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Deep learning via LSTM models for COVID-19 infection forecasting in India

Rohitash Chandra 1 *, Ayush Jain 2 ‡, Divyanshu Singh Chauhan 3 ‡

1\. UNSW Data Science Hub & School of Mathematics and Statistics, University
of New South Wales, Sydney, Australia

2\. Department of Electronics and Electrical Engineering, Indian Institute of
Technology Guwahati, Assam, India

3\. Department of Mechanical Engineering, Indian Institute of Technology
Guwahati, Assam, India

‡These authors contributed equally to this work.

* Corresponding author

E-mail<EMAIL_ADDRESS>(RC)

## Abstract

The COVID-19 pandemic continues to have major impact to health and medical
infrastructure, economy, and agriculture. Prominent computational and
mathematical models have been unreliable due to the complexity of the spread
of infections. Moreover, lack of data collection and reporting makes modelling
attempts difficult and unreliable. Hence, we need to re-look at the situation
with reliable data sources and innovative forecasting models. Deep learning
models such as recurrent neural networks are well suited for modelling
spatiotemporal sequences. In this paper, we apply recurrent neural networks
such as long short term memory (LSTM), bidirectional LSTM, and encoder-decoder
LSTM models for multi-step (short-term) COVID-19 infection forecasting. We
select Indian states with COVID-19 hotpots and capture the first (2020) and
second (2021) wave of infections and provide two months ahead forecast. Our
model predicts that the likelihood of another wave of infections in October
and November 2021 is low; however, the authorities need to be vigilant given
emerging variants of the virus. The accuracy of the predictions motivate the
application of the method in other countries and regions. Nevertheless, the
challenges in modelling remain due to the reliability of data and difficulties
in capturing factors such as population density, logistics, and social aspects
such as culture and lifestyle.

##  1 Introduction

The coronavirus disease 2019 (COVID-19) is an infectious disease caused by
severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) [1, 2, 3] which
became a global pandemic [4]. COVID-19 was first identified in December 2019
in Wuhan, Hubei, China with the first confirmed (index) case was traced back
to 17th November 2019 [5]. The COVID-19 pandemic forced many countries to
close their borders and enforced a partial or full lockdown which had a
devastating impact on the world economy [6, 7, 8]. Other major impact has been
on agriculture [9, 10] which is a major source of income for the population in
rural areas, especially in the developing world.  The sudden lockdown in some
countries created a number of problems, especially for low income communities
[11, 12], and migrant workers [13]. Currently (8th October, 2021) [14], more
than 238 million cases have been reported across the world which resulted in
more than 4.8 million deaths, and about 215 million have recovered [15, 16]. A
significant portion of the recovered suffer from ”long-covid” [17, 18], a term
which refer to pro-longed health problems which can last for months to entire
lifetime. In terms of vaccinations (8th October, 2021) [14], 46.3 % of the
world population has received at least one dose and 6.4 billion doses have
been administered globally. Furthermore, about 2.4 % of population in low-
income countries have received at least one dose.

The case of India has been unique when it comes to management of COVID-19
pandemic [13]. The first COVID-19 case in India was reported on 30 January
2020. India had two major waves of infections, where the first wave was from
April to October 2020 and the second wave was from February to June 2021 [19].
India currently (8th October, 2021) [14, 15] has 33,935,309 confirmed cases
with 450,408 deaths which makes the largest in Asia, the second highest in the
world after the United States. The fatality rate of COVID-19 in India is among
the lowest in the world as it ranks 124th with 322 deaths in a million people.
In comparison, United States has 2,197 and the United Kingdom has 2,013 deaths
in a million people. The second wave (2021) had a devastating effect on the
Indian health system and during the time around its peak in daily cases, India
had highest daily infection in the world [14, 15]. On the bright side, India
also has one of the fastest recovery rates in the world with 236,610 active
cases, and ranks 9th in the world although 2nd in total cases.

In terms of COVID-19 forecasting, prominent computational and statistical
models have been unreliable due to the complexity of the spread of infections
[20, 21, 22]. Given lack of data, it is challenging to develop a model while
taking into consideration population density, effect of lock-downs, effect of
viral mutations and variants such as the delta variant [23], logistics and
travel, and qualitative social aspects such culture and lifestyle [24].
However, culture and lifestyle are examples of variable of interest that
cannot be measured quantitatively. Due to qualitative nature of certain
variables of interest such as lifestyle, and lack of data collection,
modelling attempts have been mostly unreliable [25]. We need to re-look at the
situation with latest data sources and most comprehensive forecasting models
[26, 27, 28]. Moreover, a number of other limitations exists, such as noisy or
unreliable data of active cases [29], changing mortality rate given different
variants, and asymptotic carriers [30, 31]. There have been reports that the
models lack a number of limitations and failed in several situations [25].
Despite these challenges, it has been shown that country based mitigation
factors in terms of lockdown level and monitoring has a major impact on the
rate of infection [32]. We note that limited work has been done using deep
learning-based forecasting models for COVID-19 in India, although the country
has one of world’s largest population with highly populated and highly dense
cities. There is a need to evaluate latest deep learning models for
forecasting COVID-19 in India, that takes into account both the first (2020)
and the second wave (2021) of infections.

Deep learning models such as recurrent neural networks (RNNs) are well suited
for modelling spatiotemporal sequences [33, 34, 35, 36, 37] and modeling
dynamical systems, when compared to simple neural networks [38, 39, 40]. The
limitation in training RNNs for long-term dependencies in sequences where data
sequences span hundreds or thousands of time-steps [41, 42] have been
addressed by long short-term memory networks (LSTMs) [35]. LSTMs have been
used for COVID-19 forecasting in China [43] with good performance results when
compared to epidemic models. LSTMs have also been used for COVID-19
forecasting in Canada [44]. Other deep learning models such as convolutional
neural networks (CNNs) have recently shown promising performance for time
series forecasting [45, 46]. Hence, they would also be suited for capturing
spatiotemporal relationship of COVID-19 transmission with neighbouring states
in India.

In this paper, we employ LSTM models in order to forecast the spread of COVID-
infections among selected states in India. We select Indian states with
COVID-19 hotpots and capture the first and second wave of infections in order
to later provide two months ahead forecast. We first employ univariate and
multivariate time series forecasting approaches and compare their performance
for short-term (4 days ahead) forecasting. We also present visualisation and
analysis of the COVID-19 infections and provide open source software framework
that can provide robust predictions as more data gets available. The software
framework can also be applied to different countries and regions.

The rest of the paper is organised as follows. Section 2 presents a background
and literature review of related work. Section 3 presents the proposed
methodology with data analysis and Section 4 presents experiments and results.
Section 5 provides a discussion with discussion of future work and Section 6
concludes the paper.

##  2 Related Work

The pandemic has greatly affected and transformed work environment and
lifestyle. COVID-19 lockdowns and restrictions of movement has given rise to
e-learning [47, 48, 49] and telemedicine [50], and created opportunities in
applications for geographical information systems [51]. The lockdown showed
positive impact on the environment [52, 53], especially for highly populated
and industrial nations with high air pollution rate [54]. Zambrano-Monserrate
et. al highlighted the positive indirect effects revolve around the reduction
air pollutants in China, France, Germany, Spain, and Italy [55]. However, the
way medical pollutants and domestic waste were discarded during lockdowns has
been an issue [55]. COVID-19 lockdowns and infection management raised
concerns about prejudices against minorities and people of colour in developed
countries such as the United States [56]. Furthermore, there has been a
significant impact on mental health across the globe [57, 58].

It has been shown that in some countries, comprehensive identification and
isolation policies have effectively suppressed the spread of COVID-19. Huang
et. al [59] presented an evaluation of identification and isolation policies
that effectively suppressed the spread of COVID-19 which further contributed
to reduce casualties during the phase of a dramatic increase in diagnosed
cases in Wuhan, China. The authors recommended that governments should swiftly
execute the forceful public health interventions in the initial stage of the
pandemic. However, such policies have not been that effective for other
countries, such as the first wave of infections and associated lockdowns in
India [26].

###  2.1 Modelling and forecasting COVID-19

A number of machine learning and statistical models have been used for
modelling and forecasting COVID-19 in different parts of the world. Saba and
Elsheikh presented simple autoregressive neural networks for forecasting the
prevalence of COVID-19 outbreak in Egypt which showed relatively good
performance when compared to officially reported cases [22]. Yousaf et. al
used auto-regressive integrated moving average (ARIMA) model for forecasting
COVID-19 for Pakistan [21]. The model predicted that the number of confirmed
cases would increase by factor of 2.7 giving 95 % prediction interval by the
end of May 2020, to 5681 - 33079 cases. However, Pakistan reported around
70,000 cases [14] end of May 2020, and hence the model was poor in prediction.
Velásquez and Lara used Gaussian process regression model for forecasting
COVID-19 infection in the United States [20]. The authors show that COVID-19
would peak in United States around July 14th 2020, with about 132,074 deaths
and 1,157,796 infected individuals at the peak stage. However, the actual
cases by July 14th reached more than 3.5 million with more than 139 thousand
deaths [14, 15] which shows that the model was close in forecasting deaths but
forecast of total cases was poor.

Chimmula and Zhand used LSTM neural networks for time series forecasting of
COVID-19 transmission in Canada [44]. The authors predicted the possible
ending point of the outbreak around June 2020 and compared transmission rate
of Canada with Italy and the United States. Canada reached the daily new cases
peak by 2nd May 2020 [14, 15], and since then, new cases has been drastically
reducing. Therefore we can say that the approach by the authors was somewhat
close in reporting the peak for COVID-19 in Canada. Chakraborty and Ghosh [27]
used hybrid ARIMA and wavelet-based forecasting model for short-term (ten days
ahead) forecasts of daily confirmed cases for Canada, France, India, South
Korea, and the United Kingdom. The authors also applied an optimal regression
tree algorithm to find essential causal variables that significantly affect
the case fatality rates for different countries. Maleki et. al [28] used
autoregressive time series models based on mixtures of normal distribution
from confirmed and recovered COVID-19 cases worldwide.

Ren et al. [24] analysed spatiotemporal variations of the epidemics before
utilizing the ecological niche models with nine socioeconomic variables for
identifying the potential risk zones for megacities such as Beijing, Guangzhou
and Shenzhen. The results demonstrated that the method was capable of being
employed as an early forecasting tool for identifying the potential COVID-19
infection risk zones. Alzahrani et al. [60] used autoregressive and ARIMA
models for COVID-19 in Saudi Arabia with data till 20th April 2020 and
predicted 7668 daily new cases by 21st May 2020 given stringent precautionary
control measures were not implemented. However, Saudi Arabia on 21st May 2020
reported 2532 actual cases [14, 15]; hence, the model has shown poor
performance. Singh et al. [61] presented a hybrid of discrete wavelet
decomposition and ARIMA models in application to one month forecast the
casualties cases of COVID-19 in most affected countries back then which
included France, Italy, Spain, United Kingdom and and United Sates. The study
found that the hybrid model was better than standalone models. Dasilva et al.
[26] employed machine learning methods such as Bayesian regression neural
network, cubist regression, k-nearest neighbors, quantile random forest, and
support vector regression with pre-processing based on variational mode
decomposition for forecasting one, three, and six-days-ahead the cumulative
COVID-19 cases in five Brazilian and American states up to April 28th, 2020.
Yang et al. [43] presented an epidemiological model that incorporated the
domestic migration data and the most recent COVID-19 epidemiological data to
predict the epidemic progression. The model predicted peak by late February,
showing gradual decline by end of April 2020. This was one of the few attempts
in prediction of COVID-19 infection trend in China [14, 15]; however, the
actual peak was observed in early February 2020 and the spread of infections
ended by the middle of March 2020.

Next, we review key studies of COVID-19 forecasting with deep learning models
in India. Anand et al. [62] focused on forecasting of COVID-19 cases in India
using RNNs such as LSTM and gated-recurrent units (GRU) with the dataset from
30th January 2020 to 21st July 2020. Bhimala et al. [63] incorporated the
weather conditions of different states to make improve forecasting of the
COVID-19 cases in different states of India. The authors made assumption that
different humidity levels in different states will lead to varying
transmission of infection within the population. They demonstrated that LSTM
model performed better in the medium and long range forecasting scale when
integrated with the weather data. Shetty [64] presented real-time forecasting
using a simple neural network for the COVID-19 cases in the state of Karnataka
in India where parameter selection for the model was based on cuckoo search
algorithm. The study reported that the mean-absolute percentage error (MAPE)
was reduced from 20.73 % to 7.03 % and the proposed model was further tested
on the Hungary COVID-19 dataset and reported promising results. Tomar and
Gupta [65] developed LSTM model for 30-day ahead prediction of COVID-19
positive cases in India where they also studied the effect of preventive
measures on the spread of COVID-19. They showed that with preventive measures
and lower transmission rate, the spread can be reduced significantly. Gupta et
al. [66] forecasted COVID-19 cases of India using support vector machines,
prophet, and linear regression models. Similarly, Bodapati et al. [67]
forecasted the COVID-19 daily cases, deaths caused and recovered cases with
the help of LSTM networks for the whole world. Chaurasia and Pal [68] used
several forecasting models such as simple average, single exponential
smoothing, Holt winter method, and ARIMA models for COVID-19 pandemic.

A number of machine learning methods used in conjunction with deep learning
models for COVID-19 forecasting for the rest of the world. Battineni et al.
[69] forecasted COVID-19 cases using a machine learning method known as
prophet logistic growth model which estimated that by late September 2020, the
outbreak can reach 7.56, 4.65, 3.01 and 1.22 million cases in the United
States, Brazil, India and Russia, respectively. Nadler et al. [70] used a
model embedded in a Bayesian framework coupled with a LSTM network to forecast
cases of COVID-19 in developed and developing countries. Istaiteh et al. [71]
compared the performance of ARIMA, LSTM, multilayer perceptron and
convolutional neural network (CNN) models for prediction of COVID-19 cases all
over the world. They reported that deep learning models outperformed ARIMA
model, and furthermore CNN outperformed LSTM networks and multi-layer
perceptron. Pinter et al. [72] used hybrid machine learning methods consisting
of adaptive network-based fuzzy inference systems (ANFIS) and mutlilayer
perceptron (simple neural network) for COVID-19 infections and mortality rate
in Hungary.

##  3 Methodology: Forecasting COVID-19 novel infections with deep learning
models

We need to reconstruct the original time series into a state-space vector in
order to train deep learning models for multi-step-ahead prediction. Taken’s
theorem expresses that the reconstruction can reproduce important features of
the original time series [73]. Hence, an embedded phase space
$Y(t)=[(x(t),x(t-T),...,x(t-(D-1)T)]$ can be generated given an observed time
series $x(t)$; where $T$ is the time delay, $D$ is the embedding dimension
(window size) $t=0,1,2,...,N-D-1$, and $N$ is the length of the original time
series. Appropriate values for $D$ and $T$ need to selected to efficiently
apply Taken’s theorem for reconstruction [74]. Taken’s proved that if the
original attractor is of dimension $d$, then $D=2d+1$ would be sufficient
[73].

###  3.1 LSTM network models

Recurrent neural networks (RNNs) have been prominent for modelling temporal
sequences. RNNs feature a context layer to act as memory in order to project
information from current state into future states, and eventually the output
layer. Although number of different RNN architectures exist, the Elman RNN
[33, 75] is one of the earliest which has been prominent for modelling
temporal sequences and dynamical systems [76, 39, 77].

Training RNNs in the early days has been a challenging task. Backpropagation-
through-time (BPTT) which is an extension of the backpropagation algorithm has
been prominent in training RNNs [34]. BPTT features gradient-descent where the
error is backpropagated for a deeper network architecture that features states
defined by time. The RNN unfolded in time is similar to a multilayer
perceptron that features multiple hidden layers. A major limitation of BPTT
for simple RNNs has been the problem of learning long-term dependencies given
vanishing and exploding gradients [78]. The LSTM network addressed this
limitation with better capabilities in remembering the long-term dependencies
using memory cells in the hidden layer [35]. The memory cells help in
remembering the long-term dependencies in data as shown in Figure 1.

Fig 1:  LSTM memory cell in the LSTM recurrent neural network.

The LSTM network model calculates a hidden state output $h_{t}$ by

$\displaystyle i_{t}$
$\displaystyle=\sigma\big{(}x_{t}U^{i}+h_{t-1}W^{i}\big{)}$ (1) $\displaystyle
f_{t}$ $\displaystyle=\sigma\big{(}x_{t}U^{f}+h_{t-1}W^{f}\big{)}$
$\displaystyle o_{t}$
$\displaystyle=\sigma\big{(}x_{t}U^{o}+h_{t-1}W^{o}\big{)}$
$\displaystyle\tilde{C}_{t}$
$\displaystyle=\tanh\big{(}x_{t}U^{c}+h_{t-1}W^{c}\big{)}$ $\displaystyle
C_{t}$ $\displaystyle=\sigma\big{(}f_{t}\ast
C_{t-1}+i_{t}\ast\tilde{C}_{t}\big{)}$ $\displaystyle h_{t}$
$\displaystyle=\tanh(C_{t})\ast o_{t}$

where, $i_{t}$, $f_{t}$ and $o_{t}$ refer to the input, forget and output
gates, at time $t$, respectively. $c$ refers to the memory cell. $x_{t}$ and
$h_{t}$ refer to the number of input features and number of hidden units,
respectively. $W$ and $U$ are the weight matrices adjusted during learning
along with $b$, which is the bias. Note that all the gates have the same
dimensions $d_{h}$, which is given by the size of hidden state.
$\tilde{C}_{t}$ is the intermediate cell state, and $C_{t}$ is the current
cell memory. The initial values at $t=0$ are given by $C_{0}=0$ and $h_{0}=0$.
Note that we denote (*) as element-wise multiplication.

###  3.2 Bi-directional LSTM networks

Conventional RNN and LSTM networks only make use of previous context state for
determining future states. Bidirectional RNNs (BD-RNNs) [79] on the other
hand, process information in both directions with two separate hidden layers
which are then propagated forward to the same output layer. Hence, two
independent RNNs are placed together to allow both backward and forward
information about the sequence at every time step. The forward hidden sequence
$h_{f}$, the backward hidden sequence $h_{b}$, and the output sequence $y$ are
computed by iterating the backward layer from $t=T$ to $t=1$, and the forward
layer from $t=1$ to $t=T$.

Bi-directional LSTM networks (BD-LSTM) [80] can access longer-range context or
state in both directions similar to BD-RNNs. BD-LSTM networks were originally
proposed for word-embedding in natural language processing [80] tasks and have
been used in several real-world sequence processing problems such as phoneme
classification [80], continuous speech recognition [81], and speech synthesis
[82].

BD-LSTM networks intake inputs in two ways; one from past to future, and
another from future to past by running information backwards so that state
information from the future is preserved. Given two hidden states combined in
any point in time, the network can preserve information from both past and
future as shown in Figure 2.

Fig 2:  Bi-directional LSTM recurrent neural network.

###  3.3 Encoder-Decoder LSTM networks

The encoder-decoder LSTM network (ED-LSTM) [83] was introduced as a sequence
to sequence model for mapping a fixed-length input to a fixed-length output.
The length of the input and output may differ which makes them applicable in
automatic language translation tasks (English to French for example) which can
be extended to multi-step series prediction where both the input and outputs
are of variable lengths. A latent vector representation is used to handle
variable-length input and outputs by first encoding the input sequences, one
at a time and then decoding it. We consider the input sequence
$(x_{1},...,x_{n})$ with corresponding output sequence $(y_{1},...,y_{m})$,
and estimate the conditional probability of the output sequence given an input
sequence, i.e. $p(y_{1},...,y_{m}|x_{1},...,x_{n})$. In the encoding phase,
given an input sequence, the ED-LSTM network computes a sequence of hidden
states. In the decoding phase, it defines a distribution over the output
sequence given the input sequence as shown in Figure 3.

Fig 3:  Encoder-Decoder LSTM recurrent neural network. Note that the outputs
$(y_{1},...,y_{m})$ with corresponding input $(x_{1},...,x_{n})$ are not
explicitly shown.

###  3.4 India: Situation Report: 8th October, 2021

We provide a visual representation of the total number of COVID-19 infections
for different states and union territories in India based on data till 8th
October, 2021.

Tables 1 2, 3, and 4 provide a rank of top ten Indian states with total cases
1st of every month. We see that largely populated states such as Maharashtra
(population estimate of 123 million [84]) has been leading India in number of
total cases through-out 2020. We note that state of Uttar Pradesh has estimate
population of 238 million has managed better. Delhi has a relatively smaller
population (estimated 19 million [84]), but high population density and hence
been one of the leading states with COVID-19 infections (in top 6 throughout
2020). Tables 3 and 4 show that in 2021, Maharashtra continued leading;
however, the second position was overtaken by Kerala from February which
maintained the position since then. We note that from February to June 2021,
India experienced the second-wave of infections from the delta-variant of the
virus, with Maharashtra and Kerala leading most of the time in terms of
monthly infections. The first peak for novel cases in India was reached on
September 16th 2020 with 97,894 daily and 93,199 weekly average novel cases
[15]. The daily novel cases were steady for several months and then raised
again from February 2021 for the second wave of infections. The peak of the
second wave was reached around 7th May 2021, with 401,078 daily and weekly
average of 389,672 novel infections [15]. The peak of deaths was reached
around 21st May 2021 with 4194 deaths and 4188 weekly average.

Figures 4 and 5 present the total number of novel weekly cases for different
groups of Indian states and union territories, which covers both the first and
second wave of infections. We notice that the number of cases significantly
increased after May 2020 which marks the first wave and then declined. Figure
4 (Panel a) focusing on major affected states show that Maharastra led the
first and second wave of infections followed by Karnataka. In Figure 4 Panel
(b), considering the Eastern states, we find that new cases in West Bengal
drastically increased for the first wave of infections and it took Bihar
longer to reach the peak when compared to Odisha and the others. In the second
wave, West Bengal led the other states by a large margin. In the Northern
states, shown in Figure 5 (Panel a), we find that Uttar Pradesh leading the
first and second wave of infections which is not surprising since it is the
most populous state of India. In the case of the relatively lowly populated
states (small states) shown in Figure 5 (Panel b), we find that Goa and
Tripura lead the first wave of infections and later in the second wave, Goa
overtakes the rest of the states, significantly.

---

(a) Major affected states

(b) Eastern states

Fig 4: Weekly average of new cases for groups of Indian states and union
territories [15].

---

(a) Northern states

(b) Small states

Fig 5: Weekly average of new cases for groups of Indian states and union
territories [15].

Figure 6 presents daily active cases and cumulative (total) deaths for key
Indian states for 2021 [15]. We notice that the different states, such as
Maharastra and Tamil Nadu have few to several weeks of lag in reaching the
peak of novel daily cases. In terms of deaths, we do not see a sharp increase
after July 2021 in most of states. Note that we chose not to show daily deaths
in the same graphs since the scales between active cases and deaths are quite
different.

Fig 6:  Daily active cases and cumulative death in key states of India for 2021 [15].  Rank | April | May | June | July | August
---|---|---|---|---|---
1 | Maharashtra | Maharashtra | Maharashtra | Maharashtra | Maharashtra
| (302) | (10498) | (67655) | (174761) | (422118)
2 | Kerala | Gujarat | Tamil Nadu | Tamil Nadu | Tamil Nadu
| (241) | (4395) | (22333) | (90167) | (245859)
3 | Tamil Nadu | Delhi | Delhi | Delhi | Andhra Pradesh
| (234) | (3515) | (19844) | (87360) | (140933)
4 | Delhi | Madhya Pradesh | Gujarat | Gujarat | Delhi
| (152) | (2719) | (16779) | (32557) | (135598)
5 | Uttar Pradesh | Rajasthan | Rajasthan | Uttar Pradesh | Karnataka
| (103) | (2584) | (8831) | (23492) | (124115)
6 | Karnataka | Tamil Nadu | Madhya Pradesh | West Bengal | Uttar Pradesh
| (101) | (2323) | (8089) | (18559) | (85461)
7 | Telengana | Uttar Pradesh | Uttar Pradesh | Rajasthan | West Bengal
| (96) | (2281) | (7823) | (18014) | (70188)
8 | Rajasthan | Andhra Pradesh | West Bengal | Telengana | Telengana
| (93) | (1463) | (5501) | (16339) | (62703)
9 | Andhra Pradesh | Telengana | Bihar | Karnataka | Gujarat
| (83) | (1039) | (3815) | (15242) | (61438)
10 | Gujarat | West Bengal | Andhra Pradesh | Andhra Pradesh | Bihar
| (82) | (795) | (3679) | (14595) | (51233)
Table 1: Rank of states by number of novel total cases taken at the 1st of every month for April to August 2020 [15]. The number of novel cases are shown in brackets.  Rank | September | October | November | December
---|---|---|---|---
1 | Maharashtra | Maharashtra | Maharashtra | Maharashtra
| (792541) | (1384446) | (1678406) | (1823896)
2 | Andhra Pradesh | Andhra Pradesh | Karnataka | Karnataka
| (434771) | (693484) | (823412) | (884897)
3 | Tamil Nadu | Karnataka | Andhra Pradesh | Andhra Pradesh
| (428041) | (601767) | (823348) | (868064)
4 | Karnataka | Tamil Nadu | Tamil Nadu | Tamil Nadu
| (342423) | (597602) | (724522) | (781915)
5 | Uttar Pradesh | Uttar Pradesh | Uttar Pradesh | Kerala
| (230414) | (399082) | (481863) | (602982)
6 | Delhi | Delhi | Kerala | Delhi
| (174748) | (279715) | (43310) | (570374)
7 | West Bengal | West Bengal | Delhi | Uttar Pradesh
| (162778) | (257049) | (386706) | (543888)
8 | Bihar | Odisha | West Bengal | West Bengal
| (136457) | (219119) | (373664) | (483484)
9 | Telengana | Kerala | Odisha | Odisha
| (127697) | (196106) | (290116) | (318725)
10 | Assam | Telengana | Telengana | Telengana
| (109040) | (193600) | (240048) | (270318)
Table 2: Rank of states by number of novel total cases taken at the 1st of every month for September to December 2020 [15]. The number of novel cases are shown in brackets.  Rank | January | February | March | April | May
---|---|---|---|---|---
1 | Maharashtra | Maharashtra | Maharashtra | Maharashtra | Maharashtra
| (2026399) | (2155070) | (2812980) | (4602472) | (5746892)
2 | Karnataka | Kerala | Kerala | Kerala | Karnataka
| (939387) | (1059403) | (1124584) | (1571183) | (2604431)
3 | Kerala | Karnataka | Karnataka | Karnataka | Kerala
| (929178) | (951251) | (997004) | (1523142) | (2526579)
4 | Andhra Pradesh | Andhra Pradesh | Andhra Pradesh | Uttar Pradesh | Tamil Nadu
| (887836) | (889916) | (901989) | (1252324) | (2096516)
5 | Tamil Nadu | Tamil Nadu | Tamil Nadu | Tamil Nadu | Andhra Pradesh
| (838340) | (851542) | (886673) | (1166756) | (1693085)
6 | Delhi | Delhi | Delhi | Delhi | Uttar Pradesh
| (635096) | (639289) | (662430) | (1149333) | (1691488)
7 | Uttar Pradesh | Uttar Pradesh | Uttar Pradesh | Andhra Pradesh | Delhi
| (600299) | (603527) | (617194) | (1101690) | (1426240)
8 | West Bengal | West Bengal | West Bengal | West Bengal | West Bengal
| (569998) | (575118) | (586915) | (828366) | (1376377)
9 | Odisha | Odisha | Chhattisgarh | Chhattisgarh | Chhattisgarh
| (335072) | (337191) | (349187) | (728700) | (971463)
10 | Rajasthan | Rajasthan | Odisha | Rajasthan | Rajasthan
| (317491) | (320336) | (340917) | (598001) | (939958)
Table 3: Rank of states by number of novel total cases taken at the 1st of every month for January to May 2021 [15]. The number of novel cases are shown in brackets.  Rank | June | July | August | September
---|---|---|---|---
1 | Maharashtra | Maharashtra | Maharashtra | Maharashtra
| (6061404) | (6303715) | (6464876) | (6541119)
2 | Kerala | Kerala | Kerala | Kerala
| (2924165) | (3390761) | (4057233) | (4613937)
3 | Karnataka | Karnataka | Karnataka | Karnataka
| (2843810) | (2905124) | (2949445) | (2972620)
4 | Tamil Nadu | Tamil Nadu | Tamil Nadu | Tamil Nadu
| (2479696) | (2559597) | (2614872) | (2655572)
5 | Andhra Pradesh | Andhra Pradesh | Andhra Pradesh | Andhra Pradesh
| (1889513) | (1966175) | (2014116) | (2045657)
6 | Uttar Pradesh | Uttar Pradesh | Uttar Pradesh | Uttar Pradesh
| (1706107) | (1708441) | (1709335) | (1709761)
7 | West Bengal | West Bengal | West Bengal | West Bengal
| (1499783) | (1528019) | (1548604) | (1565645)
8 | Delhi | Delhi | Delhi | Delhi
| (1434188) | (1436265) | (1437764) | (1438685)
9 | Chhattisgarh | Chhattisgarh | Odisha | Odisha
| (994480) | (1002008) | (1007750) | (1023735)
10 | Rajasthan | Odisha | Chhattisgarh | Chhattisgarh
| (952422) | (977268) | (1004451) | (1005229)
Table 4: Rank of states by number of novel total cases taken at the 1st of
every month for June to September 2021 [15]. The number of novel cases are
shown in brackets.

##  4 Results

In this section, we present results of prediction of COVID-19 daily cases in
India using prominent LSTM neural network models that includes, BD-LSTM and
ED-LSTM with architectural details given earlier (Section 3).

###  4.1 Experimental Design

Our experiments consider the evaluation of the respective models for
univariate and multivariate prediction tasks. The data has been accessed from
Indian Institute of Statistical Science - Bangalore [85], which was originally
sourced from Ministry of Health and Family Welfare, Government of India
website [86]. The dataset is based on daily novel cases which is normalised
taking the maximum number of daily cases over the entire data into account. We
start our analysis from 15th April 2020 and use rolling mean of 3 days to
smoothen the original data. We reconstruct the univariate and multivariate
time series into a state-space vector using Taken’s theorem [73] with selected
values for embedding dimension window ($D=6$) and time-lag ($T=2$) for multi-
step ahead (MSA) prediction. We consider four prediction horizons; i.e.
$MSA=4$, where each step is a prediction horizon.

The Adam optimizer is used for training the respective LSTM models. Table 5
and Table 6 describe the topology for the respective LSTM models for
univariate and multivariate cases, respectively. In case of multivariate
model, the input contains four features which represents the adjacent states
in relation to the state taken into account; i.e. the case of Maharashtra
(Maharashtra, Gujarat, Madhya Pradesh, Uttar Pradesh) and the case of Delhi
(Delhi, Rajasthan, Uttar Pradesh, Haryana). In multivariate model of India, we
take all the states as input features to the multivariate model. We note that
similar to univariate model, the multivariate model considers a selected
embedding dimension window ($D=6$) for multi-step-ahead prediction ($MSA=4$).
Table 5 and 6 provides the details for the respective LSTM model typologies in
terms of the hidden neurons and layers.

Method | Input | Hidden layer 1 | Hidden layer 2 | Output
---|---|---|---|---
LSTM | (6,1) | 32 | 32 | (1,4)
BD-LSTM | (6,1) | 32 | 16 | (1,4)
ED-LSTM | (6,1) | 32 | - | (1,4)
Table 5: Respective LSTM model topologies for the univariate case. Method | Input | Hidden-layer | Output
---|---|---|---
LSTM | (6,4) | 32 | (1,4)
BD-LSTM | (6,4) | 32 | (1,4)
ED-LSTM | (6,4) | 32 | (1,4)
Table 6: Respective LSTM model topologies for the multivariate case.

We review the performance of the respective methods in terms of scalability
and robustness which refers to the ability of maintaining consistent
prediction performance as the prediction horizon increases. We use the root
mean squared error (RMSE) in Equation 2 as the main performance measure for
prediction accuracy

$RMSE=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(y_{i}-\hat{y}_{i})^{2}}$ (2)

where $y_{i},\hat{y}_{i}$ are the observed data, predicted data, respectively.
$N$ is the length of the observed data. We use RMSE for each prediction
horizon and for each problem, we report the mean error for the respective
prediction horizons.

We present the mean and 95 % confidence interval for 30 experiment runs with
different initialisation of model parameter space (weights and biases) in all
the experiments. We use a dropout rate of 0.2 for the respective models in all
the experiments.

###  4.2 Prediction performance

We first evaluate the optimal strategy for creating training and testing
datasets. We use static-split of training samples from 15th April 2020 to 15th
May 2021. Our test set features data from 16th May 2021 to 27th September
2021; hence, the training data covers half of the second wave of the cases. In
random-split, we create the train and test sets by randomly shuffling the
dataset with the same size of the dataset as done for the static-split. We
show results for entire case of India, and two leading states of COVID-19
infections, i.e. Maharashtra and Delhi. We investigate the effect of the
univariate and multivariate approaches on the three models, (LSTM, BD-LSTM,
ED-LSTM). Finally, using the best model, we provide a two month outlook for
novel daily cases with a recursive approach, i.e. by feeding back the
predictions into the trained models.

Figure 7 shows univariate LSTM, BD-LSTM and ED-LSTM models with a static-split
of train/test dataset. Figure 8 shows univariate random splitting of
train/test datasets using the same models. We observe that the prediction for
the India dataset has a unique trend where the model is improving with
increase in the prediction horizon (steps) when compared to Maharashtra and
Delhi cases (Panels d and f). The corresponding cases in random-split given in
Figure 8 show a different trend and better accuracy (with lower RMSE) where
ED-LSTM provides the best test accuracy. In general, we find that random-split
with ED-LSTM provides the best performance accuracy for the given univariate
models.

Figure 9 shows results for the multivariate approach, where we use the same
methods used in the univariate approach (LSTM, ED-LSTM, BD-LSTM). We find that
ED-LSTM model gives best performance for the test datasets for all the
respective datasets. Figure 10 shows results for the case of random shuffling
of train/test dataset using the respective methods. We notice that ED-LSTM at
times, provides slightly worse performance when compared to BD-LSTM. Moreover,
the performance is not as good when compared to static-split (Figure 9) and in
general, we find that ED-LSTM with static-split provides the best performance
accuracy.

Tables 7 8 provide a summary of results in terms of the test dataset
performance accuracy (RMSE) by the respective models for random-split and
static-split, which have been given in Figures 7, 8, 9 and 10. In the
univariate models, ED-LSTM provides the best performance accuracy across most
of the three different datasets while LSTM performs best only for a single
case (Figure 7, Panel a). In multivariate models, BD-LSTM and ED-LSTM provide
the best performance accuracy for most cases while LSTM performs best only for
a single case (Figure 10, Panel a).

---

(a) India (train and test)

(b) India (test horizon)

(c) Maharashtra (train and test)

(d) Maharashtra (test horizon)

(e) Delhi (train and test)

(f) Delhi (test horizon)

Fig 7: Univariate LSTM, BD-LSTM and ED-LSTM model performance accuracy (RMSE)
with a static-split for the train and test datasets, and test prediction
horizons (steps). The error bars represent the mean and 95 % confidence
interval for 30 experiment runs.

---

(a) India (train and test)

(b) India (test horizon)

(c) Maharashtra (train and test)

(d) Maharashtra (test horizon)

(e) Delhi (train and test)

(f) Delhi (test horizon)

Fig 8: Univariate LSTM, BD-LSTM and ED-LSTM model performance accuracy (RMSE)
with a random-split for the train and test datasets, and the test prediction
horizons (steps). The error bars represent the mean and 95 % confidence
interval for 30 experiment runs.

---

(a) India (train and test)

(b) India (test horizon)

(c) Maharashtra (train and test)

(d) Maharashtra (test horizon)

(e) Delhi (train and test)

(f) Delhi (test horizon)

Fig 9: Multivariate model performance accuracy (RMSE) using LSTM, BD-LSTM and
ED-LSTM with a static-split for the train and test datasets, and test
prediction horizon (steps). The error bars represent the mean and 95 %
confidence interval for 30 experiment runs.

---

(a) India (train and test)

(b) India (test horizon)

(c) Maharashtra (train and test)

(d) Maharashtra (test horizon)

(e) Delhi (train and test)

(f) Delhi (test horizon)

Fig 10: Multivariate model performance accuracy (RMSE) using LSTM, BD-LSTM and
ED-LSTM with a random-split for the train and test datasets, and test
prediction horizons (steps). The error bars represent the mean and 95 %
confidence interval for 30 experiment runs.

Model | India | Delhi | Maharashtra
---|---|---|---
| Random Split | Static Split | Random Split | Static Split | Random Split | Static Split
| RMSE | Std. Dev. | RMSE | Std. Dev. | RMSE | Std. Dev. | RMSE | Std. Dev. | RMSE | Std. Dev. | RMSE | Std. Dev.
LSTM | 19734 | 1703 | 35540 | 6728 | 1568 | 34 | 266 | 30 | 4762 | 195 | 1925 | 160
BD-LSTM | 21058 | 1746 | 37948 | 6301 | 1628 | 75 | 242 | 22 | 4653 | 214 | 1748 | 195
ED-LSTM | 10732 | 1038 | 62595 | 8932 | 825 | 2 | 435 | 185 | 2365 | 146 | 1594 | 543

Table 7: Univariate model performance accuracy on test dataset (RMSE mean and
standard deviation for 30 experimental runs across 4 prediction horizons).

Model | India | Delhi | Maharashtra
---|---|---|---
| Random Split | Static Split | Random Split | Static Split | Random Split | Static Split
| RMSE | Std. Dev. | RMSE | Std. Dev. | RMSE | Std. Dev. | RMSE | Std. Dev. | RMSE | Std. Dev. | RMSE | Std. Dev.
LSTM | 19524 | 496 | 13325 | 2145 | 1413 | 38 | 1693 | 650 | 3981 | 162 | 1983 | 414
BD-LSTM | 18677 | 521 | 9271 | 1438 | 1449 | 43 | 2021 | 259 | 3888 | 108 | 1886 | 389
ED-LSTM | 22274 | 2174 | 15250 | 6356 | 1621 | 163 | 801 | 394 | 4925 | 503 | 2211 | 478

Table 8: Multivariate model prediction accuracy on the test dataset (RMSE mean
and standard deviation for 30 experimental runs across 4 prediction horizons).

---

(a) India LSTM

(b) India BD-LSTM

(c) Maharashtra LSTM

(d) Maharashtra BD-LSTM

(e) Delhi LSTM

(f) Delhi BD-LSTM

Fig 11: Recursive univariate LSTM and BD-LSTM models predictions for next 60
days (October and November 2021). The uncertainty (95 % confidence interval
shaded in green) and mean prediction is shown in solid black line.

Next, we select two univariate recursive models using random-split for the
three datasets to provide a two months outlook for COVID-19 daily infections.
In this approach, we use the predictions using the test dataset and extend it
further for two months (October and November 2021), recursively. Figure 11
presents results for univariate LSTM and BD-LSTM models. The uncertainty (95 %
confidence interval shaded in green) and mean prediction is shown in solid
black line for 30 experiment runs. We notice that there is a trend of general
decline in cases and we also find that the LSTM models well capture the spike
and fall in cases every few days.

##  5 Discussion

The COVID-19 pandemic in India was hit by two major peaks with one in May-
October 2020 and the other more deadly in April-June 2021. Surprisingly, the
first Indian peak in new cases was reached around the time when the government
began lifting nationwide lockdown and focused more on state-level and hot-spot
based lock downs [87, 88]; however, there were strict restrictions, such as
maintaining social distance and use of face-masks [89]. The second wave struck
due to multiple factors and highly-infectious variant-of-concern, also known
as SARS-CoV-2 delta variant [23]. A lack of preparation by the authorities in
setting up temporary hospitals, shortage of resources such as oxygen and poor
management of lockdowns led to major rise of the cases.

There are number of challenges in COVID-19 forecasting due to the nature of
the infections, reporting of cases, and effect of lock downs. Nevertheless,
despite the challenges and given limited dataset, we have been successful in
developing LSTM models for forecasting trend of daily new cases. Our long-term
forecasts for two months (October and November 2021) show a steady decline in
new cases in India in the respective states. We find that Delhi’s two monthly
forecasts provide (Figure 11) more uncertainty when compared to Maharashtra
and India datasets. We also notice that there is similar level of uncertainty
by LSTM and BD-LSTM models for India and Delhi datasets. The major reason the
uncertainties are different when you compare Delhi and Maharashtra with rest
of India is due to the difference in the trend of cases. In Delhi [15],
multiple peaks were observed since the first wave of infections in 2020,
whereas in the India dataset, there were only two major peaks. In Maharashtra,
a minor peak was observed in November 2021 (Figure 4, Panel a) after the first
wave of infections. Hence, the tends captured in the training dataset were
relatively different from the states (Maharashtra and Delhi), when compared to
India dataset. This suggests that the predictions for Maharashtra and Delhi
are less certain since they had multiple peaks and outbreaks in the past. The
second wave of infections in 2021 began in Maharashtra [90, 91] which has been
the state that held one of the most number of COVID-19 cases and novel daily
infections (Tables 1 - 4) [15].

The model uncertainty increases due to the limitations in the dataset and
models. Our framework has been limited in capturing social-cultural aspects,
population density, and level of lockdowns due to missing information and
data. Moreover, inter-state travels and the chaotic nature of spread of
COVID-19 infections makes it increasingly harder to provide reliable long-term
forecasts. In order to improve forecasting results, the models need to
incorporate more features in the data. The model needs to capture features
such as travel behaviour, level of lockdowns, compliance in masks and other
restrictions, social and cultural lifestyle, local area population density,
work and income thresholds, state-wise vaccination rate, and accessibility to
information.

We take into account the population density as five Indian cities make the top
50 mostly densely populated cities in the world [92], where Mumbai ranks 5th
and Delhi the 40th. The impact of COVID-19 on Indian gross domestic product
(GDP) is significant, but not as bad when compared to some of the developed
western nations [93, 94]. One of the most crucial aspect of management of
spread of COVID-19 infections is the role the government played in timely
closing their international borders and enforcing lock-downs to various
degrees. We need to note that different countries have different geographical
and population dynamics, such as population density and culture. It is not a
good idea to compare cities given difference in population density although
the overall population may be similar. Overall, it is also important to look
at cultural factors such as rituals [95], and role of nuclear and extended
families [96]. In countries such as India, there is large portion of inter-
state migrant workers [97] and also a large portion of the population is in
rural areas [98] that also have extended families. These factors made further
challenges in containing the spread of COVID-19 infections and are hard to be
captured by computational and mathematical models.

In future work, it is important to incorporate robust uncertainty
quantification in collection and sampling data model training and model
parameters; hence, Bayesian deep learning framework for COVID-19 forecasts
would be needed [99, 100, 101, 102]. Moreover, ensemble-based learning methods
can be used to combine the different types of LSTM models used in this study.
We could also develop similar models for death rate and other trends related
to COVID-19. Moreover, deep learning models could be used to jointly model the
rise and fall of cases and the effect it has on the economy.

##  6 Conclusions

We presented a framework for employing LSTM-based models for COVID-19 daily
novel infection forecasting for India. Our research incorporated some of the
latest and most prominent forecasting tools via deep learning, and highlighted
the challenges given limited data and the nature of the spread of infections.

Our results show the challenges of forecasting given limited data which is
highly biased given that we have two major peaks when considering the pandemic
in India. We found that the India and Maharashtra datasets had similar trend
in novel cases and model performance. We evaluated univariate and multivariate
LSTM-based models with different ways of creating training and test data. The
LSTM model variants showed certain strengths and limitations in different
scenarios that made it difficult to choose a single model. Generally, we found
that the univariate random-split ED-LSTM model provides the best test
performance in comparison to rest of the models. Therefore, the data from the
adjacent states did not have much effect in the multivariate model since it
could not outperform the univariate model. The two months ahead forecast
showed a general decline in new cases; however, the authorities need to be
vigilant.

## Software and Data

Data and open source code in Python is available for further analysis:
https://github.com/sydney-machine-learning/LSTM-COVID-19-India.

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