IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v185y2021icp325-346.html
   My bibliography  Save this article

Optimal vaccine for human papillomavirus and age-difference between partners

Author

Listed:
  • Madhu, Kalyanasundaram
  • Al-arydah, Mo’tassem

Abstract

We introduce a two sex age-structured mathematical model to describe the dynamics of HPV disease with childhood and catch up vaccines. We find the basic reproduction number (R0) for the model and show that the disease free equilibrium is locally asymptotically stable when R0≤1. We introduce an optimal control problem and prove that optimal vaccine solution exists and is unique. Using numerical simulation, we show that 77% childhood vaccination controls HPV disease in a 20 years period, but 77% catch up vaccine does not. In fact, catch up vaccine has a slight effect on HPV disease when applied alone or with childhood vaccine. We estimate the optimal vaccine needed to control HPV in a 25 year period. We show that reducing the partners between youths and adults is an effective way in reducing the number of HPV cases, the vaccine needed and the cost of HPV. In sum, we show that choosing partners within the same age group is more effective in controlling HPV disease than providing adult catch up vaccination.

Suggested Citation

  • Madhu, Kalyanasundaram & Al-arydah, Mo’tassem, 2021. "Optimal vaccine for human papillomavirus and age-difference between partners," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 325-346.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:325-346
    DOI: 10.1016/j.matcom.2021.01.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421000033
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.01.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ellen Brooks-Pollock & Ted Cohen & Megan Murray, 2010. "The Impact of Realistic Age Structure in Simple Models of Tuberculosis Transmission," PLOS ONE, Public Library of Science, vol. 5(1), pages 1-6, January.
    2. Al-arydah, Mo’tassem & Smith̏, Robert, 2011. "An age-structured model of human papillomavirus vaccination," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 629-652.
    3. Pang, Liuyong & Ruan, Shigui & Liu, Sanhong & Zhao, Zhong & Zhang, Xinan, 2015. "Transmission dynamics and optimal control of measles epidemics," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 131-147.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kimberly M. Thompson, 2016. "Evolution and Use of Dynamic Transmission Models for Measles and Rubella Risk and Policy Analysis," Risk Analysis, John Wiley & Sons, vol. 36(7), pages 1383-1403, July.
    2. Fu, Xinjie & Wang, JinRong, 2022. "Dynamic stability and optimal control of SISqIqRS epidemic network," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    3. Richard Pitman & David Fisman & Gregory S. Zaric & Maarten Postma & Mirjam Kretzschmar & John Edmunds & Marc Brisson, 2012. "Dynamic Transmission Modeling," Medical Decision Making, , vol. 32(5), pages 712-721, September.
    4. Abdelaziz, Mahmoud A.M. & Ismail, Ahmad Izani & Abdullah, Farah A. & Mohd, Mohd Hafiz, 2020. "Codimension one and two bifurcations of a discrete-time fractional-order SEIR measles epidemic model with constant vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Ali Khaleel Dhaiban & Baydaa Khalaf Jabbar, 2021. "An optimal control model of COVID-19 pandemic: a comparative study of five countries," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 790-809, December.
    6. Berhe, Hailay Weldegiorgis & Makinde, Oluwole Daniel & Theuri, David Mwangi, 2019. "Co-dynamics of measles and dysentery diarrhea diseases with optimal control and cost-effectiveness analysis," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 903-921.
    7. Pang, Liuyong & Zhao, Zhong & Song, Xinyu, 2016. "Cost-effectiveness analysis of optimal strategy for tumor treatment," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 293-301.
    8. Chu-Chang Ku & Peter J Dodd, 2019. "Forecasting the impact of population ageing on tuberculosis incidence," PLOS ONE, Public Library of Science, vol. 14(9), pages 1-13, September.
    9. Jose Diamantino Hernández Guillén & Ángel Martín del Rey & Roberto Casado Vara, 2020. "On the Optimal Control of a Malware Propagation Model," Mathematics, MDPI, vol. 8(9), pages 1-16, September.
    10. Qureshi, Sania & Jan, Rashid, 2021. "Modeling of measles epidemic with optimized fractional order under Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    11. Li, Can & Guo, Zun-Guang & Zhang, Zhi-Yu, 2017. "Transmission dynamics of a brucellosis model: Basic reproduction number and global analysis," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 161-172.
    12. Juliet Nakakawa & Joseph Y. T. Mugisha & Michael W. Shaw & William Tinzaara & Eldad Karamura, 2017. "Banana Xanthomonas Wilt Infection: The Role of Debudding and Roguing as Control Options within a Mixed Cultivar Plantation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2017, pages 1-13, December.
    13. Md Abdul Kuddus & Michael T Meehan & Lisa J White & Emma S McBryde & Adeshina I Adekunle, 2020. "Modeling drug-resistant tuberculosis amplification rates and intervention strategies in Bangladesh," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-26, July.
    14. Solis, Francisco J. & Gonzalez, Luz M., 2018. "Analytical and numerical modeling of the evolution of human papillomavirus infected cells," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 28-35.
    15. Nudee, K. & Chinviriyasit, S. & Chinviriyasit, W., 2019. "The effect of backward bifurcation in controlling measles transmission by vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 400-412.
    16. Al-arydah, Mo’tassem & Smith̏, Robert, 2011. "An age-structured model of human papillomavirus vaccination," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 629-652.
    17. Chung‐Min Liao & Yi‐Hsien Cheng & Yi‐Jun Lin & Nan‐Hung Hsieh & Tang‐Luen Huang & Chia‐Pin Chio & Szu‐Chieh Chen & Min‐Pei Ling, 2012. "A Probabilistic Transmission and Population Dynamic Model to Assess Tuberculosis Infection Risk," Risk Analysis, John Wiley & Sons, vol. 32(8), pages 1420-1432, August.
    18. Graciani Rodrigues, C.C. & Espíndola, Aquino L. & Penna, T.J.P., 2015. "An agent-based computational model for tuberculosis spreading on age-structured populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 52-59.
    19. Xu, Rui & Wang, Zhili & Zhang, Fengqin, 2015. "Global stability and Hopf bifurcations of an SEIR epidemiological model with logistic growth and time delay," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 332-342.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:325-346. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.