An SIR Model for COVID-19 Outbreak in India

Authors

  • S. Sweatha Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai, India https://orcid.org/0000-0003-2423-0575
  • P. Monisha Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai, India
  • S. Sindu Devi Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Ramapuram, Chennai 60089, India https://orcid.org/0000-0002-0907-4837

DOI:

https://doi.org/10.26713/cma.v13i2.1729

Keywords:

Reproduction number, Fuzzy basic reproduction number, Runge-Kutta method

Abstract

In this paper, we have proposed a SIR fuzzy epidemic model by taking the transmission rate and recovery rate as fuzzy numbers. The basic reproduction number and the fuzzy basic reproduction number have been computed. Further by considering the initial values for the susceptible, infected and recovered population the numerical simulation has been carried out using Runge-Kutta method. We can predict the transmission of the virus and prevent the COVID-19 outbreak in India with the results obtained from the proposed SIR model.

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References

M. Abdy, S. Side, S. Annas, W. Nur and W. Sanusi, An SIR epidemic model for COVID-19 spread with fuzzy parameter: the case of Indonesia, Advances in Difference Equations 2021 (2021), Article number: 105, DOI: 10.1186/s13662-021-03263-6.

J.L. Aron and I.B. Schwartz, Seasonality and period-doubling bifurcations in an epidemic model, Journal of Theoretical Biology 110(4) (1984), 665 – 679, DOI: 10.1016/S0022-5193(84)80150-2.

L.C. DE Barros, M.B.F. Leite and R.C. Bassanez, The SI epidemiological models with a fuzzy transmission parameter, Computers & Mathematics with Applications 45 (2003), 1619 – 1628, DOI: 10.1016/s0898-1221(03)00141-x.

R. Cherniha and V. Davydovych, A mathematical model for the COVID-19 outbreak and its applications, Symmetry 12(6) (2020), 990, DOI: 10.3390/sym12060990.

S.S. Devi and K. Ganesan, A new approach for the solution of fuzzy initial value problems through Runge-Kutta method, Journal of Informatics and Mathematical Sciences 12(2) (2020), 149 – 157, DOI: 10.26713/jims.v12i2.1144.

O. Diekmann, J.A.P. Heesterbeek and J.A.J. Metz, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, Journal of Mathematical Biology 28 (1990), 365 – 382, DOI: 10.1007/bf00178324.

P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Bioscience 180(1–2) (2002), 29 – 48, DOI: 10.1016/s0025-5564(02)00108-6.

W.O. Kermack and A.G. McKendrick, Contributions to the mathematical theory of epidemics–I, Bulletin of Mathematical Biology 53 (1991), 33 – 55, DOI: 10.1007/bf02464423.

N.A. Kudryashov, M.A. Chmykhov and M. Vigdorowitsch, Analytical features of the SIR model and their applications to COVID-19, Applied Mathematical Modelling 90 (2021), 466 – 473, DOI: 10.1016/j.apm.2020.08.057.

P.K. Mondal, S. Jana, P. Haldar and T.K. Kar, Dynamical behavior of an epidemic model in a fuzzy transmission, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 23(5) (2015), 651 – 665, DOI: 10.1142/S0218488515500282.

F. Ndaïrou, I. Area, J.J. Nieto and D.F. Torres, Corrigendum to “Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan” [Chaos Solitons Fractals 135 (2020), 109846], Chaos, Solitons & Fractals, 141 (2020), 110311, DOI: 10.1016/j.chaos.2020.110311.

F. Ndaïrou, I. Area, J.J. Nieto and D.F. Torres, Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan, Chaos, Solitons & Fractals 135 (2020), 109846, DOI: 10.1016/j.chaos.2020.109846.

K. Roosa, Y. Lee, R. Luo, A. Kirpich, R. Rothenberg, J.M. Hyman, P. Yan and G. Chowell, Short-term forecasts of the COVID-19 epidemic in Guangdong and Zhejiang, China: February 13–23, 2020, Journal of Clinical Medicine 9(2) (2020), 596, DOI: 10.3390/jcm9020596.

R. Verma, S.P. Tiwari and R.K. Upadhyay, Dynamical behaviour of fuzzy SIR epidemic model, in: Advances in Fuzzy Logic and Technology, Springer International Publishing (2017), 482 – 492, DOI: 10.1007/978-3-319-66827-7_45.

H.M. Youssef, N.A. Alghamdi, M.A. Ezzat, A.A. El-Bary and A.M. Shawky, A modified SEIR model applied to the data of COVID-19 spread in Saudi Arabia, AIP Advances 10(12) (2020), 125210, DOI: 10.1063/5.0029698.

L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338 – 353, DOI: 10.1016/S0019-9958(65)90241-X.

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Published

17-08-2022
CITATION

How to Cite

Sweatha, S., Monisha, P., & Devi, S. S. (2022). An SIR Model for COVID-19 Outbreak in India. Communications in Mathematics and Applications, 13(2), 661–669. https://doi.org/10.26713/cma.v13i2.1729

Issue

Vol. 13 No. 2 (2022)

Section

Research Article

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