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How Misuse of Statistics Can Spread Misinformation:
A Study of Misrepresentation of COVID-19 Data
Shailesh Bharati 1*, Rahul Batra 2
1*, 2 Symbiosis School of Economics,
Symbiosis International (Deemed University), Pune, India
*E-mail: shailesh.bharati@sse.ac.in
Abstract
This paper investigates various ways in which a pandemic such as the novel coronavirus, could be
predicted using different mathematical models. It also studies the various ways in which these
models could be depicted using various visualization techniques. This paper aims to present
various statistical techniques suggested by the Centres for Disease Control and Prevention in order
to represent the epidemiological data. The main focus of this paper is to analyse how
epidemiological data or contagious diseases are theorized using any available information and later
may be presented wrongly by not following the guidelines, leading to inaccurate representation
and interpretations of the current scenario of the pandemic; with a special reference to the Indian
Subcontinent.
Keywords
Covid-19, Novel Coronavirus, Python, Mathematical modelling, Statistics, Logarithmic Scale,
Graphs, Epidemiological Ddata, Data Visualisation Theory, Infectious Diseases.
1. Introduction
Many studies since the beginning of twentieth century (Khaleque., 2017) involving mathematical
and statistical modelling of various epidemics such as Ebola, HIV/AIDS, (Zakary., 2016) and other
diseases have helped estimate the probabilities of occurrences, predict the outbreaks across various
geographies, provide short term and long term projection of cases in varying degrees of reliability
and accuracy, and all in all have helped us understand the impact of epidemics on our lives. Policy
makers have utilized these models as an important tool for decision making, where recently we
saw many countries setting up lockdown in the economy as a whole or parts. Some researchers
have strongly argued about the impact of social media in our lives. They have also depicted how
important media can be and benefit overcome the discrepancies in passing on the information
correctly to the public and help in avoiding or at least controlling such severe outbreaks (Zakary.,
2016).
The data of COVID-19 outbreak is studied by several researchers and data scientists by applying
different mathematical models (Rao et al., 2020; Chang et al. 2020). Many studies have been
covered on this pandemic using meaningful results after applying various mathematical models.
Majority of the pandemics demonstrate an exponential curve at the earlier stages of transmission
and eventually flatten out (Junling et al., 2014). To study the predictions of the spread of infections
due to the Novel Coronavirus, the SIR model is the best suited mathematical model. This model
works on an assumption that, an individual once recovered from this infection, is unlikely to
become susceptible again to the same infection (Kermack & McKendrick, 1991).
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The SIR is a compartment model (Herbert, 2000) and is used to include information of individuals
who may be susceptible, or infectious or recovered and deceased. Generally, an individual is
counted into one of the three potential categories viz., susceptible or infected or re-covered which
is denoted by their initials S, I, and R respectively. Here susceptible individual is the one who is
at the risk of getting infected. The infected individuals are the susceptible individuals who get
infected by the corona virus although they may be asymptomatic or symptomatic. The recovered
are those individuals who have recovered, or quarantined, or died from the disease. So far, in most
of the studies taken in case of India, have shown quite a significant predictive ability with respect
to the growth of infections due to Covid-19 in India.
Recently, a survey revealed that ~67% of Indians trust the media for nCov-19 related news
(Gulankar, n.d.). These numbers for 2019 were on average at ~44-47% with almost no changes for
over two years (Grimm et al., 2016). This represents a massive change of about ~22% pts. This
presents a great opportunity to mislead the general public about the ongoing pandemic, which will
be divulged into later, first we shall understand how pandemics are theorized, using models;
namely: SIR, SIRS, SIER, SIERS these models are explained in terms of increasing complexity
which implies that SIERS model captures the current pandemic to the highest degree.
2. Review of Literature
2.1. Mathematical Modelling Methods
Many modifications have been made to the SIR and the SIS model in order to include and study
other relevant variables in order to improve the model and build predictions (Anastassopoulou et
al., 2020; Corman et al., 2020; Gamero et al., 2020; Huang et al., 2020; Hui et al., 2020; Rothe et
al., 2020; Singh, 2020). Generally, in the SIR model, the infections from viruses which are
contracted only once by individuals are accounted. Hence, susceptible individual who gets infected
by the virus is subsequently removed, from the dynamics. A person once removed cannot take part
again. While, in the SIS modelling, a person can be included under the susceptible category in case
he gets infected again. (Tiwari, 2020) The SIQR model which stands for Susceptible, Infected,
Quarantine, and Recovered is a modified version of the SIR model. This model categorizes the
infected individuals into two groups, viz., those who get quarantined and others who are
asymptomatic. Hence, basically in the mathematical form of the SIQR model, an extra variable “Q
stands for Quarantine” is added which represent the infected individuals who show symptoms and
get quarantined. Apart from SIQR, the SIRS model used the exact same equation except assuming
that the immunity wanes over time (Common Cold). Another model named the SIER model adds
an extra parameter ‘E’. The parameter ‘E’ represents the exposed and represents the time
difference between exposed to the disease and until symptoms show up (Infected). Another model,
the SIERS model assumes waning away of immunity over time with a latent infectious disease.
Khaleque & Sen quantified the infection probability of the Ebola outbreak which happened in
Liberia, Guinea and Sierra Leone, (West African countries) between 2014 and 2016, using the SIR
model on the Euclidean network. They concluded that the SIR model fitted well to the data. The
authors were successfully able to estimate the time / period at which the infections would peak.
Zakary et al., in their first approach, used the SIR model in order to analyse the benefits of
awareness programs implemented by the government, in order to make the public aware about the
dangers of the disease. They concluded that these awareness programs focused to the specified
region, along with the aim to control the outbreak, were sensitive to enough contacts proportional
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to the high risk group. In their second approach the authors considered the inter-domain
interventions of travel restrictions of the susceptible persons across high risk to low risk domains.
After adding the control on travel ban of susceptible people between high risk domains and
infective of high risk domains. In their conclusion, they also suggested that the social media could
certainly play an important role in spreading awareness and educating the public and help in
HIV/AIDS prevention.
Malavikaa et al., was able to predict the short term scenario in case of India and the States with
high incidence, with great accuracy, using logistic modelling. Moreover, the SIR model was used
by the authors to forecast the active cases and the period at which the curve would reach the peak
and eventually flatten out. The authors suggested this model to be used for planning and preparing
the healthcare system. The Time Interrupted Regression modelling was used for analyzing
interventions of lockdown and their impact on the spread of active cases. The study did not find
any evidence which would prove the positive correlation between the impact of lockdown and the
reduction in new cases by breaking the chain of infection among the public.
2.2. Statistics and Graphs
CDC “Centres for Disease Control and Prevention” mentions best practices / guidelines for
describing the Epidemiologic data, called as descriptive epidemiology. CDC gives very much
importance to the interpretation of the data and has set guidelines for the graphical representation
of the data. Some relevant ones are mentioned below. Such as the aspect ratio of graphs,
appropriate scaling, representing dependent and independent variable, usage of types of lines,
comparing two lines on a graph and also some relevant points to adhere to the principles of
mathematics while plotting data and representation of equal units of the transformed data such as
logarithmic, ranked and normalized with equal distances on the axis.
The CDC manual also mentions the guidelines for plotting propagated epidemic curves. COVID–
19 falling in to the category of a propagated epidemic, it seems reasonable to follow the guidelines
set by CDC so as to avoid wrong interpretations. Propagated epidemics show propagated patters
and show four characteristics by the CDC (Fontaine, 2018).
“Characteristics of Propagated Epidemic Curves
1. They encompass multiple generation periods for the agent.
2. They begin with a single or limited number of cases and increase with a gradually
increasing upslope.
3. Often, a periodicity equivalent to the generation period for the agent might be obvious
during the initial stages of the outbreak.
4. After the outbreak peaks, the exhaustion of susceptible hosts usually results in a rapid
downslope.”
Guidelines for representing disease rates against time.
The CDC manual has also defined the way in which to illustrate the disease rates against time.
Temporal disease rates are plotted against time taken on the x axis while the magnitude of rate of
the epidemic is represented on the y axis. Usually if the rates of a disease vary more in their order
of magnitude, a logarithmic scale is recommended especially for epidemiologic purposes. The
CDC also suggests to the usage of logarithmic scale when researchers want to compare two or
more population groups.
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The CDC also specifies the guidelines to measure disease or any other health conditions on a
continuous scale and no by counting directly. Although, an individuals’ measure may vary over
and above a specified cut off value. Hence, the CDC quotes, “To calculate incidence, special care
therefore is needed to avoid counting the same person every time a fluctuation occurs above or
below the cut-off point. A more precise approach involves computing the average and dispersion
of the individual measurements. These can then be compared among groups, against expected
values, or against target values. The averages and dispersions can be displayed in a table or
visualized in a box-and-whisker plot that indicates the median, mean, interquartile range, and
outliers”
Ehrenberg, A.S.C. in his work “Rudiments of Numeracy” in 1977, has summarized, “Many tables
of data are badly presented. It is as if their producers either did not know what the data were saying
or were not letting on.” He has also talked about the difference in graphs and tables in his sixth
rule studied in the same work. He claims that people usually find it easier or comfortable to read
the graphs instead of tables, which is only partially true. Although, graphs fall short in representing
the quantitative aspects seen in the epidemiological data, but they do communicate or make some
qualitative aspects more prominent for the viewer. Qualitative aspects such as a curve rather than
a straight line, if some phenomena have increased or is smaller than a larger value and so on; are
represented distinguishably using the graphs. Such a claim shouldn’t misled us, into thinking that
one can only draw out or retain very trivial information from using a graph. In his work, he has
quoted that, “Most graphs do not show simple patterns or dominant numbers which can readily be
grasped. Success in graphics seems to be judged in producer rather than consumer terms: by how
much information one can get on to a graph (or how easily), rather than by how much any reader
can get off again (or how easily).”
The literature review studied, clearly points towards the fact that although, researchers have been
using various mathematical models since earlier days, in order to study the predictions of
epidemiological data, there are guidelines on how the results of those predictions should be
represented using graphs and tables for right or correct interpretations by the public. Following the
same lines, this paper attempts to analyse the way in which sources depict the data in various forms
and what wrong interpretations are being made out of those depictions.
3. Methodology
Due to unavailability of Primary Data, this Investigative Analysis uses data compiled by various
sources such as ICMR (Indian Council of Medical Research, New Delhi), MoHFW (Ministry of
Health and Family Welfare, Government of India), and various State welfare sources. We consulted
data for the number of cases detected in the three states Maharashtra, Kerala and Karnataka, because
the mathematical many researchers have performed mathematical modelling showing the
predictions of the outbreak in India; for these three states, using Logistic Growth and SIR Models'.
Hence, we have use the values imputed in these papers for actualising the models. The data
available for India is from 30th January 2020 to 28th August 2020 (197 days) and the data available
for the States of Maharashtra, Kerala and Karnataka is from 14th March 2020 to 28th August 2020
(168 days). The summary of the statistics is presented in the appendix. We have studied the
available data for total number of cases as a function of time (t) along with other variables such as
Total Confirmed Cases, Daily Confirmed, Daily Recovered, Daily Deceased, Total Recovered and
Total Deceased.
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We would like to express our gratitude to the Covid-19 India Org Data Operations Group for
providing data using research friendly APIs, the Organization is appropriately cited as well. The
data was then treated using Python 3.x using appropriate SciPy Packages keeping in line the
objectives of the research, similarly all visualizations found in this paper are also done using the
same. All visualisations are strictly generated by Matplotlib, we have also tried our best to maintain
uniformity in order to compare graphs wherever we felt necessary.
4. Theoretical Framework and Analysis
It is important to understand that all of these models focus only on the susceptible part of the
population or alternatively assume that the entire population is susceptible to the virus / disease.
4.1. The SIR Model
The SIR “Susceptible Infected Recovered” Model was presented by W. 0. Kermack and A. G.
McKendrick (Kermack & McKendrick, 1933, p. 110) and is mathematically expressed as follows:
‘s’ = number of individuals who are susceptible
‘i’ = number of individuals who are infected
‘r’ = number individuals who are removed (i.e., including re-covered and dead)
These can be expressed as Ordinary Differential Equations as follows:
𝑑𝑆
/
𝑑𝑡
=−
𝛽𝑆𝐼
/
𝑁
𝑑𝐼
𝑑𝑇 ( = − 𝛽𝑆𝐼
𝑁(– (𝛾𝐼
𝑑𝑅
𝑑𝑇 ( = (𝛾𝐼
Where;
𝑠( = !
"
,
𝑖( = #
"
,
𝑟( = $
"
Substituting these in the Ordinary Differential Equations we get
𝑑𝑆
𝑑𝑇 = −𝛽𝑠𝑖
𝑑𝐼
𝑑𝑇 ( = −𝛽𝑠𝑖(– (𝛾𝑖
𝑑𝑅
𝑑𝑇 ( = (𝛾𝑖
Hence s + i + r = 1 is constant, we use this equation to check for faults in the simulations
●
𝛽𝑆𝐼
/
𝑁
is the rate at which the susceptible population encounters the infected population.
𝛽
is
a model parameter with units of 1/units per day
●
𝛾
i is the rate the infected population recovers (this model assumes resistance to further
infection). I is the size of the infected population
●
𝑅
0=
𝛽
/
𝛾
(Basic Reproduction Rate)
For reference, we ran the parameters for Influenza as the characteristics of the disease fit the
characteristics of the SIR Model, we use the parameters provided in (Mahaffy, J. M., 2018)
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Graph 1: SIR model of SARS-nCOV-2019
Source: Covid-19 India Org Data Operations Group
Although, SARS-nCOV-2019 does not fit all assumptions of the SIR model (latent period of
infection) running the same simulations (Mackolil & Mahanthesh, 2020)
Graph 2: SIR model of Influenza
Source: Covid-19 India Org Data Operations Group
It seems to be extremely clear, the difference between the two graphs. The difference in the above
two graphs 1 and 2, i.e., SIR Models of SARS-nCOV-2019 and Influenza is stark. When both
diseases are simulated for the same period of time influenza does not even infect the entire
susceptible population however SARS-nCOV-2019 infects the entire possible population. A
massive difference can be seen in the R0 1.99 and 2.73 respectively.
4.2. The SIRS Model
This model uses the exact same equation except assumes that immunity wanes over time (Common
Cold).
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4.3. The SIER Model
The SIER model adds an extra parameter ‘e’. The parameter ‘e’ represents exposed and represents
the time difference between exposed to the disease and until symptoms show up (Infected), for
SARS-nCOV-2019 it stands between 7-28 days (Lauer SA et. al, 2020)
The Ordinary Differential Equations then change to:
𝑑𝑆
𝑑𝑇 = −𝛽𝑠𝑖
𝑑𝑒
𝑑𝑇 ( = −𝛽𝑠𝑖 − 𝛼𝑒
𝑑𝑖
𝑑𝑇 =αe(– (γi
𝑑𝑟
𝑑𝑇 ( = (𝛾𝑖
Re-running these simulations for imputed values for the State of Kerala (Mackolil & Mahanthesh,
2020)
Graph 3: SIER model for the State of Kerala
Source: Covid-19 India Org Data Operations Group
4.4. The SIERS Model
The SIERS model assumes waning away of immunity over time with a latent infectious disease.
In the next section, we introduce these models to give a reference so as to understand the graphs
generated using actual pandemic data.
4.5. Logarithmic Scales
Before we get into the specifics of what logarithmic scale means we would first like to pose a
question using graphs.
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Graph 4: Types of Cancer Cases (linear scale)
Source: (Siegel et al., 2020)
In order to show the difference in type of diseases and how they are represented using different
scales, in the graph above, various types of cancers are plotted across time period using the linear
scale. Cancer and novel corona virus, both the diseases are extremely different in nature; cancer is
not communicable in the same means as SARS-nCOV-2019. The latter represents a disease which
on average spreads to 2 - 3 people (Lauer et al., 2020) and cannot be represented using the similar
graphs. The CDC recommends ‘semi-log’ plots for the same (Fontaine, 2018)
(Smyth, n.d.)
A log scale differs from a linear in terms of data represented in a unit of the graph. To make it
clear, we present the outbreak of the disease in the State of Maharashtra, Kerala and Karnataka, in
two different ways. The graphs on the left hand side represent the data of confirmed cases in the
three states using linear scale and the ones on the right hand side represent the same data using the
logarithmic scale.
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Graph 5: Confirmed Cases in Maharashtra, Kerala and Karnataka (Linear and Log Scale)
Source: Covid-19 India Org Data Operations Group
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Same data, two different perspectives? The first graph on the left side for each states is a ‘linear’
graph and the second one on the right hand side is a semi-log graph, the differentiating factor being
how the y-scale is depicted, the y-scale in the second graph multiplies every unit by a factor of 10
and so forth however the linear graph adds up with 1,00,000 cases per unit (Maharashtra), 10,000
cases per unit (Kerala) and 50,000 cases per unit (Karnataka). The reason we use a semi-log plot
is because of the nature of these diseases, these diseases do not spread in a linear fashion and are
rather exponential in nature, therefore the graphs also must take this into account when visualizing.
CDC recommends the use of semi-log plot, however neither of these graphs seem to be incorrect.
A reason highlighted by the London School of Economics is the fact that the public do not
understand ‘Semi Log’ plots however this also leads to inaccurate representation of the outbreak
(London School of Economics, 2020).
4.6. Not all data is created equally
Every state did not follow the same timeline i.e. First incidents of the disease were not on the same
day for every state of the country. This creates an opportunity for the states who had breakouts at
later stages could prepare for it beforehand. This however, presents another opportunity for
incorrect visualisation of the breakout in different states.
Graph 6: Confirmed cases in Telangana and Arunachal Pradesh plotted against Dates
Source: Covid-19 India Org Data Operations Group
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Graph 7: Confirmed cases in Telangana and Arunachal Pradesh plotted against Days since Po
Source: Covid-19 India Org Data Operations Group
The two plots, graph 6 and 7, although present the same data, they have minor differences, first,
both of these graphs use different X-axis; the first one uses dates however the second one uses
‘Days since P0’. This hides the fact that Arunachal Pradesh experienced its first case approximately
after 15 days as compared to Telangana, this presents an opportunity to better prepare itself for the
surge and thereby handle it much better, the second graph completely shadows this fact and shows
an inaccurate view of the states, this leads to formation of incorrect views and opinions
4.7. Testing is a secret well kept
It is also to be noted that as the pandemic has stretched over for months. The government's testing
efforts have also increased exponentially. This could also hide the fact that the outbreak initially
could be bigger than recorded, however due to lack of testing could not be detected in its early
stages, this also leads to the infection spreading in the initial stages much more than it was recorded
causing the current ‘exponential’ growth.
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Graph 8: Covid – 19 Testing in India
Source: Covid-19 India Org Data Operations Group
5. Discussion
The mathematical models help in quantifying the probability of infection, while the researcher
hopes that the proposed model matches the real data. With respect to that, this epidemic measured
using different scales either on X-axis or Y-axis may also change the way in which the data is
portrayed. There are two important explanations that can be given to support the use of logarithmic
scales while charting or graphing the data. The first explanation that can be given in order to use
the logarithmic scale is that it helps to normalize the skewness in the distribution which may have
turned out due to few large values in the data. The second point we can raise over here, is that the
logarithmic scale helps when one has to represent a percentage change or factors which show
multiplicative trends.
In case of usage of graphs for comparing a single phenomenon across two states using same time
line may result in wrong depiction and thus should be avoided. In such cases, proper use of variable
helps generate accurate output and thus correct interpretation. Through this study, we have shown
how the same data could be presented in ways which are unnoticeable to the general public and
could therefore deceive them of the complete picture.
Acknowledgement
The authors believe in the Open Source Community, all code for the research is publicly available
at github.com/rahulbatra065/covid19-paper. Please feel free to mail us for any queries regarding
the same
Conflict of Interest: There is no conflict of interest among the authors
Funding: Self-funded
Ethical approval: Not applicable
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16
Appendix
Data Sheets
Table 1: Covid-19 related indicators for India
Daily
Confirmed
Total
Confirmed
Daily
Recovered
Total
Recovered
Daily
Deceased
Total
Deceased
Total
Observations
(Count)
197
197
197
197
197
197
Mean
(Average)
12485.41
378625.51
8886.44
236708.47
244.44
9181.57
Standard
Deviation
18176.75
607071.56
14381.19
410026.07
315.21
13161.70
Minimum
Value
Observed
0
1
0
0
0
0
25th
Percentile
27
198
2
20
1
4
50th
Percentile
3344
56351
1295
16776
103
1889
75th
Percentile
18205
491193
12064
285672
414
15309
Maximum
Value
Observed
67066
2459626
57759
1750629
2004
48156
Source: Covid-19 India Org Data Operations Group
Table 2: State-wise Covid-19 related indicators (Confirmed Cases)
Maharashtra
Kerala
Karnataka
Total Observations (Count)
168
168
168
Mean (Average)
4452.35
412.52
1897.33
Standard Deviation
4350.37
637.24
2739.65
Minimum Value Observed
3
0
0
25th Percentile
552
10.75
17
50th Percentile
2762.5
80.5
214.5
75th Percentile
8016
642.75
3660
Maximum Value Observed
14888
2543
9386
Source: Covid-19 India Org Data Operations Group
