Skip to main content
SpringerLink
Log in
Book cover

International Conference on Recent Advances in Pure and Applied Mathematics

ICRAPAM 2018: Mathematical Analysis II: Optimisation, Differential Equations and Graph Theory pp 207–219Cite as

An SIRS Age-Structured Model for Vector-Borne Diseases with Infective Immigrants

  • Conference paper
  • First Online:

  • 530 Accesses

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 307))

Abstract

In this paper, we develop a SIRS age-structured model with infective immigrants. We consider a fraction of the juvenile immigrants and a fraction of the adult immigrants to be infective. We calculate the equilibrium points and then check the stability of these points. The reproduction number is calculated using the Next- Generation Method. Mathematical simulation for the model is also conducted using MATLAB. It is observed that an increase in the infective immigrants does not affect the total infective persons in the population. However, there is an increase in the infective population if the rate of immigration is increased. Also, the recovered population increases as the recovery rate increases. It is seen that as the mosquito population increases due to an increase in their birth rate, the infective human population also increases.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. A.A. Lasharia, G. Zamanb, Optimal control of a vector borne disease with horizontal transmission. Nonlinear Anal.: R. World Appl. 13, 203–212 (2012)

    Article  MathSciNet  Google Scholar 

  2. G. Kuniyoshi, P. dos Santos, Mathematical modelling of vector-borne diseases and insecticide resistance evolution. J. Venom. Anim. Toxins Incl. Trop. Dis. 23, 34 (2017)

    Google Scholar 

  3. H.-M. Wei, X.-Z. Li, M. Martcheva, An epidemic model of a vector-borne disease with direct transmission and time delay. J. Math. Anal. Appl. 342(2), 895–908 (2007)

    Article  MathSciNet  Google Scholar 

  4. M. Ozair, A.A. Lashari, H. Jung, Y. Seo, B.N. Kim, Stability analysis of a vector-borne disease with variable human population. Abstr. Appl. Anal. (2013). https://doi.org/10.1155/2013/293293

    Article  MathSciNet  Google Scholar 

  5. N.H. Shah, J. Gupta, SEIR model and simulation for vector borne diseases. Appl. Math. 4, 13–17 (2013)

    Article  Google Scholar 

  6. C. Mukandavirea, G. Musukab, G. Magombedzea, Z. Mukandavirea, Malaria model with immigration of infectives and seasonal forcing in transmission. Int. J. Appl. Math. Comput. 2(3), 1–16 (2010)

    Google Scholar 

  7. F. Forouzannia, A.B. Gumel, Mathematical analysis of an age structured model for malaria transmission dynamics. Math. Biosci. 247, 80–94 (2014)

    Article  MathSciNet  Google Scholar 

  8. L.N. Massawe, E.S. Massawe, O.D. Makinde, Dengue in Tanzania—vector control and vaccination. Am. J. Comput. Appl. Math. 5(2), 42–65 (2015)

    Google Scholar 

  9. P. Pongsumpun, I.M. Tang, Transmission of dengue hemorrhagic fever in an age structured population. Math. Comput. Model. 37, 949–961 (2003)

    Article  MathSciNet  Google Scholar 

  10. S. Olaniyi, O.S. Obabiyi, Mathematical model for malaria transmission dynamics in human and mosquito populations with nonlinear forces of infection. Int. J. Pure Appl. Math. 88(1), 125–156 (2013)

    Article  Google Scholar 

  11. S. Side, M.S.M. Noorani, SEIR model for transmission of dengue fever. Int. J. Adv. Sci. Eng. Inf. Technol. 2 (2012)

    Article  Google Scholar 

  12. J. Tumwiine, J.Y.T. Mugisha, L.S. Luboobi, A host-vector model for malaria with infective immigrants. J. Math. Anal. Appl. 361, 139–149 (2010)

    Article  MathSciNet  Google Scholar 

  13. J. Tumwiine, S. Luckhaus, J.Y.T. Mugisha, L.S. Luboobi, An age-structured mathematical model for the within host dynamics of malaria and the immune system. J. Math. Model. Algorithems 7, 79–97 (2008)

    Article  MathSciNet  Google Scholar 

  14. F. Brauer, P. van den Driessche, Models of transmission of diseases with immigration of infectives. Math. Biosci. 171, 143–154 (2001)

    Article  MathSciNet  Google Scholar 

  15. J.M. Addawe, J.E.C. Lope, Analysis of age-structured malaria transmission model. Philipp. Sci. Lett. 5(2) (2012)

    Google Scholar 

  16. M. El hia, O. Balatif, M. Rachik, J. Bouyaghroumni, Application of optimal control theory to an SEIR model with immigration of infectives. Int. J. Comput. Sci. Iss. 10(2) (2013)

    Google Scholar 

  17. https://www.indiatoday.in/india/north/story/children-most-vulnerable-to-vector-borne-disease-59997-2009-11-04

  18. www.who.int/heca/infomaterials/vector-born.pdf

  19. O. Diekmann, J.A.P. Heesterbeek, J.A.J. Metz, On the definition and the computation of the basic reproduction ratio Ro in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365–382 (1990)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The infrastructure support provided by FORE School of Management, New Delhi in completing this paper is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Amity School of Applied Sciences, Amity University Haryana, Gurgaon, India

    Nisha Budhwar

  2. FORE School of Management, Qutub Institutional Area, New Delhi, India

    Sunita Daniel

  3. Department of Applied Mathematics, Delhi Technological University, New Delhi, India

    Vivek Kumar

Authors
  1. Nisha Budhwar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sunita Daniel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vivek Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nisha Budhwar .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, Delhi Technological University, New Delhi, India

    Naokant Deo

  2. Department of Mathematics, Netaji Subhas University of Technology, New Delhi, India

    Vijay Gupta

  3. Department of Mathematics, Lucian Blaga University of Sibiu, Sibiu, Romania

    Ana Maria Acu

  4. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    P. N. Agrawal

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Budhwar, N., Daniel, S., Kumar, V. (2020). An SIRS Age-Structured Model for Vector-Borne Diseases with Infective Immigrants. In: Deo, N., Gupta, V., Acu, A., Agrawal, P. (eds) Mathematical Analysis II: Optimisation, Differential Equations and Graph Theory. ICRAPAM 2018. Springer Proceedings in Mathematics & Statistics, vol 307. Springer, Singapore. https://doi.org/10.1007/978-981-15-1157-8_18

Download citation

Publish with us

Policies and ethics

Search

Navigation