Using Machine Learning to Determine the

Causal Relationship of Age on COVID-19

Symptom Progression Period, Infection Rate

Percentage, and Recurring Symptoms

Aditya K. Mittal

, Henry Zhao

, Aadhi T. Kumaraswamy

, Megan S. Jacob

, and Rohan S. Ayyagari

Advisor: Keshav Rao

Aspiring Scholars Directed Research Program, 43505 Mission Blvd, Fremont, CA 94539

Due to rising COVID-19 rates and a shortage of re-

searchers, more research must be done to combat future

COVID-19 resurgences and to reduce the number of infected.

Using datasets from California and Kaggle, machine learning

models were used to predict future outcomes for COVID-19,

speciﬁcally in the ﬁeld of age groups. Using k-means cluster-

ing, the average symptom progression period per age group be-

fore hospitalization was found, and polynomial regression was

then used to predict the percentage each age group took in the

amount of total positive cases. Afterward, speciﬁc datasets were

analyzed to look at the symptoms reported for each patient, and

graphs were created to show how many patients had a speciﬁc

symptom. The project showed evidence of three factors that

show a relationship between age and symptoms: older patients

have a longer onset period, the young adult age range has a

higher likelihood of infection, and between all the age ranges,

the symptoms are similar. This project proved a causal relation-

ship for age on symptom progression period and infection per-

centage by age group, which will provide invaluable information

to future researchers developing a cure.

age groups | COVID-19 | k-means clustering | polynomial regression |

symptoms

Correspondence: keshav.rao@fremontstem.com

Introduction

The purpose of the project is to determine the direct causal re-

lationship between the age of COVID-19 patients and symp-

tom type, the likelihood of infection, and the symptom pro-

gression period. In California itself as of August 10, 2020,

there have been 563,000 total conﬁrmed cases and 10,365 to-

tal deaths. Science has shown that COVID-19 is the deadliest

to older people with pre-existing health conditions. How-

ever, research must be done to see how that information will

provide a plausible cure to the growing epidemic. Due to it

being airborne, the chance of infection increases drastically,

making the disease more dangerous than before. If we could

predict how much the virus will spread in the future, neces-

sary steps can be taken to combat COVID-19.

Through this experiment, a three-pronged approach

was implemented to determine age’s general effect on

COVID-19. First, using unsupervised machine learning al-

gorithms to create age range clusters, the average symptom

progression period from symptom onset to hospitalization

was calculated and analyzed. Second, speciﬁcally looking

at California, the infected for each age group as compared to

the sum infected people for all ages was determined for each

day and examined using graphical analysis; future percent-

ages were determined using polynomial regression. Lastly,

the most recurring symptoms for each group were determined

from a patient dataset containing the patients’ age and current

symptoms. Using this three-pronged approach, it is now pos-

sible to predict certain factors of a patient depending on age,

a ﬁnding that will be discussed in greater detail in the study.

These predictions will undoubtedly help many that are

misinformed, and will help the general public make better-

informed decisions regarding COVID-19. These predictions

will form the basis for whether there is a causal relationship

of age on symptom progression period, death rate, and spe-

ciﬁc symptoms of COVID-19. By learning about speciﬁc

symptoms for each age group, more individuals will be able

to determine whether they have the disease, and stop the dis-

ease from spreading further. COVID-19 has already taken

millions of lives and infected many others, which is why this

research is vital to contain the spread of the virus.

Methods

K-Means Clustering

An unsupervised machine learning algorithm, k-means clus-

tering aims to ﬁnd clusters within an n-dimensional space

containing points using distance as a heuristic

. The algo-

rithm attempts to minimize the squared mean distance of the

points from each centroid. The number of centroids are cho-

sen beforehand as a hyperparameter, and is largely depen-

dent on the type of the data; centroids form the center of each

cluster, and were used to ﬁnd the average symptom progres-

sion period for the study. The study’s data was plotted on a

two-dimensional space against age and number of days from

symptom onset to hospitalization. Outliers were removed be-

forehand to remove inaccuracy with our clusters, and an el-

bow curve was plotted to determine the number of clusters

and centroids necessary

K-means clustering helped show the optimal age

ranges using the data provided. Advantages of k-means clus-

338 | ASDRP Summer 2020 Effect of Age on COVID-19 Symptoms

tering are its computational speed in determining clusters and

its easy implementation. However, it was difﬁcult to deter-

mine optimal clusters as the clusters changed depending on

where the initial centroids were placed

. To ﬁx this, many

clustering algorithms were run with different initial centroids,

and the age ranges for each cluster were determined from the

aggregate clusters. Additionally, it was difﬁcult to determine

the number of clusters, even with an elbow curve, as the op-

timal score-cluster ratio changes for every dataset.

For the study, the sklearn and matplotlib libraries from

Python were used for running the algorithm and plotting the

results. The sklearn libraries helped greatly with the sim-

pliﬁcation and overall effectiveness of the algorithm, which

allowed the study to produce accurate results. Additionally,

the matplotlib library allowed for the graphing of the elbow

curve and the ﬁnal clusters, which helped with the visualiza-

tion of the ﬁnal result of the algorithm.

Polynomial Regression

A supervised machine learning algorithm, polynomial regres-

sion is largely used to predict trends in the data from data that

can be easily visualized on scatter plots. To run the model,

a n

degree polynomial is ﬁtted to the scatter plot that at-

tempts to reduce the error between points and their predicted

points on the polynomial line. To reﬁne it, this error is cal-

culated as the sum of the squared distances between the real

point and the predicted point and minimized over a series of

iterations. Although a common and simple-to-use algorithm,

polynomial regression does have the risk of overﬁtting, which

is where the model generalizes well to training data, but not

to testing data. Nevertheless, polynomial regression provided

an efﬁcient way to predict from time series data, and multiple

models were created to reduce the risk of overﬁtting.

The process of implementing polynomial regression

was done using the matplotlib and sklearn modules. Using

these modules, we were able to use the infection percent-

age dataset that was derived from the California datasets and

graph the existing and predicted lines for each age group pro-

vided in the dataset.

First, it was necessary to change the unit in which the

dates would be measured. Individual dates would not work

due to their format (MM-DD-YYYY), since it is not possible

to just take a date and perform mathematical operations on

them. This was a signiﬁcant drawback encountered in the

experiment and it was changed such that each row is ‘Day

X’ after the date 04-02-2020, the very ﬁrst date, so that in

reality, each number is also the same as its index and go up

one by one, removing any conﬂicts in which our algorithm

would not be able to provide a proper value.

Afterward, we then imported the sklearn module,

speciﬁcally the linear regression and polynomial regression

segments, along with the matplotlib module for us to make

scatter plots. A function was then created which would take

the age ranges, graph them, and then plot the polynomial re-

gression line on top of it. In this case, the regression model

used a degree of four. This function allowed us to graph all

of our data along with their respective polynomial regression

lines and also predicted the percentages for the next “X” days

as inputted. After running the function with all of the age

groups, a new data frame was created in a similar format to

the infection percentage dataset except the predicted values

created by the polynomial regression model were appended

to the existing data frame.

Using a for loop, we then graphed the original dataset

along with the prediction dataset together with different col-

ors so that we can see the original values and the predictions

that were given by polynomial regression.

Data Mining

With the datasets used, the concept of data mining was im-

plemented into our project. Both datasets were displayed in

columnar format, which allowed for an easier manipulation

of the data into a Pandas data frame. The original datasets

had many columns that were not of use for this project, for

example, the location of the case and the web link to the case

report. On top of this there were many NaNs and missing

data. In order to analyze the data at the highest possible level,

to compare just age and symptoms, the concept of data min-

ing was used to create a new dataset based off of the origi-

nal one with just the data that was needed. Data mining is

the discovery of structures and patterns in large and complex

data sets. There are two aspects to data mining: model build-

ing and pattern detection

. For the purpose of this project,

both aspects of data mining were incorporated. Model build-

ing was used for the k-means clustering method, and pattern

detection was used for the polynomial regression.

There were a variety of data mining Python functions

used to create the new dataset. First, all the missing data and

values were dropped from the dataset using row-wise impu-

tation through Pandas

. Afterward, all the columns besides

the age of the patients and the list of symptoms were dropped

as well. Lastly, a function sorted the data frame by age and

stored the results in a new dataset.

The data mining that was applied to the original dataset

helped greatly with the machine learning algorithms’ accu-

racies. Due to this process, the data was converted into an

easier format for model building and pattern detection.

Datasets Extracted

Due to the time and money constraints of this paper,

datasets were compiled by an external party to ease the

computational power required to make such datasets.

There were two main datasets that were extracted: one

to analyze the death rate percentage for each age group

and one to analyze the symptom progression period

and recurrent symptoms in each age group. The ﬁrst

dataset can be found here: https://data.ca.

gov/dataset/covid-19-cases/resource/

339d1c4d-77ab-44a2-9b40-745e64e335f2.

Additionally, the second dataset can be found here:

https://www.kaggle.com/sudalairajkumar/

novel-corona-virus-2019-dataset?select=

COVID19_line_list_data.csv. Both were displayed

in tabular format, which allowed for easy manipulation of

Effect of Age on COVID-19 Symptoms ASDRP Summer 2020 | 339

the data into a Pandas data frame and the running of k-means

clustering on certain columns.

Results

Symptom Progression Period

Using k-means clustering, the symptom progression period

was determined from a patient dataset with ages ranging from

18-80 years old. Using an elbow curve as shown in Figure 1,

the optimal number of clusters was determined to be six clus-

ters, against the dataset provided. The symptom progression

period was calculated by taking the patient’s symptom onset

date and ﬁnding the number of days to hospitalization. Al-

though not an exact measurement of symptom progression,

generally, worse symptoms of COVID-19 necessitate hospi-

talization, while milder symptoms can be handled at home.

Fig. 1. Elbow curve used to determine the optimal number of clusters needed to

cluster age based on symptom progression period.

The symptom onset period varied from 1-35 days

throughout all of the age ranges. Using k-means clustering,

four signiﬁcant clusters were extracted from the data, as the

other two clustered only a few data points together. The ﬁrst

cluster had a mean symptom progression period of 9.5 days

for the age range of 18-33 years old. The second cluster had

a mean symptom progression period of 10.5 days for the age

range of 34-49 years old. The third cluster had a mean symp-

tom progression of 11 days for the age range of 50-64 years

old. Lastly, the fourth cluster had a mean symptom progres-

sion period of 14.4 days for the age range of 65-80 years old.

From plotting a trendline through this data and analyzing the

clusters, it was determined that there was a positive correla-

tion between age and symptom progression period. A graph

of the clusters can be seen in Figure 2.

Most Recurring Symptoms

Using the Kaggle dataset, symptoms were extracted for each

of the patients and compiled to create a comprehensive list

of symptoms for each age group. Given the availability of

data, it was found optimal to bucket the age ranges into three

groups: 18-49 years old, 50-65 years old, and 65+ years old.

For the 18-49 year old age group, the symptoms were gen-

erally commonplace, including fever, sore throat, malaise,

and runny nose. Fever was the highest for this age group,

Fig. 2. K-means clustering to determine the clusters based on symptom progres-

sion period and age range.

Fig. 3. The top most recurring symptoms for the 65+ age group from the Kaggle

dataset.

which has already been proven as the most common symp-

tom

. Therefore, the data provided for these symptoms was

largely insigniﬁcant and did not provide any breakthroughs.

Additionally, sore throat, malaise, and runny nose have all

also been proven as common symptoms of COVID-19

. For

the 50-65 year old age group, the predicament is similar, as

many of the most common symptoms, such as fever, cough,

malaise, and headache, have already been proven to be com-

mon symptoms of COVID-19.

However, for the 65+ years old age group, joint pain,

shortness of breath, and vomiting become common symp-

toms for the age group, which contrasts to that of the ﬁrst

two age groups. Joint pain is common in older people; there-

fore, that can be the cause of the reporting of that symptom

while in the hospital

. Additionally, shortness of breath is

commonplace for older people, while vomiting is common

for older patients suffering from COVID-19

. A ﬁgure of the

most recurring symptoms for the 65+ years old age group can

be seen in Figure 3.

Percent Infected by Age Range

Using polynomial regression, the percent infected per age

range was determined from a California dataset. The dataset

was split into two axes, four different age ranges, and the

number of days after April 2, 2020. Using polynomial re-

gression, we were able to predict the percent change that each

age group will be infected. The age ranges were from 0-17,

18-49, 50-64, and 65+. The ranges were color-coded and

graphed on top of each other in Figure 4.

340 | ASDRP Summer 2020 Effect of Age on COVID-19 Symptoms

Fig. 4. This graph implements polynomial regression that predicts the percent

infected by age range for the next ﬁfty days.

April 2nd to present day, it seemed that the age ranges’s

percentages were staying the same. For the age range 0-17,

the number of cases in California were under one percent.

For the age ranges 18-49, the number of cases were between

65 percent to 67 percent and has been slowly decreasing. For

the 50-64 range, the number of cases has stayed at a steady

20 percent of total cases in California. Finally, for the 65+

age range, the percent of cases increased from 11 percent to

13 percent. The polynomial regression also modeled what

the future could hold for COVID-19 in California. The model

predicts 175 days after April 2nd, which would be September

24th. The 0-17 age range seems to increase up to 4 percent of

total cases. 18-45 age range seems to decrease to 51 percent

of total cases. The 50-64 age range seems to make a slight

increase to the 21 percent mark. Finally the 65+ age range

increases up to 23 percent of total cases in California.

Discussion

Symptom Progression Period

Using k-means clustering, it was determined that a positive

correlation existed between age and symptom progression

period. Although symptom progression period increasing

with age seems to be against the common consensus, es-

pecially with the majority of COVID-19 patients being el-

derly, viewing this issue from a biological perspective proves

a causal relationship between the two factors. As the human

body ages, it encounters more and more diseases, which al-

lows the immune system to create antibodies against a wealth

of diseases. Therefore, many common symptoms that oc-

cur, such as dry cough and fever, would be abated due to the

strength of the immune system

. Due to this, hospitalization

would occur at a later date, as the symptoms are weaker and

progress slower.

However, although this may seem to be the case, stud-

ies show that although immune systems vary heavily between

individuals, they stay relatively the same for a single individ-

ual. In this case, a single variation in age would not be the

cause of a weaker or stronger immune system

. This would

suggest that the study may have had an inherent ﬂaw, pos-

sibly caused by a smaller sample size than the one needed

to provide a non-biased conclusion. Due to the heavy bio-

logical backing associated with the latter study, it is safe to

assume that the former would have less backing than the lat-

ter. However, a biological study must be done to further test

age’s effect on symptom progression period.

Most Recurring Symptoms

Across all age groups, the top ﬁve symptoms consisted of

fever and joint pain. As previously discussed, these have

been proven to be common symptoms of COVID-19, and

can likely be disregarded as a signiﬁcant outcome. After an-

alyzing the entire list of symptoms provided by the dataset,

joint pain seems to be the only symptom that does not recur

for other age groups. Due to the likelihood of joint pain in-

creasing with age, this also does not appear to be a signiﬁcant

ﬁnding. Reasons for these ﬁndings vary, but it could be due to

the small sample size of the dataset, similar to the symptom

progression period dataset. Obscure and infrequent symp-

toms would not be picked up in this dataset, as only a few

thousands of patients were analyzed. As a result, this data

does not provide a comprehensive list of symptoms, and can-

not be accurately relied upon for providing symptom data.

Lastly, due to region-speciﬁc symptoms, it is impossible to

accurately determine the most recurring symptoms globally.

This dataset primarily consisted of data from Southeast Asia

and Europe, as the data was taken in January and February.

Therefore, it does not account for the symptoms elsewhere,

which provides a skewed ﬁnding.

Throughout each age group, study participants faced

several varying symptoms on a case by case basis. With each

age range, the number of people surveyed also differed, im-

pacting a few of the statistics consequently. In the 0-17 age

range 12 individuals were surveyed, in the 18-49 age range

165 individuals were surveyed, in the 50-65 age range 130

individuals were surveyed, and in the 65+ age range 355 in-

dividuals were surveyed. Consequently, it is visible that the

symptoms analysis for the 65+ age range used data from the

most study participants. This may have been due to the higher

risk faced by elderly in regards to COVID-19. Due to the

larger amount of data, it can also be reasonably inferred that

the conclusions drawn from the 65+ age range yield a higher

accuracy than those from the other age ranges. On the other

hand the 0-17 age range only contained data from 12 partic-

ipants so is likely to have the least accurate results out of all

the present age ranges analyzed.

Along with impacting the degree of accuracy of the re-

sults, the amount of data available for each age range also

impacts the comparison between the various age ranges. In

the 0-17 age range 5 out of 12 individuals experienced fever

symptoms, in the 18-49 age range 5 out of 165 individuals

experienced fever symptoms, in the 50-65 age range 56 out

of 130 individuals experienced fever symptoms, and in the

65+ age range 142 out of 355 individuals experienced fever

symptoms. In this scenario it is difﬁcult to compare the num-

bers alone. Age range 0-17 had 5 cases of the fever reported

and age range 65+ had 142 cases reported. In comparison to

the ﬁndings in the 0-17 age range, the 65+ age range seems to

have a higher likelihood of facing fever as a symptom. How-

Effect of Age on COVID-19 Symptoms ASDRP Summer 2020 | 341

ever, once converted to percentages it is found that only 40%

of the occurrences reported fever for the 65+ age range while

42% reported fever for the 0-17 age range. Consequently, al-

though the numbers are lower, the results show that both age

ranges have a similar likelihood of reporting fever as a symp-

tom. This principle applies to all of the age ranges and all of

the symptoms as they are compared against each other.

Percent Infected by Age Range

Using polynomial regression, we were able to draw nu-

merous conclusions about the percentage of infected people

throughout different age groups. Since April 2nd, we can see

that most of the cases were in the age range of 18-49. While

at ﬁrst, this may seem like an extensive range, our machine

learning model for how the percent of infected by age range

shows that this number will decrease from 65% to only 51%

by September 24th (175 days after April 2nd). Furthermore,

the infected rates among people in the age range from 0-17

will shoot up from less than 1% to 4% of total cases. The age

range of 65+ almost doubles from around 12% to 23%. Any

other age ranges did not experience any signiﬁcant changes

in their infected percentages.

We can see that closer to the start of the outbreak, it

was generally older people getting affected by the virus, but

as time progresses, we can see that infected rates for younger

age groups are slowly increasing and accounting for a more

substantial majority of total cases. While the age group of 18-

49 is an extensive range as opposed to other ranges such as

50-64, spanning for only 14 years, it has overall decreased

from the start of the pandemic, whereas the youngest age

range has been increasing exponentially. This rate of increase

in the percentage of infected is more evidence that young

adults are getting infected more often and have a higher plau-

sibility of actually getting infected. These changes in per-

centages between different age groups are notable because it

allows for new possibilities and potential ﬁndings in subse-

quent research, which will overall help when developing a

cure for the disease.

Conclusion

The aim of this study was to determine age’s overall relation-

ship with COVID-19 symptoms and infection rate. After con-

ducting the research, it is determined that a causal relation-

ship could be found between age and COVID-19 symptoms.

Three major ﬁndings were extracted from the data: older pa-

tients are likely to experience slower symptom progression

than younger patients, the young adult age range has the high-

est likelihood of getting infected with COVID-19, and symp-

toms generally remain constant across all age groups. Us-

ing these results, it is now possible to determine when life-

threatening symptoms will occur for certain age groups, so

that hospitals can determine the most efﬁcient way to treat the

patients. Additionally, knowing what age ranges are affected

the most will provide future researchers more data to work

with when trying to develop a cure for the disease. More

research must be done to further prove these causal relation-

ships, but from preliminary analysis, a relationship can be

determined.

AUTHOR INFORMATION

Aditya Mittal contributed towards the use of k-means clustering in the symp-

tom progression period section and the use of data science libraries in the most

recurring symptoms section. Henry Zhao contributed towards the use of polyno-

mial regression in the percent infected by age range section. Aadhi Kumaraswamy

contributed data mining, extraction, and manipulation of the California and Kaggle

datasets. Megan Jacob contributed towards the ﬁnding of datasets and the usage

of datasets in machine learning algorithms. Rohan Ayyagari contributed towards

the ﬁnding of datasets and the creation of the structure of the research paper.

ACKNOWLEDGEMENTS

Thanks to Keshav Rao for guiding the team through the research paper

and teaching the various components of how to write it. Thanks Aspiring Scholars

Directed Research Program for providing the resources for the team to complete

the study.

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342 | ASDRP Summer 2020 Effect of Age on COVID-19 Symptoms