# Using SIR Model and Recurrence Formula to Predict the Spread of COVID-19 in Sambalpur: A Mathematical Study

• Roushnee Naik Department of Science and Mathematics, Regional Institute of Education (NCERT), Bhubaneswar, Odisha, India https://orcid.org/0000-0002-5606-7744
• S. Kapoor Department of Science and Mathematics, Regional Institute of Education (NCERT), Bhubaneswar, Odisha, India
Keywords: COVID-19, SIR Model, recurrence formula, spread

### Abstract

Corona Virus has spread across the globe and is creating havoc. Lockdown is being imposed worldwide depending on the number of cases. Everyone are advised to wear masks, follow social distancing, and use hand sanitizers to keep them safe. But all these precautions are not enough to curb the spread of the disease. People are still getting infected even after taking proper precautions and obeying the lockdown rule. We need to know in advance the approximate number of infected people so that we can devise better precautionary measures to curb the spread of the virus. So we use a simple SIR Model and solve it using basic differentiation and integration techniques and then use recurrence formula approach to predict the spread of COVID-19 in the city of Sambalpur of Odisha state. We compare the outcome of the model with the real time data and we arrive at the conclusion that the model is efficient in predicting the spread using the recurrence formula till the date 05/06/2021.

### Author Biographies

Roushnee Naik, Department of Science and Mathematics, Regional Institute of Education (NCERT), Bhubaneswar, Odisha, India

Roushnee Naik 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.(Mathematics) at Govt. Autonomous College, Rourkela.

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

S. Kapoor is an Assistant Professor of Mathematics at the Regional Institute of Education, Bhubaneswar (A Unit of National Council of Educational Research and Training, Delhi). He completed his Ph. D in Mathematics at IIT Roorkee.

Dr Kapoor is presently working in the fields of Computational Fluid Dynamics, Applied Numerical Method, Hydrodynamics Stability in Porous Media.

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