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Optimal control with multiple human papillomavirus vaccines.

Tufail Malik1, Mudassar Imran2, Raja Jayaraman3

  • 1Department of Applied Mathematics & Sciences, Khalifa University, Abu Dhabi, UAE.

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|January 23, 2016
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Summary

This study models human papillomavirus (HPV) vaccination strategies using mathematical models. Optimal control theory identifies dynamic vaccination schedules that minimize HPV prevalence and costs compared to constant vaccination.

Keywords:
Bivalent vaccineHuman papillomavirusNonavalent vaccineOptimal vaccine switch timeQuadrivalent vaccine

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Public Health

Background:

  • Human papillomavirus (HPV) poses a significant global health burden.
  • Vaccination is a key strategy for HPV prevention, but optimal deployment remains complex.
  • Different HPV vaccines (bivalent, quadrivalent, nonavalent) offer varying coverage and efficacy.

Purpose of the Study:

  • To develop and analyze a mathematical model for HPV transmission dynamics.
  • To investigate optimal control strategies for HPV vaccination programs.
  • To compare dynamic vaccination schedules with constant vaccination approaches.

Main Methods:

  • Construction and analysis of a two-sex, deterministic ordinary differential equations model.
  • Computation of disease-free equilibrium and effective reproduction number (Rv).
  • Application of optimal control theory to time-dependent vaccination rates.

Main Results:

  • Stability analysis of the disease-free equilibrium based on Rv.
  • Sensitivity analysis to identify key parameters influencing HPV prevalence.
  • Demonstration that dynamic vaccination strategies can outperform constant controls in reducing infections and costs.

Conclusions:

  • Optimal control theory provides a framework for designing effective, adaptive HPV vaccination programs.
  • Dynamic switching between vaccine types, including the nonavalent vaccine, can enhance program efficiency.
  • Mathematical modeling is crucial for optimizing public health interventions against HPV.