Skip to main content
SpringerLink
Log in

Dynamical study of lumpy skin disease model with optimal control analysis through pharmaceutical and non-pharmaceutical controls

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

Lumpy skin disease (LSD) is an infectious disease that affects cattle population. The disease has disrupted economy of the affected countries due to decline in dairy products and sometimes due to death of the infected cattle. It is therefore necessary to develop a mathematical model that may help to eradicate the disease in an optimal way. For this, we propose a new mathematical model not only to understand the disease flow patterns but also to suggest strategies to control disease optimally. We examine the proposed model for existence of a unique solution and prove that the solutions are positive and bounded. We estimate the reproduction number \(\mathcal {R}_0\) to measure disease contagiousness and to test the proposed model for local and global stability at disease-free and endemic equilibrium points. We also present graphs to verify theoretical results of global stability at equilibrium points. We perform sensitivity analysis to determine the most influential parameters of the reproduction number \(\mathcal {R}_0\) and show their impact on \(\mathcal {R}_0\) graphically. The primary goal of this research is to test various possible disease prevention methods in order to find the best one. Therefore, we build an optimal control problem to explore the effects of treatment and precautionary measures on disease control in three different cases. In the first case, we analyze the impact of treatment strategy on the disease control and present the corresponding results graphically. In the second control methodology, we study the impact of adopting precautionary measures on sickness with possible end from society. In the third case, we implement treatment and adopting precautionary measure strategies together to observe their combined effect on disease control. Findings of all the three cases along with discussions and graphs will be presented and concluded at the end.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The data sets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.]

References

  1. R. Magori-Cohen et al., Mathematical modelling and evaluation of the different routes of transmission of lumpy skin disease virus. Vet. Res. 43, 1 (2012)

    Article  Google Scholar 

  2. S. Babiuk, T.R. Bowden, D.B. Boyle, D.B. Wallace, R.P. Kitching, Capripoxviruses: an emerging worldwide threat to sheep, goats and cattle. Transbound. Emerg. Dis. 55, 263–272 (2008)

    Article  Google Scholar 

  3. A.I.K. Butt, H. Aftab, M. Imran, T. Ismaeel, Mathematical study of lumpy skin disease with optimal control analysis through vaccination. Alex. Eng. J. 72, 247–259 (2023). https://doi.org/10.1016/j.aej.2023.03.073

    Article  Google Scholar 

  4. O.O. Onyejekwe, A. Alemu, B. Ambachew, A. Tigabie, Epidemiological study and optimal control for Lumpy Skin Disease (LSD) in Ethiopia. Adv. Infect. Dis. 9, 8–24 (2019). https://doi.org/10.4236/aid.2019.91002

    Article  Google Scholar 

  5. W.F. Alfwan, M.H. DarAssi, F.M. Allehiany et al., A novel mathematical study to understand the Lumpy skin disease (LSD) using modified parameterized approach. Results Phys. 51, 106626 (2023). https://doi.org/10.1016/j.rinp.2023.106626

    Article  Google Scholar 

  6. E.I. Agianniotaki, K.E. Tasioudi, S.C. Chaintoutis, P. Iliadou, O. Mangana-Vougiouka, A. Kirtzalidou, T. Alexandropoulos, A. Sachpatzidis, E. Plevraki, C.I. Dovas, Lumpy skin disease outbreaks in Greece during 2015–16, implementation of emergency immunization and genetic differentiation between field isolates and vaccine virus strains. Vet. Microbiol. 201, 78–84 (2016)

    Article  Google Scholar 

  7. E.I. Agianniotaki, S.C. Chaintoutis, A. Haegeman, K.E. Tasioudi, I. De Leeuw, P.D. Katsoulos, A. Sachpatzidis, K. De Clercq, T. Alexandropoulos, Z.S. Polizopoulou, E.D. Chondrokouki, C.I. Dovas, Development and validation of a TaqMan probe-based real-time PCR method for the differentiation of wild type lumpy skin disease virus from vaccine virus strains. J. Virol. Methods 249, 48–57 (2017)

    Article  Google Scholar 

  8. F. Baldacchino, M. Desquesnes, S. Mihok, L.D. Foil, G. Duvallet, S. Jittapalapong, Tabanids: neglected subjects of research, but important vectors of disease agents. Infect. Genet. Evolut. 28(596), 615 (2017)

    Google Scholar 

  9. P.M. Beard, Lumpy skin disease: a direct threat to Europe. Vet. Record. 178, 557–558 (2017)

    Article  Google Scholar 

  10. J. Ben-Gera, E. Klement, E. Khinich, Y. Stram, N.Y. Shpigel, Comparison of the efficacy of Neethling lumpy skin disease virus and x10RM65 sheep-pox live attenuated vaccines for the prevention of lumpy skin disease the results of a randomized controlled field study. Vaccine 33, 4837–4842 (2015)

    Article  Google Scholar 

  11. A. Anwar, K. Na-Lampang, N. Preyavichyapugdee, V. Punyapornwithaya, Lumpy skin disease outbreaks in Africa, Europe, and Asia (2005–2022): multiple change point analysis and time series forecast. Viruses 14, 2203 (2022). https://doi.org/10.3390/v14102203

    Article  Google Scholar 

  12. S.B. Sudhakar, N. Mishra, S. Kalaiyarasu, S.K. Jhade, D. Hemadri, R. Sood, G.C. Bal, M.K. Nayak, S.K. Pradhan, V.P. Singh, Lumpy skin disease (LSD) outbreaks in cattle in Odisha state, India in August 2019, epidemiological features and molecular studies. Transbound. Emerg. Dis. 67, 2408–2422 (2020)

    Article  Google Scholar 

  13. EFSA (European Food Safety Authority), Scientific report on lumpy skin disease: I. Data collection and analysis. EFSA J. 15(4), 4773 (2017). https://doi.org/10.2903/j.efsa.2017.4773

  14. EFSA (European Food Safety Authority), Scientific report on lumpy skin disease II. Data collection and analysis, EFSA J. 16(2), 33, 5176 (2018). https://doi.org/10.2903/j.efsa.2018.5176

  15. M.I. Khalil, M.F.R. Sarker, F.Y. Hasib, S. Chowdhury, Outbreak investigation of lumpy skin disease in dairy farms at Barishal, Bangladesh. Turk. J. Agric. Food Sci. Technol. 9, 205–209 (2021)

    Google Scholar 

  16. A.I.K. Butt, D.B.D. Chamaleen, S. Batool, M.A.L. Nuwairan, A new design and analysis of optimal control problems arising from COVID-19 outbreak. Math Methods Appl Sci. (2023). https://doi.org/10.1002/mma.9482

    Article  MathSciNet  Google Scholar 

  17. M. Rafiq, W. Ahmad, M. Abbas, D. Baleanu, A reliable and competitive mathematical analysis of Ebola epidemic model. Adv. Differ. Equ. 540(1), 1–24 (2020)

    MathSciNet  MATH  Google Scholar 

  18. A. Hanif, A.I. Kashif Butt, W. Ahmad, Numerical approach to solve Caputo–Fabrizio fractional model of corona pandemic with optimal control design and analysis. Math. Methods Appl. Sci. (2023). https://doi.org/10.1002/mma.9085

    Article  MathSciNet  Google Scholar 

  19. D. Baleanu, M. Hasanabadi, A.M. Vaziri, A. Jajarmi, A new intervention strategy for an HIV, AIDS transmission by a general fractional modeling and an optimal control approach. Chaos, Solitons Fractals 167, 113078 (2023). https://doi.org/10.1016/j.chaos.2022.113078. ISSN:0960–0779

  20. D. Baleanu, A. Jajarmi, H. Mohammadi, S. Rezapour, A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative. Chaos, Solitons Fractals 134, 109705 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  21. D. Baleanu, F. Akhavan Ghassabzade, J.J. Nieto, A. Jajarmi, On a new and generalized fractional model for a real cholera outbreak. Alex. Eng. J. 61(11), 9175–9186 (2022)

    Article  Google Scholar 

  22. I. Ali, S.U. Khan, Threshold of stochastic SIRS epidemic model from infectious to susceptible class with saturated incidence rate using spectral method. Symmetry 14, 1838 (2022). https://doi.org/10.3390/sym14091838

    Article  ADS  Google Scholar 

  23. I. Ali, S.U. Khan, Dynamics and simulations of stochastic COVID-19 epidemic model using Legendre spectral collocation method. AIMS Math. 8(2), 4220–4236 (2023). https://doi.org/10.3934/math.2023210

    Article  MathSciNet  Google Scholar 

  24. R. Begum, O. Tunç, H. Khan, H. Gulzar, A. Khan, A fractional order Zika virus model with Mittag–Leffler kernel. Chaos Solitons Fractals 146, 110898 (2021)

    Article  MathSciNet  Google Scholar 

  25. W. Ma, Y. Takeuchi, T. Hara, E. Beretta, Permanence of an SIR epidemic model with distributed time delays. Tohoku Math. J. 54, 581–591 (2002)

    MathSciNet  MATH  Google Scholar 

  26. N. Yoshida, T. Hara, Global stability of a delayed SIR epidemic model with density dependent birth and death rates. J. Comput. Appl. Math. 201(2), 339–347 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. M.Y. Li, An Introduction to Mathematical Modeling of Infectious Diseases (Springer, Cham, 2018)

    Book  MATH  Google Scholar 

  28. A.I.K. Butt, M. Imran, D.B.D. Chamaleen, S. Batool, Optimal control strategies for the reliable and competitive mathematical analysis of Covid-19 pandemic model. Math. Methods Appl. Sci. (2022). https://doi.org/10.1002/mma.8593

    Article  Google Scholar 

  29. W. Ahmad, M. Rafiq, M. Abbas, Mathematical analysis to control the spread of Ebola virus epidemic through voluntary vaccination. Eur. Phys. J. Plus. 135(10), 1–34 (2020)

    Article  Google Scholar 

  30. A. Hanif, A.I.K. Butt, Atangana–Baleanu fractional dynamics of dengue fever with optimal control strategies. AIMS Math. 8(7), 15499–15535 (2023). https://doi.org/10.3934/math.2023791

    Article  MathSciNet  Google Scholar 

  31. R. Magori-Cohen, Y. Louzoun, Y. Herziger, E. Oron, A. Arazi, E. Tuppurainen, N.Y. Shpigel, E. Klement, Mathematical modelling and evaluation of the different routes of transmission of lumpy skin disease virus. Vet. Res. 43, 1–13 (2012)

    Article  Google Scholar 

  32. A. Ayesha, N.-L. Kannika, P. Narin, P. Veerasak, Lumpy skin disease outbreaks in Africa, Europe, and Asia (2005–2022): multiple change point analysis and time series forecast. Viruses 14(10), 2203 (2022)

    Article  Google Scholar 

  33. M. Sompop, H. Adsadang, R. Thaned, A. Orapun, P. Pawares, K. Noppasorn, B. Noppawan, P. Veerasak, Modelling epidemic growth models for lumpy skin disease cases in Thailand using nationwide outbreak data, 2021–2022. Infect Dis Model. 8(1), 282–93 (2023)

    Google Scholar 

  34. C. Castillo-Chavez, Z. Feng, W. Huanz, P.V.D. Driessche, D.E. Kirschner, On the computation of RO and its role in global stability, In Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction (Springer, Berlin/Heidelberg, Germany, 2002)

    Google Scholar 

  35. W. Ahmad, M. Abbas, Effect of quarantine on transmission dynamics of Ebola virus epidemic: a mathematical analysis. Eur Phys J Plus 136(4), 1–33 (2021)

    Article  Google Scholar 

  36. W. Ahmad, M. Abbas, M. Rafiq, D. Baleanu, Mathematical analysis for the effect of voluntary vaccination on the propagation of Corona virus pandemic. Results Phys. 31, 104917 (2021)

    Article  Google Scholar 

  37. P. Van Den Drissche, Reproduction numbers of infectious disease models. Infect. Dis. Model. 2, 288–303 (2017)

    Google Scholar 

  38. N. Chitnis, J.M. Hyman, J.M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull. Math. Biol. 70(5), 1272–1296 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  39. L.S. Pontryagin, V.G. Boltyanskii, The Mathematical Theory of Optimal Processes (Golden and Breach Science Publishers, New York, 1986)

    Google Scholar 

  40. K. Fister, S. Lenhart, J. McNally, Optimizing chemotherapy in an HIV model. Electron. J. Differ. Equ. 32, 112 (1998)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa, 31982, Saudi Arabia

    Azhar Iqbal Kashif Butt & Meraa Arab

  2. Department of Mathematics, GC University, Lahore, Pakistan

    Azhar Iqbal Kashif Butt & Tariq Ismaeel

  3. Tandy School of Computer Science, The University of Tulsa, Tulsa, OK, USA

    Muhammad Imran

  4. Department of Mathematics, Sahara Medical College Narowal, Narowal, Pakistan

    Maroof Gohar

  5. Department of Mathematics, Division of Science and Technology, University of Education, Lahore, 54770, Pakistan

    Muhammad Afzal

  6. Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan

    Hassan Aftab

Authors
  1. Azhar Iqbal Kashif Butt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hassan Aftab
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muhammad Imran
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tariq Ismaeel
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Meraa Arab
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Maroof Gohar
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Muhammad Afzal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Azhar Iqbal Kashif Butt or Tariq Ismaeel.

Ethics declarations

Conflict of interest

This work does not have any conflicts of interest.

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

Butt, A.I.K., Aftab, H., Imran, M. et al. Dynamical study of lumpy skin disease model with optimal control analysis through pharmaceutical and non-pharmaceutical controls. Eur. Phys. J. Plus 138, 1048 (2023). https://doi.org/10.1140/epjp/s13360-023-04690-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-023-04690-y

Search

Navigation