Abstract
The objective of this article is to build an SEIR epidemic system for episode COVID-19 (novel crown) with fuzzy numbers. Mathematical models might assist with investigating the transmission elements, forecast and control of Covid-19. The fuzziness in the infection rate, increased death owing to COVID-19, and recovery rate from COVID-19 were all deemed fuzzy sets, and their member functions were used as fuzzy parameters in the SEIR system. The age lattice technique is used in the SEIR system to calculate the fuzzy basic reproduction number and the system’s stability at infection-free and endemic equilibrium points. Computer simulations are provided to comprehend the subtleties of the proposed SEIR COVID-19 model.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alzahrani, E., Khan, M.A.: Modeling the dynamics of Hepatitis E with optimal control. Chaos Solitons Fract 116, 287–301 (2018)
Barros, L.C., Bassanezi, R.C., Leite, M.B.F: The SI epidemiological models with a fuzzytransmission parameter. Comput. Math. Appl. 45, 1619–1628 (2003)
Zhou, L., Fan, M.: Dynamics of an SIR epidemic model with limited resources visited. Nonlinear Anal. Real World Appl. 13, 312–324 (2012)
Mccluskey, C.C.: Complete global stability for an SIR epidemic model with delay- distributed or discrete. Nonlinear Anal. 11(1), 55–59 (2010)
Bjornstad, O.N., Finkenstadt, B.F., Grenfell, B.T.: Dynamics of measles epidemics: estimating scaling of transmission rates using a time series SIR model. Ecol. Monogr. 72(2), 169–184 (2002)
Hu, Z., Ma, W., Ruan, S.: Analysis of SIR epidemic models with nonlinear incidence rate and treatment. Math. Biosci. 238(1), 12–20 (2012)
Diekmann, O., Heesterbeek, H., Britton, T.: Mathematical tools for understanding infectious disease dynamics. In: Princeton Series in Theoretical and Computational Biology. Princeton University Press, Princeton (2013)
Hethcote, H.W.: The mathematics of infectious disease. SIAM Rev. 42, 599–653 (2000)
He, S., Peng, Y., Sun, K.: SEIR modeling of the COVID-19 and its dynamics. Nonlinear Dyn. 101, 1667–1680 (2020)
Overton, C.E.: Using statistics and mathematical modeling to understand infectious disease outbreaks: COVID-19 as an example. Infect. Dis. Model. 5, 409–441 (2020)
Das, P., Upadhyay, R.K., Mishra, A.K.: Mathematical model of COVID-19 with comorbidity and controlling using non-pharmaceutical interventions and vaccination. Nonlinear Dyn. 106, 1213–1227 (2021)
Haitao, S., Zhongwei, J., Zhen, J., Shengqiang, L.: Estimation of COVID-19 outbreak size in Harban. China. Nonlinear Dyn. 106, 1229–1237 (2021)
Shidong, Z., Guoqiang, L., Huang, T.: Vaccination control of an epidemic model with time delay and its application to COVID-19. Nonlinear Dyn. 106, 1279–1292 (2021)
Mwalili, S., Kimathi, M., Ojiambo, O., Gathungu, D.: Seir model for COVID-19 dynamics incorporating the environment and social distancing. BMC Res. Notes (2020)
Shikha, J., Sachin, K.: Dynamical analysis of SEIS model with nonlinear innate immunity and saturated treatment. Eur. Phys. J. Plus 136 (2021)
Jafelice, R., Barros, L.C., Bassanezei, R.C., Gomide, F.: Fuzzy modeling in symptomatic HIV virus infected population. Bull. Math. Biol. 66, 1597–1620 (2004)
Massad, E., Burattini, M.N., Ortega, N.R.S.: Fuzzy logic and measles vaccination: designing a control strategy. Int. J. Epidemiol. 28, 550–557 (1999)
Mondal, P.K., Jana, S., Halder, P., Kar, T.K.: Dynamical behavior of an epidemic model in a fuzzy transmission. Int. J. Uncertain. Fuzziness Knowl-Based Syst. 23, 651–665 (2015)
Nagarajan, D., Lathamaheswari, M., Broumi, S., Kavikumar, J.: A new perspective on traffic control management using triangular interval type-2 fuzzy sets and interval neurosophic sets. Oper. Res. Perspect. 6, 100099 (2019)
Mishra, B.K., Pandey, S.K.: Fuzzy epidemic model for the transmission of worms in computer network. Nonlinear Anal. Real World Appl. 11(5), 4335–4341 (2010)
Gakkhar, S., Chavda, N.C.: Impact of awareness on the spread of dengue infection in human population. Appl. Math. 4(8), 142–147 (2013)
Phaijoo, G.R., Gurung, D.B.: Mathematical model of dengue disease transmission dynamics with control measures. J. Adv. Math. Comput. Sci. 23(3), 1–2 (2017)
Arqub, O.A., El-Ajou, A.M., Shawagfeh, N.: Analytical solutions of fuzzy initial value problem by HAM. Appl. Math. Inform. Sci. 7, 1903–1919 (2013)
Brauer, F., Castillo-Chavez, C.: Mathematical models in population biology and epidemiology. Texts Appl. Math. 2 (2012)
Acknowledgements
Supported by Organization Aditya College of Engineering and Technology, Surampalem, AP. and Vellore Institute of Technology, Vellore, Tamilnadu.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Murthy, B.S.N., Srinivas, M.N., Srinivas, M.A.S. (2022). Analysis of Fuzzy Dynamics of SEIR COVID-19 Disease Model. In: Banerjee, S., Saha, A. (eds) Nonlinear Dynamics and Applications. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-99792-2_119
Download citation
DOI: https://doi.org/10.1007/978-3-030-99792-2_119
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-99791-5
Online ISBN: 978-3-030-99792-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)