Forecasting of COVID-19 Pandemic Using ARIMA and Fb-Prophet

Models: UK Case Study

Victor Chang

, Oghara Efetobore Akpomedaye

, Vitor Jesus

, Qianwen Ariel Xu

Karl Hall

and Meghana Ashok Ganatra

Department of Operations and Information Management, Aston Business School, Aston University, Birmingham, U.K.

Information Systems and AI Research Group, School of Computing and Digital Technologies, Teesside University,

Middlesbrough, U.K.

drazarx3@gmail.com and meghana.ganatra@gmail.com

Keywords: COVID-19 Prediction, ARIMA, PROPHET, Health Analytics.

Abstract: This study aims to provide insights into predicting future cases of COVID-19 infection and rates of virus

transmission in the UK by critically analyzing and visualizing historical COVID-19 data, so that healthcare

providers can prepare ahead of time. In order to achieve this goal, the study invested in the existing studies

and selected ARIMA and Fb-Prophet time series models as the methods to predict confirmed and death cases

in the following year. In a comparison of both models using values of their evaluation metrics, root-mean-

square error, mean absolute error and mean absolute percentage error show that ARIMA performs better than

Fb-Prophet. The study also discusses the reasons for the dramatic spike in mortality and the large drop in

deaths shown in the results, contributing to the literature on health analytics and COVID-19 by validating the

results of related studies.

1 INTRODUCTION

According to WHO data, the United Kingdom, the

United States, Mexico, France, and Brazil are among

the countries most affected by the pandemic. On

January 30, 2020, the first two verified cases of

COVID-19 were discovered in the United Kingdom

(Gaur et al., 2020 ). Since then, COVID-19 has

mutated into numerous variants, including "Alpha,"

which was first found in the UK, "Beta," in South

Africa, "Gamma," in Brazil, and "Delta," in India,

causing two devastating infection waves in the UK

and other areas of the world. Finally, the Omicron

variant made its appearance and is now the most

common. In recent months, the UK has observed a

reduction in infection rates following multiple

vaccination campaigns and early adherence to strict

regulatory laws such as face masking, social

distancing, and prohibitions on religious, cultural,

and educational gatherings. Furthermore, those who

https://orcid.org/0000-0002-8012-5852

https://orcid.org/0000-0002-5884-0446

https://orcid.org/0000-0003-0360-7193

https://orcid.org/0000-0003-2863-3312

were considered to be very sensitive to serious

sickness were advised to stay home in self-isolation

and avoid social interactions. Artificial intelligence

technology has also been deployed to help in COVID-

19 diagnosis, screening, prediction, and drug

repurposing. The UK National Health Service (NHS)

test and trace service help people with symptoms that

are associated with COVID-19 to get tested and then

follow up with those who test positive.

Regardless, the pandemic will persist as a global

health issue for at least a few more years. There are

expectations that additional waves of the pandemic

will occur due to the virus's dynamic nature, which

has previously mutated into other variants. As such, it

is necessary to study how the virus spreads so we can

learn from visualization and prediction of the current

situation and be better prepared for the following

waves and their impact. To this end, AI predictive

modeling can be employed to analyze and forecast

COVID-19 based on past and current data.

Chang, V., Akpomedaye, O., Jesus, V., Xu, Q., Hall, K. and Ganatra, M.

Forecasting of COVID-19 Pandemic Using ARIMA and Fb-Prophet Models: UK Case Study.

DOI: 10.5220/0011990300003485

In Proceedings of the 8th International Conference on Complexity, Future Information Systems and Risk (COMPLEXIS 2023), pages 85-93

ISBN: 978-989-758-644-6; ISSN: 2184-5034

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

AI and Big Data research has been at the forefront

of the COVID-19 battle, especially in the detection

and forecasting of the disease spread. Time series–

based forecasting methods, such as Auto-Regressive

Integrated Moving Average (ARIMA), Fb-Prophet,

Nonlinear Autoregression Neural Network

(NARNN), and Long-Short Term Memory (LSTM)

approaches, have recently been popular in AI

predictive analysis (Wang et al., 2020). Therefore,

this study is focused on time series analysis and

forecasting of the COVID-19 cases in the UK using

ARIMA and Fb-Prophet predictive models. We have

chosen these models as they are most suitable for

time-series forecasting. They capture different

aspects of underlying patterns, which is the main

requirement of COVID-19 data to predict the trend

based on data. This will help improve our

understanding of how COVID-19 spreads and allow

us to plan ahead to mitigate the crisis. Furthermore, a

comparison between these models is conducted to

determine which performs better.

2 LITERATURE REVIEW

Starting in December 2019, every country has been

dealing with COVID-19 outbreaks; as a result,

forecasting future instances using different time

series forecasting models or algorithms based on

historical data is now a focus of recent research.

Gecili et al. (2021) implemented four models on

COVID-19 data from USA and Italy: 1) the Holt

model, which uses dual exponential smoothing; 2) the

ARIMA model; 3) the TBATS model (Trigonometric

Exponential smoothing state space model with Box-

Cox transformation, ARIMA errors, Trend and

Seasonal component), and 4) the Cubic Smoothing

Spline model based on a stochastic state space model

that permits the use of a possible strategy for

predicting the smoothing parameter. The result

showed that ARIMA and Cubic Smoothing Spline

Models performed better than TBATS and Holt-

Winter models, with smaller prediction errors and

narrower prediction intervals. Similar results were

obtained by (Sharma et al., 2021). by applying

ARIMA with a further decomposition of the time

series to test for unit roots and validate against data

from multiple countries. They employed the root-

mean-square error (RMSE) to evaluate the prediction

performance; (Benvenuto et al., 2019) further

justified ARIMA's prediction properties through

descriptive analysis.

Based on the COVID-19 dataset of confirmed

cases in China (Ye and Yang, 2021) proposed an

uncertain time series detection model. The aim of this

model is to analyze the evolution of the confirmed

cases. They compared their model with other classical

methods to deal with time series datasets and found

that the proposed method outperformed other

methods in describing the COVID-19 epidemic by

reducing the estimated variance of the disturbance

term to an acceptable value.

In the work of Rasjid et al. (2021), LSTM and

Savitzky-Golay Smoothing methods were employed

to create prediction models for predicting the death

and infected COVID-19. They applied the prediction

models to the dataset from Indonesia and compared

their performance. The results showed that the LSTM

forecast has a clear upward trend and is consistent

with the Time Series data.

In a COVID-19 dataset gathered from the Kaggle

website for Indonesia (Satrio et al., 2021) investigate

the application of ARIMA and Fb-Prophet models to

forecast the confirmed deaths and recovered cases.

The performance and accuracy of these models'

outputs were compared using R

, Mean Squared Error

(MSE), Mean Absolute Error (MAE), and Mean

Forecast Error (MFE). The results of the error

measurements indicated that the Prophet model

outscored the ARIMA model with minimal

differences between the actual data.

Dwivedi et al. (2021) examined the efficacy and

suitability of the Fb-Prophet and the ARIMA

prediction models to the Indian COVID-19 dataset

with confirmed deaths and recovered cases, which

was collected from the COVID-19 India site.

Comparing these two models showed that ARIMA

surpasses Prophet in terms of its prediction accuracy.

In order to forecast future COVID-19 infections

and mortalities in Bangladesh, (Sarkar et al., 2020)

used ARIMA and machine learning algorithms in

their research and evaluated them by RMSE. The Fb-

Prophet model delivered the best forecasting result

with exceptional precision among other forecasting

models, including Holt's Linear Regression, Support

Vector Regression, and Holt's Winter Additive

Model.

As the COVID-19 pandemic is becoming a

prevalent danger for humankind worldwide (Arora et

al., 2021) investigated the COVID-19 data from a

source at Johns Hopkins University for five months

in 2020 and predicted the trend in weeks using

ARIMA and regression models. The evaluation

results from error measurement by Root Mean

Squared Logarithmic Error (RMSLE) showed that

ARIMA outperformed regression models.

By examining the most recent literature relating to

the prediction of COVID-19 confirmations and

COMPLEXIS 2023 - 8th International Conference on Complexity, Future Information Systems and Risk

mortality, it can be concluded that ARIMA and

Fbprophet are the least geographically constrained

compared to other methods and demonstrate good

predictive power (Battineni et al., 2020). Therefore,

ARIMA and Fbprophet were chosen for this study to

examine the UK context. In addition, error metrics are

also used to evaluate our models by measuring the

difference between predicted and actual data.

3 MATERIALS AND

METHODOLOGY

Using the Google Colab IDE, effective data analysis

techniques and prediction models are implemented in

Python 3.8. ARIMA and Fb-Prophet models from the

openly available packages “statsmodels” and “Fb-

Prophet”, respectively, are used to forecast COVID-

19 confirmed cases in the UK for the next 365 days.

Finally, the evaluation metrics root mean square error

(RMSE), mean absolute error (MAE) and mean

absolute percentage error (MAPE) of both models are

compared to find the best forecasting model. The

workflow of this study is presented in Figure 1.

Figure 1: Study Workflow.

3.1 Forecasting Models

3.1.1 Fb-Prophet

Fb-Prophet is a forecasting algorithm developed by

Meta. This model is based on the additive regression

technique, which recognizes patterns, seasons, and

holidays before combining them to improve forecast

accuracy (Anandatirtha et al., 2020). This model uses

a combination of non-linear and linear algorithms, as

well as time as a regressor. It is expressed as follows.

= (1)

where g(t) is the trend function; piecewise linear

or logical growth to fit non-periodic changes in the

value of the time series, s(t) are the periodical

variations (e.g., week after week/yearly irregularity),

h(t) are the effects of holidays that occur on irregular

schedules over a day or more, and e(t) is any unusual

change which is not accommodated by the model.

The model's input is always a time series with two

components: t is time, and y is the total number of

occurrences in a given country.

3.1.2 Arima (Autoregressive Integrated

Moving Average Model)

ARIMA is a common time-series model that can be

used to detect linear trends in definite time values.

ARIMA forecasts future values by examining the

differences between values in the time series.

ARIMA(p, d, q) models are a fusion of integrated

autoregressive (AR) and moving average (MA)

models.





=cϕ







ϕ







…ϕ





















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…



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(2)

Where:

 : the value of the time series at time t

 c: the constant or intercept term

 p: the order of the autoregressive (AR) part

of the model

 d: the degree of difference needed to make

the time series stationary

 q: the order of the moving average (MA) part

of the model

 ϕ_: the coefficient of the ith lagged

observation in the AR part of the model

 θ_: the coefficient of the ith lagged error

term in the MA part of the model

 _: the error term at time t

Parameter Evaluation By Testing for Stationarity.

In time series, stationary is a crucial component. For

data to be stationary, it has a mean, variance, and

autocorrelation structure that remain constant across

time. A model cannot forecast on non-stationary time

series data. Hence the first step in ARIMA time series

forecasting is to calculate the number of differencing

necessary to make the series stationary.

The Augmented Dickey-Fuller (ADF) test was

used to determine whether or not the time series data

Forecasting of COVID-19 Pandemic Using ARIMA and Fb-Prophet Models: UK Case Study

were stationary before calculating the parameters for

the ARIMA model (Alzahrani et al., 2020). This

approach aims to maintain the reliability of the test

based on white noise. Assume that the significance

level is 5%, and the null hypothesis is that the series

is not stationary. Suppose the critical value of the

ADF test is greater than 0.05. the null hypothesis is

accepted and the time series is confirmed to be non-

stationary. In this case, differences of varying degrees

are then used in the series to produce a stationary

series (Wanjuki et al., 2021).

3.2 Quantitative Study

3.2.1 Data Source and Description

The datasets for this study were obtained from the

GitHub account of the Johns Hopkins University

Centre for Systems Science and Engineering's (JHU

CSSE) data repository for the 2019 Novel

Coronavirus Visual Dashboard (Alzahrani, et al.,

2020)

Two different time series datasets were obtained:

confirmed cases and deaths, containing information

collected daily throughout the globe and is updated in

real-time.

3.2.2 Data Preprocessing

Data cleaning was carried out in order to acquire

useful data for analysis, visualization, and

forecasting. The columns "Province," "Lat," and

"Long" were dropped from the dataframe since they

were no longer needed. Meanwhile, the data

collection dates columns are transposed to a single

column and indexed as a timestamp for time series

forecasting. Missing values in each of the datasets

were also checked and replaced with zeros.

As this study focuses on the COVID-19 cases in

the United Kingdom, the data samples from the UK

were extracted from the global COVID-19 time series

repository. For each dataset, there are 807 data

samples, recording the number of confirmed/death

from January 22, 2020 to April 7, 2022.

Calculations for the following statistical

information were obtained:

UK daily percentage growth rate in the past 30

days = (Active cases of the current day – Active cases

30 days ago / Active cases 30 days ago) *100

UK daily death rate = (Daily deaths / Daily

confirmed cases) *100

UK death rate = (Accumulated deaths /

Accumulated confirmed cases) *100

3.3 Model Performance Evaluation

Metrics

The performance of each of the models mentioned

above is evaluated using a widely popular accuracy

measurement function. These measures are explained

below.

3.3.1 Mean Absolute Percentage Error

(MAPE)

MAPE is derived as the mean absolute percent

inaccuracy for each time period, excluding actual

values divided by real values and assesses the

accuracy of the forecast as a percentage—the better

the forecast, the lower the MAPE.

=

100









−







 (3)

3.3.2 Mean Absolute Error (MAE)

MAE calculates the absolute value of an anticipated

value. After that, we simply add up all of the absolute

values that have been recorded. A better fit is

evidenced by a reduced MAE value.

=

∑|





−



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

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(4)

3.3.3 Root Mean Squared Error (RMSE)

It evaluates the forecast model's absolute fit to the

data or how close the model's predicted values are to

the observed data points. It's frequently used as an

evaluation metric as well as a loss function.

=

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

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−



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(5)

In equations (3) to (5), n is the number of

observations, _ is the actual value, and _ is the

predicted value.

4 DATA VISUALISATION AND

ANALYSIS

4.1 Summary of COVID-19 in the UK

Our analysis is based on the code (COVID-19 data,

2023). From Figure 2, we can observe that confirmed

COMPLEXIS 2023 - 8th International Conference on Complexity, Future Information Systems and Risk

cases are rising rapidly from July 2021 onwards till

April 2022, while the death rates are below the 0.5

percentile. Although the number of deaths is

significantly lower than the number of confirmed

cases, these huge numbers imply how much people's

lives and work are affected. Moreover, it remains on

an upward trend and has not plateaued, meaning that

the impact continues.

Figure 3 indicates the confirmed case growth in

the UK from March 13, 2022, to April 11, 2022. It is

shown that the few days have the highest count up to

1.0 and other days below 0.6. This can give us an idea

of the upcoming few days ahead.

Figure 4 shows there is a peak in the death rate in

the UK in May 2020, with a maximum percentile of

15 and then a slow decline begins. Between October

and late November 2021, the mortality rate drops

sharply to about 3%, and after September 2021, the

rate drops to below 2%. This helps us understand that

the impact of COVID-19 on death rates is reduced

and stabilized in the span of two years.

4.2 Forecasting UK Confirmed Cases

by Fb-Prophet

Figure 5 shows Fb-Prophet's prediction of confirmed

cases for the coming year (365 days) from March 1,

2022. The black line indicates the original data points

in the training set. The shaded area in the light blue

color indicates the uncertainty level with an upper and

lower boundary, and the dark blue line indicates the

prediction. The uncertainty intervals can be used to

make more informed decisions. In the case of

predicting confirmed cases of COVID-19, healthcare

providers can prepare in advance based on the upper

limit of the uncertainty interval. In the future, there

may be a steady increase in the number of cases.

Therefore, the UK government should plan to act

accordingly to prevent this as much as possible.

Figure 2: UK Confirmed and Death cases.

Figure 3: Confirmed cases growth rate from 3/13/2022 to 4/11/2022 in the UK.

Forecasting of COVID-19 Pandemic Using ARIMA and Fb-Prophet Models: UK Case Study

Figure 4: COVID-19 death rate percentage in the UK.

Figure 5: Fb-Prophet 365 days forecast.

Figure 6: Forecast trend and seasonality.

Figure 6 shows the trend of the COVID-19

confirmed cases and the seasonality (in a week, a

month, and a year) of the time series data. The first

sub-figure of Figure 6 shows a high increase in cases

around June 2022, and there is predicted to be a

steady increase leading into 2023. The weekly

forecast shows a high increase in cases from Tuesday

to Friday and then a steady drop. The monthly

forecast shows a steady curve in cases from January

1 to January 18 and then a huge drop until the end of

the month before an extreme spike. The yearly

forecast shows a high increase in cases from January

1 to March 1 and then a steady drop till the end of the

year and a hike on January 1 again.

COMPLEXIS 2023 - 8th International Conference on Complexity, Future Information Systems and Risk

Figure 7: ADF Test for initial data (left) and for logarithmic values (right).

4.3 Forecasting UK Confirmed Cases

by ARIMA

The result of the stationary test is shown in Figure 7.

As shown in this figure, the rolling mean and original

data are trending in the same path while the rolling

standard deviation is constant. In addition, the p-value

of the test is 0.98 (p > 0.05). Therefore, the time-

series data appeared to be non-stationary based on the

ADF test result, and the variance between the data

must be compressed using the log scale of the data.

After transforming the data into the log form, this

study conducted the ADF Test again to check the

stationary values. The null hypothesis was rejected

because, after applying the initial difference, d(0), the

p-value produced was less than the significance level

(p 0.05), and the statistical ADF was smaller than all

the other critical bounds. The results are shown in

Figure 7.

After checking the dataset for the stationary, the

stepwise search by (Hyndman and Khandaka, et al

2008) was conducted to figure out the order for the

best ARIMA model. The results show that the order

for the best model is ARIMA(3,2,3)(0,0,0)[0], with

the minimum Akaike’s Information Criterion (AIC)

of 21,376.38 and Bayesian Information Criterion of

21410.04. The parameters obtained were then used to

train the Arima model and make predictions on the

test set. The results (Figure 8) of the ARIMA model

validate the increasing trend forecast by Fb-Prophet.

Figure 8: ARIMA Forecast.

The Linear trend is almost perfect, which may

happen due to the following reasons.

• The model is overfitting the data, it may fit the

trend too close.

• The data exhibits the linear trend, ARIMA is

perfectly capturing a trend component of the

time series, it also indicates that the model is

removing the trend component from the data,

so it is not a cause of concern.

5 ANALYSIS AND FINDINGS

A comparison of active cases in the UK and some

other countries worst hit by the pandemic is shown in

Figure 3. In the graph, the UK was 4th on the list of

countries with the most active cases. The percentage

growth rate of confirmed cases from March 13, 2022

to April 11, 2022, was calculated and visualized in

Figure 3. March 21 and April 8, 2022, recorded the

highest and lowest confirmed case growth rates,

respectively.

Figure 9: Active Cases from Jan 2020 to Jan 2023.

Americas

67%

SouthEas

t Asia

22%

Eastern

Mediterr

anean

Africa

Americas

SouthEast Asia

Eastern

Mediterranean

Forecasting of COVID-19 Pandemic Using ARIMA and Fb-Prophet Models: UK Case Study

5.1 Model Evaluation

Figures 5 and Figure 6 show the Fb-Prophet forecast

model trend of confirmed cases in the next 365 days.

These show the underlying trend in the prediction is

a linear trend while also accurately modeling weekly

and monthly seasonality. The exponential curves of

the forecast from the Fb-Prophet and ARIMA models

show there will be more confirmed cases in the next

year (365 days).

Table 1: Evaluation Metrics Comparison between Models.

Model RMSE MAE MAPE

ARIMA 473888.97 379160.07 0.02

Fb-Prophet 1539062.30 1504264.94 0.15

In order to evaluate the performance of the Fb-

Prophet and ARIMA models, error measurement

metrics, RMSE, MAE, and MAPE, were carried out

and the results are shown in Table 1. They are

commonly used metrics to evaluate the accuracy of

time series forecasting models. We have made this

comparison to determine which model gives less error

and is more accurate in predicting the result. A lower

value of the different evaluation metrics indicates a

model is well fit and has a higher prediction accuracy.

A comparison of RMSE, MAE, and MAPE shows

that the ARIMA model performed better than Fb-

Prophet. The MAE for ARIMA is 379160 and for Fb-

Prophet is 1504264, which is three times higher than

the MAE for ARIMA. Similarly, the RMSEs of the

two models show a vast difference, with ARIMA

being at 473888 and Fb-prophet at 1539062. Finally,

we compared the MAPE values of the two models at

0.02 for ARIMA and 0.15 for Fb-Prophet. The

significantly lower values of error indicators for

ARIMA show that ARIMA is better at capturing the

patterns and trends in the time series data and making

accurate forecasts than Fb-Prophet.

5.2 Forecasting Discussion

The following can be inferred from the analysis with

respect to existing literature:

• Figure 4 shows a considerable decrease in

deaths due to the deployment and adherence to

pandemic control measures such as lockdowns, social

distancing, face masking, sanitization, and

vaccination by individuals and the UK authority.

Dashtbali and Mirzaie's work in 2021 is therefore

justified. They created two models, SEIHRD and

SMEIHRDV, that accurately predicted how social

distancing and vaccination are used to manage the

COVID-19 pandemic (Mohan, et al., 2022).

• There was a drastic spike in the death rate, as

seen in Figure 4, during the early months of the

outbreak. It is evident in the work of Anderson et al.

(2020) that data collection and research to better

understand the virus's nature and behavior were

ongoing while healthcare systems were overwhelmed

due to the hospitalization cases surge (Anderson, et

al., 2020).

6 CONCLUSIONS AND

IMPLICATIONS

Predictive analysis of COVID-19 infectious disease

using a time-series model is a useful application of AI

and Big Data in the fight against the virus. The

proposed models predicted an exponential slope from

confirmed cases, implying that there will most

probably be more instances in the next 365 days.

Nevertheless, new variants, herd immunity, vaccines,

and available resources may all alter mortality case

projection curves. This study will enable the

government and healthcare providers to understand

the current situation better and prepare for the next

wave so that less damage is caused in the near future.

In the future study, we can enhance this study by

taking the latest data and adding time series

algorithms like SEIR(Suspected Exposed Infections

Removed) for short-term and long-term forecasting,

Hybrid models like combining ARIMA with LSTM

to capture trends in data.

ACKNOWLEDGEMENTS

This project is partly supported by VC Research

(VCR0000199).

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