Single and Multilayer LSTM Models for Positive COVID-19 Cases

Prediction

Asmae Berhich

, Fatima-Zahra Belouadha

and Asmae El Kassiri

AMIPS Research Team, E3S Research Center, Ecole Mohammadia d’Ingénieurs,

Mohammed V University in Rabat, Morocco

Keywords: COVID-19, prediction, single layer LSTM, multilayer LSTM, deep learning, health.

Abstract: COVID-19 is a global pandemic that has been reported first in Wuhan, China in December 2019. According

to the World Health Organization (WHO), around 1 out of every 5 people who get COVID-19 get seriously

ill and develop difficulty breathing. The virus is spreading from one person to others causing fear and a big

struggle in the world. Building accurate learning models for forecasting positive new cases would help to

better manage the crisis situation thereby helping to fight COVID-19 and save lives. For this purpose, we use

LSTM (Long Short Time Memory) model in Morocco’s case and evaluate its performance according to six

architectures. The results demonstrate that the architecture with three cells outperforms the other models and

shows the best fitting.

1 INTRODUCTION

In the past decades, technologies have played an

important role in solving several problems of

epidemics and pandemics. For the same purpose,

Artificial Intelligence, and data science have emerged

with new methods and techniques that help humanity

to prevent the spread of pandemics, and mitigate the

related risk.

Nowadays, the whole countries in the world suffer

from the COVID-19 epidemic and there is no

medicine or vaccine that prevents or cures this disease

until now. For this reason, researchers are invited to

discover and find new solutions to help governments

dealing and managing this dilemma. Many papers and

work were suggested for different purposes using

especially Machine Learning (ML) and Deep

Learning (DL) algorithms and techniques. However,

new methods and approaches still remain needed to

prevent the spread of the global pandemic. In this

context, our research aims at finding a solution for

this challenging problem using one of the most

powerful and known algorithms of DL called Long

Short-Term Memory (LSTM).

https://orcid.org/0000-0002-4388-100X

https://orcid.org/0000-0002-2355-4204

https://orcid.org/0000-0002-4842-588X

LSTM is a Recurrent Neural Network (RNN)

proposed and developed in 1997 (Hochreiter et al.,

1997). It is widely used in solving complex and hard-

learned problems in many different fields, especially

for time series data. For instance, it is used in the

seismic field (one of the most complex fields) to warn

from the incoming earthquake in a specific region

(BERHICH et al., 2020; Siami-Namini et al., 2019;

Wang et al., 2017). Our objective in this work is to

evaluate the predictions’ accuracy of the infected

cases in Morocco by applying six different LSTM

model’s architectures and comparing their efficiency

using the most popular performance metrics: MSE

(Mean Squared Error), MAE (Mean Absolute Error),

RMSE (Root Mean Squared Error), and R squared.

The rest of this paper is organized in the following

way: Section II presents the related work. Section III

gives an overview of our comparative approach by

highlighting the important steps of building our

models such as the data collection, preprocessing, and

parameterization of the learning process. Section IV

discusses and evaluates the performance of our

applied models. Section V summarizes the

conclusions and perspectives of this work.

2 RELATED WORKS

Recently, several researchers are trying to develop

and find suitable solutions and strategies to stop the

outbreak of the coronavirus disease. Data scientists

suggested some work for predicting and forecasting

new positive Covid-19 cases using ML and DL

techniques. DL and ML indeed provide effective

tools that learn trends from collected data, among

them the recurrent neural network LSTM which was

used in a lot of work as well as in this case study.

Authors in (Chimmula et al., 2020) predict the

possible ending point of coronavirus in Canada. They

apply the LSTM algorithm on the available data until

March 13, 2020 and they give predictions for 2

successive days from the 2nd to 14th day. The

findings of this work expect that the possible stopping

time of Coronavirus in Canada could be around June

2020, and a small number of infections may be

reported until December 2020. Besides, the aim in

(Arora et al., 2020) was to predict the daily and the

weekly number of positive cases in 32 states and

union territories of India. Four deep learning

techniques: LSTM, deep LSTM, convolutional

LSTM, and bidirectional LSTM were used. The

bidirectional LSTM gives the best performance

evaluated using the MAE metric. Moreover, another

research in (Tomar et al., 2020) predicts the number

of COVID-19 cases, recovered cases, and deceased

cases during 30 days ahead in India using the LSTM

model and curve fitting. Authors in (Yang et al.,

2020) apply a modified Susceptible-Exposed-

Infectious-Removed (SEIR) model to derive the

epidemic curve and artificial intelligence to predict

COVID-19 epidemic trends while giving it peaks and

sizes in China. Author in (Bouhamed, 2020) develops

DL nested sequence prediction models with also

LSTM to predict the cumulative case number and

recoveries in 79 countries. The models use the dataset

until March 13, 2020, and they are evaluated using

the R squared metric. The results were encouraging

for the newly infected cases. Predictions of

cumulative number of deaths, daily number of new

cases worldwide, and cumulative number of cases in

Europe and middle east regions were given in

(Direkoglu et al., 2020). This research provides the

predictions of the next ten days. It is based on the

reported time series data of Covid-19 and the LSTM

model with the dropout layer. The obtained results

were evaluated by the RMSE and were considered

promising since they were able to predict the possible

scenarios regionally and globally. In the same

manner, authors in (Yan et al., 2020) predict the

confirmed cases using the LSTM algorithm. They

compared the deviation between LSTM results and

the results of the digital prediction models (like

Logistic and Hill equations) with the real data. They

found that the proposed model has a smaller

prediction deviation and better fitting effect.

A hybrid model is applied in (Zandavi et al., 2020)

to forecast the number of cases and deaths in the top

ten most affected countries in Australia. This model

combines the algorithm LSTM with dynamic

behavioural models. The proposed approach

considers the effect of multiple factors, and the

parameters are optimized using the genetic algorithm.

The results showed that the hybrid model outperforms

the LSTM model. From another angle, authors in

(Alakus et al., 2020) use laboratory data to predict

which patients are likely to receive coronavirus. Their

predictive model based on DL approaches identified

patients that have COVID-19 with good accuracy.

In addition, three approaches were applied in

(Kırbaş et al., 2020) to predict the confirmed cases in

Europe: Autoregressive Integrated Moving Average

(ARIMA), Nonlinear Autoregressive neural network

(NARNN) and Long-Short term Memory (LSTM).

The LSTM model was more efficient for forecasting

14 future days. It expects that the rate of positive

cases will decrease slightly in many countries. In

(Ayyoubzadeh et al., 2020) LSTM and Linear

Regression (LR) models are suggested to forecast the

number of positive COVID-19 cases in Iran. The

results showed that LR predicted the incidence with

an RMSE of 7.5 and LSTM with an RMSE of 27.18.

These works and predictions have been performed

for different purposes under the scope of COVID-19

outbreak forecasting and would help the governments

to face the COVID-19 pandemic and help the

authorities and decision-makers to manage and deal

with their strategies. The LSTM model used

according to different learning approaches was

seeming to be promising in most of them. However,

it would be interesting to explore more approaches

using this model in order to reach better accuracy.

Besides, no study with accurate predictions, has

considered the case of the outbreak of COVID-19 in

Morocco using LSTM. Only three research

contributions consider the Morocco’s case while

using LSTM-based models (Ayris et al., n.d.;

Bouhamed, 2020; Ksantini et al., 2020). In (Ayris et

al., n.d.), authors use DSPM (Deep Sequential

Prediction Model) which is a stacked LSTM to

predict cumulative number of confirmed cases in

different countries in the world, among them

Morocco. Note that the obtained average MAE Error

Rate was 388.43 which is not a good result if we

consider Morocco’s case. We note that the studied

period matches with the confinement period in

Morocco until May 5, 2020 and that on this date, there

were 5219 confirmed cases reported while the

predicted value is 7422. Authors in (Ksantini et al.,

2020) use LSTM to predict new weekly cases of

COVID-19 pandemic based on the confinement and

the protection tools factors for different countries,

among them Morocco. We outline that this paper was

received in March 6, 2020 while the first confirmed

case in Morocco was reported in March 2, 2020, only

7 confirmed cases were reported in March 13, 2020,

and the confinement strategy was applied in March

20, 2020. We think that exploring LSTM with more

data would be interesting to have more reliable and

credible results.

In (Bouhamed, 2020), author uses LSTM to

predict the cumulative confirmed cases number in 79

countries, among them Morocco, and also considers

a dataset that range from the beginning of COVID-19

until only March 25, 2020. As we have mentioned

above, we think that this period and related data are

not sufficient to perform predictions about the virus

spread in Morocco. In addition, it is worth noting that

this work only provides projections for the next day,

which would not be interesting for decision makers

since it does not give them enough time to be able to

react to a critical situation. In this context and given

all of these reasons, our work was conducted.

3 METHODOLOGY

COVID-19 is a global pandemic and every day

millions of infected cases are reported around the

world. Our work aims to accurately predict the new

positive COVID-19 cases. For this purpose, we

explore different architectures of the LSTM

algorithm which is suitable to be used for forecasting

such time series data, and we experiment and evaluate

them in Morocco’s case. This section presents at first

the basis architecture of this recurrent neural network

before explaining the important steps that we follow

to build our models and perform our comparative

study.

3.1 RNNs Architecture and LSTM

RNNs are a category of Artificial Neural Networks

(ANNs) characterized by their state of memory. They

are composed of hidden states which are distributed

over time, allowing them to store a lot of information

about the past. They are mostly used in forecasting

applications because of their capacity to handle

sequential data of variable length (Graves, 2013).

However, their major disadvantage is their lack of

reducing and handling the problems of vanishing

gradient and explosion gradient. They can only store

short term memory because they require activations

of only the hidden layer of the pre-previous time step

(Hochreiter et al., 1997a).

The main goal of RNNs is to consider the

influence of past information in producing the output

result. To this end, they use cells represented by gates

which influence the generated output according to the

historical observations. They are especially effective

for learning temporal information (Oksuz et al.,

2019). In RNNs, a hidden state ht can be calculated

for a given input xt sequence by the equation 1 where

Whh is the weight of the previous hidden state ht-1,

xt is the current input, Wxh is the weight of the

current input state, tanh is the activation function.

The output state yt is computed according to the

equation 2 where Why is the weight at the output

state.

=tanh (W

t-1

) (1)

(2)

LSTM is considered as a sophisticated RNN and

gated memory unit, designed to avoid and resolve the

vanishing gradient problems that limit the efficiency

of simple RNNs (Hochreiter et al., 1997a). The

LSTM cells are supported by three components called

gates: the input gate, the forget gate and the output

gate. This makes it possible to address the limitations

of traditional time series forecasting techniques by

adapting the non-linearities of a given dataset and to

produce state-of-the-art results on the temporal data.

Each block of LSTM works at different time steps and

passes its output to the next block until the final

LSTM block generates the sequential output. Besides,

LSTM is hence a powerful algorithm for

implementing a sequential time series model. Its key

component is memory blocks which have been

released to tackle vanishing gradients by memorizing

network parameters for long durations. The memory

blocks in the LSTM architecture are similar to the

differential storage systems of a digital system. The

gates in LSTM help to process the information using

an activation function (sigmoid) which generates a

value between 0 and 1 as an output. The main reason

why the sigmoid activation function is used is to

transmit only positive values to the following gates to

get a clear output (Chimmula et al., 2020).

LSTM is flexible and estimates dependencies of

different time scales. The commonly used RNN

variations such as LSTM use gates and memory cells

for sequence’s prediction. In the beginning, LSTM

starts with a forget gate layer (ft) that uses a sigmoid

function combined with the previous hidden layer (ht-

1) and the current input (xt) as described in the

following equations (3, 4, 5, 6, 7 and 8) where it, čt,

ft, ot, ct, ht are the input gate, cell input activation,

forget gate, output gate, cell state, and the hidden state

respectively. Wi, Wc, Wf and Wo are their weight

matrices respectively. bi, bc, bf, and bo are the biases.

Xt is the input, ht-1 is the last hidden state, ht is the

internal state. σ is the sigmoid function.

= σ (W

. [h

t-1

, x

] + b

) (3)

=tanh (W

t-1

, x

] + b

) (4)

= σ (W

. [h

t-1

, x

] + b

) (5)

= σ (W

t-1

, x

] + b

) (6)

= f

* c

t-1

+ i

* č

(7)

=ot * tanh (c

) (8)

3.2 Our Approach for Predicting

COVID-19 Positive Cases by Single

and Multilayer LSTM

In this work, we apply six different LSTM

architectures to predict the new positive COVID-19

cases in Morocco for the 7 future incoming days. The

six-architecture called LSTM1, LSTM2, LSTM3,

LSTM4, LSTM5 and LSTM6, are respectively

single, two, three, four, five and finally six LSTM

layers. The aim of this work is to compare the

relevance of the mentioned architectures in the

context of COVID-19 spread prediction.

In the following subsections, we present the

dataset we use in this work, the preprocessing steps

of our models, the feature selection, the applied

parametrization, and finally the performance metrics

used to evaluate and compare the results.

3.2.1 Dataset

The COVID-19 dataset we use in this work is from

“Our World in Data” Website4. It shares and reports

data collected from the European Center for Disease

Prevention and Control (ECDC). The COVID-19 data

are updated daily on this website which provides data

collected from around the world.

https://ourworldindata.org/coronavirus-source-data

3.2.2 Preprocessing and Feature Selection

The preprocessing and feature selection are

fundamental stages in ML and DL approaches. The

preprocessing gives many ways and operations to

convert and transform the source data into a clean

dataset ready to be feed in the ML and DL models. It

affects the quality of the model and its results. The

feature selection provides the relevant features that

adequately affect the learning process, and may

reduce the number of variables to evolve the model

efficiency and to avoid costly computations.

Eventually, in this work we are following these steps

to prepare and select feature from the source data:

extracting the targeted data inputs, selecting

appropriate feature, filling null values, normalizing

data and adapting the timesteps to be considered for

prediction.

The source data report the worldwide COVID-19

pandemic data. Therefore, we selected just data

related to Morocco’s case we desire to study. The

time of our analyzed dataset starts from the beginning

of this pandemic in Morocco on March 02, 2020 to

June 15, 2020. This period matches with the

confinement period in Morocco. It was selected in

order to allow analysing the performance of the

proposed models in the same context since the

deconfinement data are not sufficient and could

influence their accuracy.

The source data give multiple features but not all

of them are registered for the instances of Morocco,

and not all of them are important for use in the

prediction. In our case, we have selected five

important features: the new cases, the total cases, the

new deaths, the total deaths and population. These

features are the most and highly correlated variables

to the targeted output (new COVID-19 positive

cases). Note that the correlations of total cases, new

cases, total deaths, new deaths and population are

respectively 96,63%, 100%, 96,17%, 86,75% and

67,67%.

To impute null values, we used two methods: the

first one consists of filling with the median value

whereas the second consists of applying the Key

Nearest Neighbor (KNN) algorithm. We have

experimented our data with both methods and we

have proceeded with the median since it gave better

results than the KNN algorithm.

The features in a given dataset are generally

presented in different scales. In our case, for example,

the population is presented by millions, total cases are

presented by thousands since they describe the

cumulative number of cases, and the new cases are

presented by hundreds. To make all these values on

the same scale and to add the uniformity to our

dataset, we apply the Min-Max scaler that transforms

all values between the range 0 and 1. This will delete

the noise from our data and facilitate the learning

process of our models.

Besides, COVID-19 data are time series, and

hence, the values of the actual data are required as

inputs to perform predictions for the following days.

Time series data cannot use future values as input

features, then the inputs of a time series model are the

past feature values. In this work, we adapt our model

to learn from the past timesteps in order to predict the

positive COVID-19 cases for the future 7 timesteps.

This choice was adopted due to the data size and also

in order to consider a minimum sufficient time to be

given for decision makers.

3.2.3 Parametrization

The architectures of our six LSTM models are

differentiated by the number of LSTM cells. Table I

illustrates the architecture and parametrization of

each model. All the models are using Adam

optimizer which is one of the most used stochastic

optimizers thanks to its ability to learn faster as it has

been demonstrated in (Kingma et al., 2015) using

empirical experiments. The other mentioned

parameters have been fixed after we have tuned and

tested multiple parameters until larger batch sizes

were giving better results. The adopted size is 64. In

addition, the activation function that was giving good

fitting is the Tanh function. We also note that time lag

and timestep were respectively fixed to 2 and 7 days.

3.2.4 Performance Metrics

DL and ML models’ results are measured according

to various metrics. There is exist several methods to

evaluate regression models. In our work, we are using

four performance metrics MAE, MSE, RMSE and R

squared (R2), as mentioned above.

MAE presents the average of the absolute

difference between the real and the predicted values.

MSE represents the average of the square of the

difference between the original and the predicted

values. It is sensitive to outliers and data containing a

lot of noise. RMSE is the root of the value of MSE

and it presents the standard deviation of errors. It is

useful when high errors are present. Finally, R

squared indicates the efficiency of the model fitting.

Table 1: architectures and parametrization of our models.

Mode

Parametrization

Layers

Activation

function

optimize

Batch

size

LSTM-1

LSTM cell of 75

units

Dense layer of 7

out

uts

Tanh

Ada

LSTM-2

LSTM cell of 75 units

LSTM cell of 70 units

Dense layer of 7

outputs

Tanh

Ada

LSTM-3

LSTM cell of 75 units

LSTM cell of 70 units

LSTM cell of 60 units

Dense layer of outputs

Tanh

Ada

LSTM-4

LSTM cell of 75 units

LSTM cell of 70 units

LSTM cell of 65 units

LSTM cell of 60 units

Dense la

er of out

uts

Tanh

Ada

LSTM-5

LSTM cell of 75 units

LSTM cell of 70 units

LSTM cell of 65 units

LSTM cell of 63 units

LSTM cell of 60 units

Dense la

er of out

uts

Tanh

Ada

LSTM-6

LSTM cell of 75 units

LSTM cell of 70 units

LSTM cell of 65 units

LSTM cell of 63 units

LSTM cell of 60 units

LSTM cell of 55 units

Dense layer of outputs

Tanh

Ada

4 RESULTS AND DISSCUSSION

In this section, we present and discuss the results of

our LSTM models which are based on six different

architectures. The fitting curves of each model are

shown in Fig. 1. Unlike LSTM-1 and LSTM-2, the

loss curves of the other models indeed converge to the

minimum error corresponding to the training loss. We

can see that they do not present any limitation of

overfitting or underfitting.

Regarding the prediction quality, the results

illustrated in Table II, show that the LSTM model

with three layers outperforms the other models.

LSTM-3 provided the lowest MAE, MSE and RMSE

values which are respectively equal to 19.95, 685.65

and 25.66. It also globally provided good predicted

total positive cases per week. As shown in Table III,

the total predicted cases provided by LSTM-3 are

fairly close to the real ones at least for two among

three weeks (week 1 and week 3). In other terms, it

generally provided low deviations from the total real

cases in the way that it was able to predict values

which were equal respectively to the predicted cases

minus 5% and plus 8% in the third and first weeks. It

is also worth noting, that these values as well as the

quality metrics (RMSE, MSE and MAE) confirm a

good prediction capacity and fairly high accuracy,

especially, in comparison with all related work

presented in this paper.

Table 2: test results for 21 days.

Model

Performance metrics

MAE MSE RMSE R2

LSTM-1 23.78 830.51 28.82 0.03

LSTM-2 22.7 809.58 28.45 0.05

LSTM-3 19.95 658.65 25.66 0.23

LSTM-4 22.63 791.78 28.14 0.07

LSTM-5 21.73 759.59 27.56 0.11

LSTM-6 25.1 981.71 31.33 -0.15

Figure1: Fitting curves of prediction LSTM models.

Accordingly, we calculate the total number of real

and predicted cases: of the whole test set 21 days), the

first week, the second week, and the third week

(Table 3).

Besides, Fig. 2 presents the daily real and

predicted new cases’ curves corresponding to 21

days. We can see that LSTM-3 projections still

remain very close to the real values, except for some

high peaks that LSTM-3 doesn’t catch and also for

the period ranging from June 1, 2020 to June 3, 2020.

The peaks and the bending could be explained by

the industrial and residential clusters which are

reported from time to time in the last month of

confinement in Morocco. However, we think that the

reported deviation in general could be due to the fact

that our model doesn’t take into account other

important feature such as test kits, clusters,

asymptomatic case that would influence the COVID-

19 spread. Hence, we think that the obtained results

are promising. However, we suggest trying other

features in future work in order to help the models to

learn faster and easier the epidemic trend.

Table 3: LSTM-3 deviation per week.

Week 1 Week 2 Week

Real new cases 374 352 560

LSTM-3

Predicted new

cases

409,43 480,15 528,98

Deviation 35,43 128,15 -31,02

Deviation

ercenta

9,47 36,41 -5,54

5 CONCLUSIONS

In this paper, we give a comparative study of six

LSTM models’ architectures in order to predict new

positive COVID-19 cases using data of Morocco

from March 2, 2020 to June 15, 2020. The study

shows that the LSTM with three cells gives better

results and avoids both the overfitting and the

underfitting. The results are very close to the real

values for two among three weeks, and fairly close to

the other week. Therefore, we think that the powerful

DL model LSTM which is suitable for time series

problems, could also be a suitable and promising

model to learn complex insights from COVID-19

data. Our findings and conclusions are demonstrated

and enhanced by various illustrations we provide in

this paper. Nevertheless, we plan to more explore this

potential model under other perspectives by including

other important features and investigating also the

Figure 2: Real and predictive cases curves for 21 days.

deconfinement period in order to improve the

prediction accuracy and adapt the model to various

crisis situations.

ACKNOWLEDGEMENTS

This paper is produced as part of the COVID-19

project supported by the responsible ministry

MENFPESRS and the CNRST under the grant

number COV/2020/87.

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