# Analysis of COVID-19 epidemic with intervention impacts by a fractional operator

## Authors

• Sanjay Bhatter Department of Mathematics, Malaviya National Institute of Technology Jaipur, India
• Sangeeta Kumawat Department of Mathematics, Malaviya National Institute of Technology Jaipur, India
• Bhamini Bhatia Department of Mathematics, Malaviya National Institute of Technology Jaipur, India
• Sunil Dutt Purohit Department of HEAS (Mathematics), Rajasthan Technical University, Kota, India

## Keywords:

COVID-19, Intervention measures, Caputo fractional derivative, Normalized Sensitivity index, Numerical simulations

## Abstract

This study introduces an innovative fractional methodology for analyzing the dynamics of COVID-19 outbreak, examining the impact of intervention strategies like lockdown, quarantine, and isolation on disease transmission. The analysis incorporates the Caputo fractional derivative to grasp long-term memory effects and non-local behavior in the advancement of the infection. Emphasis is placed on assessing the boundedness and non-negativity of the solutions. Additionally, the Lipschitz and Banach contraction theorem are utilized to validate the existence and uniqueness of the solution. We determine the basic reproduction number associated with the model utilizing the next generation matrix technique. Subsequently, by employing the normalized sensitivity index, we perform a sensitivity analysis of the basic reproduction number to effectively identify the controlling parameters of the model. To validate our theoretical findings, numerical simulations are conducted for various fractional order values, utilizing a two-step Lagrange interpolation technique. Furthermore, the numerical algorithms of the model are represented graphically to illustrate the effectiveness of the proposed methodology and to analyze the effect of arbitrary order derivatives on disease dynamics.

## Author Biographies

### Sanjay Bhatter, Department of Mathematics, Malaviya National Institute of Technology Jaipur, India

Sanjay Bhatter is an assistant professor of mathematics in the Department of Mathematics, Malaviya National Institute of Technology, Jaipur, Rajasthan, India. His research interests include Special Functions, Fractional Calculus, Mathematical Modeling, Integral Transforms, and Integral Inequalities.

### Sangeeta Kumawat, Department of Mathematics, Malaviya National Institute of Technology Jaipur, India

Sangeeta Kumawat received graduation degree from S.S. Jain Subodh P.G. Autonomous College, Jaipur, India and M.Sc. degree from the Central University of Rajasthan, India. Currently, She is a research scholar at Department of Mathematics, Malaviya National Institute of Technology, Jaipur, India. Her research interests include Mathematical Modelling and Fractional Calculus.

### Bhamini Bhatia, Department of Mathematics, Malaviya National Institute of Technology Jaipur, India

Bhamini Bhatia received graduation degree from Tagore Aadarsh P.G. College, Jaipur, India and M.Sc. degree from JECRC University, Jaipur, India. Currently, She is a research scholar at Department of Mathematics, Malaviya National Institute of Technology, Jaipur, India. Her research interests include Mathematical Modelling and Fractional Calculus.

### Sunil Dutt Purohit, Department of HEAS (Mathematics), Rajasthan Technical University, Kota, India

Sunil Dutt Purohit obtained his M.Sc. (Gold Medalist) and Ph.D. degree from the faculty of science at Jai Narayan Vyas University, Jodhpur, India. He also had a Joiner and Senior Research Fellowship of Council of Scientific and Industrial Research (CSIR) and then worked in the Department of Mathematics and Statistics, Jai Narayan Vyas University, Jodhpur. After that he joint as Assistant Professor and Head, Department of Basic Sciences, Maharana Pratap University of Agriculture \& Technology, Udaipur, India. Currently, he is Associate Professor of Mathematics, Department of HEAS (Mathematics), Rajasthan Technical University, Kota. His research interest includes Special functions, Fractional Calculus, Integral transforms, Basic Hypergeometric Series, Geometric Function Theory and Mathematical Physics. He has published more than 120 research papers in international esteemed journals. He is reviewer for Mathematical Reviews, USA (American Mathematical Society) and Zentralblatt MATH, Berlin since last six years. He is member, Editorial Board for number of international mathematical and interdisciplinary journals.

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## Published

2024-07-24
CITATION
DOI: 10.11121/ijocta.1515
Published: 2024-07-24

## How to Cite

Bhatter, S., Kumawat, S., Bhatia, B. ., & Purohit, S. D. (2024). Analysis of COVID-19 epidemic with intervention impacts by a fractional operator. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 14(3), 261–275. https://doi.org/10.11121/ijocta.1515

## Section

Research Articles