# Numerical Forecasting of Covid-19 Epidemic in Odisha Using S.I.R Model: A Case Study

## Authors

• S. Kapoor Department of science and Mathematics, Regional Institute of Mathematics (NCERT), Bhubaneswar, Odisha, India
• Bidisha Jana Department of science and Mathematics, Regional Institute of Mathematics (NCERT), Bhubaneswar, Odisha, India

## Keywords:

SIR model, basic reproduction number, COVID-19, lockdown, herd immunity.

## Abstract

In this paper, we study the effectiveness of SIR model (Susceptible- Infected-
Removed) in predicting the future development of infectious disease caused
by SARS-CoV-2 virus for the Indian state of Odisha. This model helps in
checking the effectiveness of controlling measures like lockdown policies
and helps in framing new strategies to control the spread of the disease.
We formulate a set of differential equations to find the rate of change of
susceptible, infected and removed population with respect to time and solve
it using Euler’s method. Using the cumulative data of confirmed cases, we
try to find the answers to the question of COVID-19 surge. Also, through this
we predict the trend in the spread of covid-19 in the state for the next few
months. The analysis includes data from March 1 (which is marked as the
start of second wave of COVID) to June 28, 2021. We propose predictions
on various parameters and factors related to the spread of COVID-19 and
on the number of susceptible, infected and removed population until June 2021. By comparing the daily recorded data with the data from our modeling
approaches, we conclude that the spread of COVID-19 can be under control
in all communities, if proper lockdown restrictions and strong policies are
implemented to control the infection rates.

## Author Biographies

### S. Kapoor, Department of science and Mathematics, Regional Institute of Mathematics (NCERT), Bhubaneswar, Odisha, India

S. Kapoor is an Assistant professor of Mathematics at the Regional Institute
of Education, Bhubaneswar. He has completed his Ph.D. in Mathemat-
ics from IIT Roorkee. His area of specialization is computational Fluid
Dynamics, Hydrodynamics stability of flow through porous media, Applied
numerical method, FEM, B- Spline FEM, SEM, SCM, Numerical solution of
PDE

### Bidisha Jana, Department of science and Mathematics, Regional Institute of Mathematics (NCERT), Bhubaneswar, Odisha, India

Bidisha Jana is a student of Mathematics. She has completed her
B.Sc(mathematics).B.Ed from Regional Institute of Education, Bhubaneswar.
She is currently pursuing M.Sc. in Mathematics at Assam University, Silchar.

## References

Bagal, D., Rath, A., Barua, A., and Patnaik, D. (2021). Estimating the

parameters of susceptible-infected-recovered model of COVID-19 cases

in India during lockdown periods. Retrieved 27 August 2021, from

Biswas, S., Ghosh, J., Sarkar, S., and Ghosh, U. (2020). COVID-19 pandemic

in India: a mathematical model study. Nonlinear Dynamics, 102(1),

CDRI Report (2020). Response to COVID-19: Odisha, India. www.cdri.wor

ld/casestudy/response-tocovid19-by-odisha.pdf.

S. Kapoor and B. Jana

COVID-19: Odisha State Dashboard. State Dashboard. (2021). Retrieved 4

September 2021, from https://statedashboard.odisha.gov.in/.

Cooper, I., Mondal, A., and Antonopoulos, C. (2021). A SIR model assump-

tion for the spread of COVID-19 in different communities. Retrieved 27

August 2021, from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7

/.

Carcione, J., Santos, J., Bagaini, C., and Ba, J. (2021). A Simulation of a

COVID-19 Epidemic Based on a Deterministic SEIR Model. Retrieved

August 2021, from https://www.frontiersin.org/articles/10.3389/fpu

bh.2020.00230/full.

Garikipati N (2020).Odisha’s quiet success in warfare on Covid-19 pan-

demic. Coverage Circle. https://www.policycircle.org/life/odishas-

quiet-success-in-war-on-covid

Hojman, S., and Asenjo, F. (2020). Phenomenological dynamics of COVID-

pandemic: Meta-analysis for adjustment parameters. Chaos: An

Interdisciplinary Journal Of Nonlinear Science, 30(10), 103120. https:

//doi.org/10.1063/5.0019742

Infection rate – Wikipedia. (2021). Retrieved 9 September 2021, from https:

//en.wikipedia.org/wiki/Infection rate

Kumar M, Ghosh S (2020).Using lessons from disaster management, Odisha

takes on Covid-19. MONGABAY. https://india.mongabay.com/2020/04

/using-lessons-from-disaster-management-odisha-takes-on-covid-19/

Kumar S, Maheshwari V, Prabhu J, Prasanna M et al (2020). Social eco-

nomic impact of COVID-19 outbreak in India. Int J Pervasive Compute

Common 16(4):309–319. https://doi.org/10.1108/IJPCC-06-2020-0053

Kwok OK, Lai F et al. (2020). Herd immunity–estimating the level required to

halt the COVID-19 epidemics in affected countries. J Infect 80(6):32–33.

Mathematical modelling of infectious disease - Wikipedia. En.wikipedia.org.

(2021). Retrieved 27 August 2021, from https://en.wikipedia.org/wiki/

Mathematical modelling of infectious disease.

Mohanty D (2020).How the Covid-19 pandemic unfolded in Odisha. Hindus-

tan Times. www.hindustantimes.com/india-news/how-the-covid-19-p

andemic-unfolded-in-odisha/story-HVv0Y5KB1mGXiP1TiKrHI.html

Mukesh Jahar, P.K. Ahluwalia and Ashok Kumar. (2020). COVID-19 Epi-

demic Forecast in Different States of India using SIR Model. Retrieved

August 2021, from https://www.medrxiv.org/content/10.1101/2020

.05.14.20101725v1.full.pdf.

Numerical Forecasting of Covid-19 Epidemic in Odisha 115

Pani MB (2020).No End to COVID-19 containment woes for residents of

Katapali in Odisha. The New Indian Express. www.newindianexpress.c

om/states/odisha/2020/jul/30/no-end-to-covid-19-containment-woes-f

or-residents-of-katapali-in-odisha-2176649.html.

Pal M (2020).Empower gram panchayats to be able to deal with crises like

COVID-19 effectively in rural areas. National Herald.. www.nationalhe

raldindia.com/india/empower-gram-panchayats-to-beable-to-deal-with

-crises-like-covid-19-effectively-in-rural-areas

Riyapan, P., Shuaib, S., and Intarasit, A. (2021). A Mathematical Model of

COVID-19 Pandemic: A Case Study of Bangkok, Thailand. Retrieved 25

August 2021, from https://www.hindawi.com/journals/cmmm/2021/6

/.

Roberto Telles, C., Lopes, H., and Franco, D. (2021). SARS-COV-2: SIR

Model Limitations and Predictive Constraints. Symmetry, 13(4), 676.

Telles, C., Roy, A., Ajmal, M., Mustafa, S., Ahmad, M., and de la Serna, J.

et al. (2021). The Impact of COVID-19 Management Policies Tailored

to Airborne SARS-CoV-2 Transmission: Policy Analysis. JMIR Public

Health And Surveillance, 7(4), e20699. https://doi.org/10.2196/20699

Tiwari, V., Deyal, N., and Bisht, N. (2021). Mathematical Modeling Based

Study and Prediction of COVID-19 Epidemic Dissemination Under the

Impact of Lockdown in India. Retrieved 25 August 2021, from https:

//www.frontiersin.org/articles/10.3389/fphy.2020.586899/full.

Zaman, G., Jung, I., Torres, D., and Zeb, A. (2021). Mathematical Modeling

and Control of Infectious Diseases. Retrieved 23 August 2021, from ht

tps://www.hindawi.com/journals/cmmm/2017/7149154/.

2022-05-07

## How to Cite

Kapoor, S., & Jana, B. (2022). Numerical Forecasting of Covid-19 Epidemic in Odisha Using S.I.R Model: A Case Study. Journal of Graphic Era University, 10(2), 95–116. https://doi.org/10.13052/jgeu0975-1416.1023

Articles