DOI QR코드

DOI QR Code

PREVENTION STRATEGIES TO CONTROL AN EPIDEMIC USING A SEIQHRV MODEL

  • Mohit Soni (Department of Mathematics, Government Holkar (Model, Autonomous) Science College) ;
  • Rajesh Kumar Sharma (Department of Mathematics, J.N.S. Government PG College) ;
  • Shivram Sharma (Government Postgraduate College)
  • Received : 2023.08.03
  • Accepted : 2023.12.28
  • Published : 2024.05.31

Abstract

This study investigates the impact of precautionary measures, such as isolating exposed individuals, wearing masks, and maintaining physical distance, on preventing infectious disease. A deterministic SEIQHRV epidemic model is employed for this purpose. The model's positivity, boundedness, disease-free, and endemic equilibrium points are identified. A sensitivity test assesses the impact of preventive measures on infected classes. Results show that a basic reproduction number less than unity drives disease eradiction, while a higher unity value encourages the adoption of preventive measures.

Keywords

References

  1. Beinane, S.A.O., Lemnaouar, M.R., Zine, R. & Louartassi, Y.: Stability analysis of Covid-19 epidemic model of type SEIQHR with fractional order. Mathematical Problems in Engineering (2022), 2022. https://doi.org/10.1155/2022/5163609
  2. Butt, A.I.K., Ahmad, W., Rafiq, M., Ahmad, N. & Imran, M.: Optimally analyzed fractional Coronavirus model with Atangana?Baleanu derivative. Results in Physics 53 (2023), 106929. https://doi.org/10.1016/j.rinp.2023.106929
  3. Butt, A.I.K., Rafiq, M., Ahmad, W. & Ahmad, N.: Implementation of computationally efficient numerical approach to analyze a Covid-19 pandemic model. Alexandria Engineering Journal 69 (2023), 341-362. https://doi.org/10.1016/j.aej.2023.01.052
  4. Carcione, J.M., Santos, J.E., Bagaini, C. & Ba, J.: A simulation of a COVID-19 epidemic based on a deterministic SEIR model. Frontiers in public health 8 (2020), 230. https://doi.org/10.3389/fpubh.2020.00230
  5. Diekmann, O., Heesterbeek, J.A.P. & Roberts, M.G.: The construction of nextgeneration matrices for compartmental epidemic models. Journal of the royal society interface 7 (2010), no. 47, 873-885. https://doi.org/10.1098/rsif.2009.0386
  6. Dwomoh, D., Iddi, S., Adu, B., Aheto, J.M., Sedzro, K.M., Fobil, J. & Bosomprah, S.: Mathematical modeling of COVID-19 infection dynamics in Ghana: Impact evaluation of integrated government and individual level interventions. Infectious Disease Modelling 6 (2021), 381-397. https://doi.org/10.1016/j.idm.2021.01.008
  7. https://www.findeasy.in/indian-states-by-life-expectancy accessed on July 15 (2022).
  8. https://www.indiacensus.net accessed on July 15 (2022).
  9. https://www.mygov.in/covid-19 accessed on July 15 (2022).
  10. James, N., Menzies, M. & Bondell, H.: Comparing the dynamics of COVID-19 infection and mortality in the United States, India, and Brazil. Physica D: Nonlinear Phenomena 432 (2022), 133158. https://doi.org/10.1016/j.physd.2022.133158
  11. Kolebaje, O.T., Vincent, O.R., Vincent, U.E. & McClintock, P.V.: Nonlinear growth and mathematical modelling of COVID-19 in some African countries with the Atangana-Baleanu fractional derivative. Communications in Nonlinear Science and Numerical Simulation 105 (2022), 106076. https://doi.org/10.1016/ j.cnsns.2021.106076
  12. La Salle, J.P.: The stability of dynamical systems. Society for Industrial and Applied Mathematics (1976).
  13. Manchein, C., Brugnago, E.L., da Silva, R.M., Mendes, C.F. & Beims, M.W.: Strong correlations between power-law growth of COVID-19 in four continents and the inefficiency of soft quarantine strategies. Chaos: An Interdisciplinary Journal of Nonlinear Science 30 (2020), no. 4. https://doi.org/10.1063/5.0009454
  14. Mandal, M., Jana, S., Nandi, S.K., Khatua, A., Adak, S. & Kar, T.K.: A model based study on the dynamics of COVID-19: Prediction and control. Chaos, Solitons & Fractals 136 (2020), 109889. https://doi.org/10.1016/j.chaos.2020.109889
  15. Memon, Z., Qureshi, S. & Memon, B.R.: Assessing the role of quarantine and isolation as control strategies for COVID-19 outbreak: a case study. Chaos, Solitons & Fractals 144 (2021), 110655. https://doi.org/10.1016/j.chaos.2021.110655
  16. Safi, M.: Mathematical Analysis of The Role of Quarantine and Isolation in Epidemiology, (2010).
  17. Safi, M.A. & Gumel, A.B.: Global asymptotic dynamics of a model for quarantine and isolation. Discrete Contin. Dyn. Syst. Ser. B 14 (2010), no. 1, 209-231. https://doi.org/10.3934/dcdsb.2010.14.209.
  18. Safi, M.A. & Gumel, A.B.: Mathematical analysis of a disease transmission model with quarantine, isolation and an imperfect vaccine. Computers & Mathematics with Applications 61 (2011), no. 10, 3044-3070. https://doi.org/10.1016/j.camwa.2011.03.095
  19. Safi, M.A. & Gumel, A.B.: Qualitative study of a quarantine/isolation model with multiple disease stages. Applied Mathematics and Computation 218 (2011), no. 5, 1941-1961. https://doi.org/10.1016%2Fj.amc.2011.07.007 https://doi.org/10.1016%2Fj.amc.2011.07.007
  20. Sharma, S. & Sharma, P.K.: A study of SIQR model with Holling type-II incidence rate. Malaya Journal of Matematik 9 (2021), no. 1, 305-311. https://doi.org/10.26637/MJM0901/0052
  21. Sharma, S. & Sharma, P.K.: Stability analysis of an SIR model with alert class modified saturated incidence rate and Holling functional type-II treatment. Computational and Mathematical Biophysics 11 (2023), no. 1, 20220145. https://doi.org/10.1515/cmb-2022-0145.
  22. Soni, M., Sharma, R.K. & Sharma, S.: The basic reproduction number and herd immunity for COVID-19 in India. Indian Journal of Science and Technology 14, no. 35, 2773-2777. https://dx.doi.org/10.17485/IJST/v14i35.797
  23. Soni, M., Sharma, R.K. & Sharma, S.: Uncertainty in the Spread of COVID-19: An Analysis in the Context of India. Indian Journal of Science and Technology 14 (2021), no. 42, 3157-3176. https://doi.org/10.17485/IJST/v14i42.1004
  24. Umdekar, S., Sharma, P.K. & Sharma, S.: An SEIR model with modified saturated incidence rate and Holling type II treatment function. Computational and Mathematical Biophysics 11 (2023), no. 1, 20220146. https://doi.org/10.1515/cmb-2022-0146