since last dose of Janssen”(cdc.gov). In addition, the effectiveness of boosters specifically designed for Omicron have the effectiveness of 60% (cnn.com) . The average healthy rate in the spreadsheet is the effectiveness of the vaccine in the simulation and the vaccine efficiency is the data from real life, according to this comparison, all of the data from simulation does not have a big variance from the real life data except the Omicron with regular vaccination. So the simulation of the effectiveness of vaccination is pretty successful while there are some more factors that need to be included for a more accurate outcome. The trend line of healthy people and healthy people who got infected align with the SIR model, with vaccination factor added within the simulation, the tendency of transmission changes
with the efficiency of vaccination. With the outcome graph, we can easily tell that without the effect of vaccination, most of the people got infected within a short period of time. However, when everyone has already been vaccinated in Bard community, the span of transmission generally being elongated to around 45 days. There is an interesting fact in this simulation that while the vaccination or a way to block the transmission is super efficient (probably bigger than 90), the transmission span of virus will be shorter than without vaccination scenario. In contrast, while the vaccination efficiency is lower than a certain threshold (I guess it’s 80 or 90), the span of transmission will be much longer than without vaccination. General discussion: This model does simulate the transmission process of a representative social network of the Bard college community, while the network is still not accurate enough for us to reach a definite conclusion. To further elaborate the simulation, I would try to implement the social network model from the Stanford database which is an accurate representation of a certain community. Also, the final result would not be helpful to compare with data released by Bard college, since I know the amount of my friends got COVID while they definitely have not been included in the published data. There is another factor that makes the simulation not realistic enough for reaching the conclusion that the efficiency of the vaccination does not mean the possibility of transmission, instead, it means that a certain percentage of the population gain the immunity to virus
hence they will not be infected. So the further elaboration on this part is to give each Person object a boolean value which determines whether they are susceptible to virus, ergo to improve the accuracy of the model. In conclusion, this model is successful in the sense of the efficiency of vaccination, the spreading span of COVID-19, and similarities with the SIR model.
Bibliography 1, https://covid.cdc.gov/covid-data-tracker/#vaccine-effectiveness 2, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7976050/ 3, https://www.cnn.com/2022/11/22/health/vaccine-effectiveness-bivalent-boosters-cdc/ind ex.html#:~:text=The%20new%20study%20found%20that,be%20vulnerable%20to%20br eakthrough%20infections.