Skip to main content

Advertisement

SpringerLink
Log in

Dynamic analysis of an Ebola epidemic model incorporating limited medical resources and immunity loss

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

In this paper, we establish an Ebola epidemic model incorporating limited medical resources and immunity loss, and also consider the tracking and quarantining of susceptible individuals. Meanwhile the stability of the disease-free equilibrium is proved. Furthermore, we deduce the existence of multiple endemic equilibria and the occurrence of bifurcation. And then, using the partial ranking correlation coefficient (PRCC), it is found that the control reproduction number is most correlated with the parameter \(\rho \) (incineration or burial rate of dead bodies). Additionally, based on the data of the Ebola epidemic in Uganda in 2022, the fitted curve of accumulated infectious cases stabilizes at 143, which is eventually consistent with the actual data. Finally, numerical simulation results indicate that the peak value of infectious individuals decreases by 52.3% when the maximum treatment recovery rate changes from 20% to 40%. And while the hospital bed-population ratio increases by 10%, the peak value of the infectious decreases by 29.1%. Simultaneously, when the rate of immune loss decreasing from 60% to 20%, the peak value of the infectious decreases by 13.2%. While enhancing the tracking and quarantining of susceptible individuals have significant impact on the prevention and control of Ebola.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. World Health Organization: Ebola virus disease. https://www.who.int/news-room/fact-sheets/detail/ebola-virus-disease. Accessed 15 May 2023

  2. Legrand, J., Grais, R.F., Boelle, P.Y., et al.: Understanding the dynamics of Ebola epidemics. Epidemiol. Infect. 135, 610–621 (2007)

    Article  Google Scholar 

  3. Feng, Z.L., Zheng, Y.Q., Hernandez-Ceronb, N., et al.: Mathematical models of Ebola-consequences of underlying assumptions. Math. Biosci. 277, 89–107 (2016)

    Article  MathSciNet  Google Scholar 

  4. Wang, X., Shi, Y., Feng, Z., et al.: Evaluations of interventions using mathematical models with exponential and non-exponential distributions for disease stages: the case of Ebola. Bull. Math. Biol. 79, 2149–2173 (2017)

    Article  MathSciNet  Google Scholar 

  5. Tadmon, C., Kengne, J.N.: Mathematical analysis of a model of Ebola disease with control measures. Int. J. Biomath. 15, 1–39 (2022)

    Article  MathSciNet  Google Scholar 

  6. Ouemba Tasse, A.J., Tsanou, B., Lubuma, J., et al.: Ebola virus disease dynamics with some preventive measures: a case study of the 2018–2020 KIVU outbreak. J. Biol. Syst. 30, 113–148 (2022)

    Article  MathSciNet  Google Scholar 

  7. Njankou, S.D., Nyabadza, F.: Modelling the role of human behaviour in Ebola virus disease (EVD) transmission dynamics. Comput. Math. Methods Med. 4150043, 1–11 (2022)

    Article  Google Scholar 

  8. Agbomola, J.O., Loyinmi, A.C.: Modelling the impact of some control strategies on the transmission dynamics of Ebola virus in human-bat population: an optimal control analysis. Heliyon 8, e12121 (2022)

    Article  Google Scholar 

  9. Seck, R., Ngom, D., Ivorra, B., et al.: An optimal control model to design strategies for reducing the spread of the Ebola virus disease. Math. Biosci. Eng. 19, 1746–1774 (2022)

    Article  MathSciNet  Google Scholar 

  10. World Health Organization: DR Congo declares end to latest Ebola outbreak. https://news.un.org/en/story/2022/07/1121922. Assesed 27 Apr 2023

  11. World Health Organization: Uganda declares end of Ebola virus outbreak. https://news.un.org/en/story/2023/01/1132352. Assessed 27 Apr 2023

  12. Zhao, J., Wang, L., Han, Z.: Stability analysis of two new SIRS models with two viruses. Int. J. Comput. Math. 95, 2026–2035 (2018)

    Article  MathSciNet  Google Scholar 

  13. Liu, Z., Tian, C.: A weighted networked SIRS epidemic model. J. Differ. Equ. 269, 10995–11019 (2020)

    Article  MathSciNet  Google Scholar 

  14. Xiang, L., Zhang, Y., Huang, J.: Stability analysis of a discrete SIRS epidemic model with vaccination. J. Differ. Equ. Appl. 26, 309–327 (2020)

    Article  MathSciNet  Google Scholar 

  15. Selvan, T.T., Kumar, M.: Dynamics of a deterministic and a stochastic epidemic model combined with two distinct transmission mechanisms and saturated incidence rate. Phys. A 619, 128741 (2023)

    Article  MathSciNet  Google Scholar 

  16. Liu, C., Cui, R.: Analysis on a diffusive SIRS epidemic model with logistic source and saturated incidence rate. Discrete Contin. Dyn. Syst. Ser. B. 28, 2960–2980 (2023)

    Article  MathSciNet  Google Scholar 

  17. Wang, W.: Backward bifurcation of an epidemic model with treatment. Math. Biosci. 201, 58–71 (2006)

    Article  MathSciNet  Google Scholar 

  18. Shan, C., Zhu, H.: Bifurcations and complex dynamics of an SIR model with the impact of the number of hospital beds. J. Differ. Equ. 257, 1662–1688 (2014)

    Article  MathSciNet  Google Scholar 

  19. Shan, C., Yi, Y., Zhu, H.: Nilpotent singularities and dynamics in an SIR type of compartmental model with hospital resources. J. Differ. Equ. 260, 4399–4365 (2016)

    Article  MathSciNet  Google Scholar 

  20. Zhao, H., Wang, L., Oliva, S.M., et al.: Modeling and dynamics analysis of Zika transmission with limited medical resources. Bull. Math. Biol. 82, 99 (2020)

    Article  MathSciNet  Google Scholar 

  21. Fan, G., Li, J., Belair, J., et al.: Delayed model for the transmission and control of COVID-19 with Fangcang shelter hospitals. SIAM J. Appl. Math. 83, 276–301 (2023)

    Article  MathSciNet  Google Scholar 

  22. Boaden, R., Proudlove, N., Wilson, M.: An exploratory study of bed management. J. Manage. 13, 234–250 (1999)

    Google Scholar 

  23. World Health Organization, World Health Statistics 2005–2011

  24. Berge, T., Lubuma, J., Ouemba Tase, A.J., et al.: Dynamics of Host-reservoir transmission of Ebola with spillover potential to humans. Electron. J. Qual. Theory 4, 1–32 (2018)

    Google Scholar 

  25. World Health Organization, WHO interventions to support the Ebola response in Uganda—September 2022-08 February 2023

  26. Djiomba, S.D., Nyabadza, F.: Modelling the potential role of media campaigns in Ebola transmission dynamics. J. Differ. Equ. 2017, 1–13 (2017)

    Google Scholar 

  27. World Health Organization: The global observatory: Explore a world of health data. https://www.who.int/countries/uga/. Assessed 27 April 2023

  28. Ma, Z., Zhou, Y., Li, C.: Qualitative and Stability Methods of Ordinary Differential Equations (in Chinese), 2nd edn. Science Press, Beijing (2015)

    Google Scholar 

  29. Sheng, Y., Jing, J., Guo, S.: The modeling and analysis of the COVID-19 pandemic with vaccination and isolation: a case study of Italy. Math. Biosci. Eng. 20, 5966–5992 (2023)

    Article  MathSciNet  Google Scholar 

  30. Dreessche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29–48 (2002)

    Article  MathSciNet  Google Scholar 

  31. Guo, S.B., Ma, W.B., Zhao, X.Q.: Global dynamics of a time-delayed microorganism flocculation model with saturated functional responses. J. Dyn. Differ. Equ. 30, 1247–1271 (2018)

    Article  MathSciNet  Google Scholar 

  32. Bai, Y.Z., Wang, X.J., Guo, S.B.: Global stability of a mumps transmission model with quarantine measure. Acta Math. Appl. Sin.-E 37, 665–672 (2021)

    Article  MathSciNet  Google Scholar 

  33. Guo, S.B., Ma, W.B.: Remarks on a variant of Lyapunov–LaSalle theorem. Math. Biosci. Eng. 16, 1056–1066 (2019)

    Article  MathSciNet  Google Scholar 

  34. Taylor, R.: Interpretation of the correlation coefficient: a basic review. JDMS 6, 35–39 (1990)

    Google Scholar 

  35. Blower, S.M., Hartel, D., Dowlatabadi, H., et al.: Drugs, sex and HIV: a mathematical model for New York City. Philos. Trans. R. Soc. B 331, 171–187 (1991)

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by the National Nature Science Foundation of China (Grant Nos. 12071445, 11901027), the China Postdoctoral Science Foundation (No. 2021M703426), the Pyramid Talent Training Project of BUCEA (No. JDYC20200327), the BUCEA Post Graduate Education Teaching Quality Improvement Project (J2023021) and the BUCEA Post Graduate Innovation Project (No. PG2023145). We thank all the individuals who provided support and guidance to this study.

Author information

Authors and Affiliations

  1. School of Science, Beijing University of Civil Engineering and Architecture, Beijing, 102616, People’s Republic of China

    Xiaojing Wang, Jiahui Li, Songbai Guo & Maoxing Liu

Authors
  1. Xiaojing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiahui Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Songbai Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Maoxing Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maoxing Liu.

Ethics declarations

Conflict of interest

The authors have no conflicts of interest in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, X., Li, J., Guo, S. et al. Dynamic analysis of an Ebola epidemic model incorporating limited medical resources and immunity loss. J. Appl. Math. Comput. 69, 4229–4242 (2023). https://doi.org/10.1007/s12190-023-01923-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-023-01923-2

Keywords

Mathematics Subject Classification

Search

Navigation