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Optimal vaccine for human papillomavirus and age-difference between partners

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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