Skip Navigation Links
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu


Stability Analysis of SIQS Mathematical Model for Pandemic Coronavirus Spread

Journal of Applied Nonlinear Dynamics 11(3) (2022) 591--603 | DOI:10.5890/JAND.2022.09.006

Vinay Verma

Faculty of Mathematical and Statistical Sciences, Institute of Natural Sciences and Humanities, Shri Ramswaroop

Memorial University, Lucknow Deva Road, Barabanki Uttar Pradesh-225003, India

Download Full Text PDF

 

Abstract

In this paper, we approach conceptual mathematical models for COVID-19 eruption and it's abstinence metering; quarantine. In this circumstance, mathematical models are a grandly tool to make use of an impressive strategy in order to fight against this pandemic. We define the positivity, boundedness of solutions and basic reproduction number. Then, we study local and global stability analysis of equilibrium to examine its epidemiological relevance. Our model represent the various transmission route in the infection dynamics, and diligence the role of the environmental reservoir in the transmission and dispersion of this disease. Simulation explication of the model ratify to the analytical results.

Acknowledgments

The author are thankful to the handling editor and anonymous both the referees for their useful comments and suggestions, which have improved the quality of this paper.

References

  1. [1]  Islam, M.S., Ira, J.I., Kabir, K.M.A., and Kamrujjaman, M. (2020), COVID-19 epidemic compartments model and Bangladesh, preprint, DOI:10.20944/preprints202004.0193.v1.
  2. [2]  Zhu, N., Zhang, D., Wang, W., Li, X., Yang, B., Song, J., Zhao, X., Huang, B., Shi, W., Lu, R., and Niu, P. (2020), A novel coronavirus from patients with pneumonia in China 2019, New England Journal of Medicine.
  3. [3]  Huang, C., Wang, Y., Li, X., Ren, L., Zhao, J., Hu, Y., Zhang, L., Fan, G., Xu, J., Gu, X., and Cheng, Z., (2020), Clinical features of patients infected with 2019 novel coronavirus in wuhan China, The Lancet, 395(10223), 497-506.
  4. [4]  National Health Commission of the People.s Republic of China (2020), http://www.nhc.gov.cn/xcs /yqfkdt/202004/ be27dc3c4a9544b081e2233537e762c3.shtml, accessed April 02.
  5. [5]  Gralinski, E.L. and Vineet, M.D. (2020), Return of the coronavirus: 2019-ncov, Viruses, 12(2), 135.
  6. [6]  Centers for disease control and prevention, (2020), 2019 novel coronavirus, https://www.cdc.gov/coronavirus/ 2019-ncov, Retrieved: 2020-03-10.
  7. [7]  Dubey, B., Dubey, P., and Dubey, U.S. (2015), Dynamics of an SIR model with nonlinear incidence and treatment rate, Appl and Appli Math, 10(2), 718-737.
  8. [8]  Dubey, B., Patra, A., Srivastava, P.K., and Dubey, U.S. (2013), Modeling and analysis of an SEIR model with different types of nonlinear treatment rates, J. Biol. Sys., 21(03), 1350023.
  9. [9]  Misra, A.K., Sharma, A., and Shukla, J.B. (2011), Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases, Math. Comput. Model., 53(5-6), 1221-1228.
  10. [10]  Misra, A.K., Rai, R.K., and Takeuchi, Y. (2019), Modeling the impact of sanitation and awareness on the spread of infectious diseases, Math. Bio. and Eng., 16(2), 667-700.
  11. [11]  Cheng, J.Z. and Shan, J. (2020), 2019 novel coronavirus: where we are and what we know Infection, 1-9.
  12. [12]  Chan, J.F.W., Yuan, S., Kok, K.H., To, K.K.W., Chu, H., Yang, J., Xing, F., Liu, J., Yip, C.C.Y., Poon, R.W.S., and Tsoi, H.W. (2020), A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: a study of a family cluster, The Lancet, 395(10223), 514-523.
  13. [13]  Coronavirus disease (COVID-19) Situation Dashboard World Health Organization (2020), https:\\experience.arcgis.com/experience /685d0ace521648f8a5beeeee1b9125cd, Retrieved : 2020-04-02.
  14. [14]  Timeline of the 2020 coronavirus pandemic in India (2020), https://en.wikipedia.org/wiki/Timeline of the 2020 coronavirus pandemic in India January, Retrieved: 2020-04-02.
  15. [15]  Yang, C. and Wang, J. (2020), A mathematical model for the novel coronavirus epidemic in Wuhan China, Math Biosci Eng., 17(3), 2708-27024.
  16. [16]  Diekmann, O., Heesterbeek, J.A.P., and Roberts, M.G. (2009), The construction of next- generation matrices for compartmental epidemic models, J. R. Soc. Interface, 7(47), 873-885.
  17. [17]  Murray, J. (2002), Mathematical Biology I, third edition Springer Verlag Heidelberg.
  18. [18]  Martcheva, M. (2015), An Introduction to Mathematical Epidemiology, Springer New York.
  19. [19]  Perko, L. (2000), Differential Equations and Dynamical Systems, Springer.