Research Article
A Study for Plausible Third Wave of COVID-19 in India through
Fuzzy Time Series Modelling Based on Particle Swarm
Optimization and Fuzzy c-Means
Niteesh Kumar ,
1
Harendra Kumar ,
1
and Kamal Kumar
2
1
Department of Mathematics and Statistics, Gurukula Kangri (Deemed to be University), Haridwar 249404, Uttarakhand, India
2
Department of Mathematics, Amity School of Applied Sciences, Amity University Haryana, Haryana, India
Correspondence should be addressed to Harendra Kumar; balyan.kumar@gmail.com and Kamal Kumar;
kamalkumarrajput92@gmail.com
Received 16 December 2021; Revised 20 January 2022; Accepted 19 February 2022; Published 16 March 2022
Academic Editor: Juan Frausto-Solis
Copyright©2022NiteeshKumaretal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
e outbreak of COVID-19 has become a global pandemic as announced by World Health Organisation. As India has already met
the two waves, named first and second wave, it is assumed that COVID-19 will again strike in India in the form of third wave. e
peak during the upcoming third wave and determination of the approximated maximum number of COVID-19 infected cases and
deaths at a particular day becomes crucial for India. To determine the peak of infectious curve, this article proposed a hybrid fuzzy
time series forecasting model based on particle swarm optimization and fuzzy c-mean technique, named as fuzzy time series particle
swarm optimization extended fuzzy c-mean technique. e proposed model works in two phases. In phase-I, particle swarm
optimization extended fuzzy c-mean method is used to form initial intervals with the help of centroids, while in phase-II, these
intervals are updated to form subintervals. In the present article, a fitness function is developed for particle swarm optimization to
increase its convergence speed and basic fuzzy c-mean is extended by using an exponential function to tolerate the effect of outliers,
named as extended fuzzy c-mean technique. e effectiveness of the proposed model has been tested based on mean square error and
root mean square error on first and second wave COVID-19 data, and the obtained results are very close to the existing data of
COVID-19 with less error rate. us, the proposed model is suitable to forecast a better approximation value of COVID-19 infected
cases and deaths in India during the upcoming third wave. is study demonstrates that third wave of COVID-19 could occur in
India, while also illustrating that it is unlikely for any such resurgence to be as large as the second wave. e proposed model predicts
that the peak of third wave will occur approximately after 40–70 days from the mid of December. Furthermore, the impact of
vaccination on infected cases and deaths during the upcoming third wave in India is also studied. With the implementation of the
vaccine on the Indian people, the peak of COVID-19 infected during third wave will be shifted in forward direction. On the basis of
the proposed model, government authorities will be enabling to know expected required resources such as hospital patient beds, ICU
beds, and oxygen concentrators during the upcoming outspread of COVID-19 like disease in future.
1. Introduction
Currently, a novel virus has affected the whole world, named
as COVID-19. e outbreak of coronavirus disease 2019
(COVID-19) has become a global pandemic as announced
by WHO. At the end month of 2019, the COVID-19 infected
cases show accelerated growth in most countries. Based on
several reports, COVID-19 was originated from Wuhan,
China, in mid-December 2019. After a few days of its
appearance, it will affect the entire world’s people because of
its rapid growth. As a result, there is a drastic change in the
growth of COVID-19 confirmed cases and the mobility rate
isatapeakinIndia.Astimepasses,thenumberofconfirmed
cases slowly decreases. But no one knows that COVID-19
shows their dangerous mode once again with more infection
rate. From the last week of April 2021, the COVID-19 in-
fected cases rapidly increased and reached their peak in
India. Due to the invention of vaccine, the situation of
Hindawi
Mathematical Problems in Engineering
Volume 2022, Article ID 5878268, 22 pages
https://doi.org/10.1155/2022/5878268