Modelling healthcare provision for an infectious disease using optimal control

  • Victoria Brown

Student thesis: Doctoral ThesisPhD


The development of a vaccine against some strains of the human papillomavirus (HPV) has led to many interesting public health questions [1]. We address some of these questions in the following work. We develop a compartmental mathematical model and examine the effect of waning immunity, vaccinating individuals prior to their becoming sexually active and the current government policy of vaccinating only females [2].We calculate parameters based on data. We consider both time-dependent and age dependent ODE models and an age- and time-dependent PDE model and compare the results. We find the “effective” R0 value, Re0, for the time-dependent models. We introduce optimal control to both the time-dependent and age-dependent ODE models to assess the most cost-effective method for introducing the vaccine into a population.We find that the duration of protection offered by the vaccine can influence whether it is possible to eradicate infection from the population. We find the critical proportion to vaccinate to eradicate the disease. We see that introducing male vaccination would lead to a greater proportion of individuals to be vaccinated if the disease is to be eradicated. The PDE model shows that the proportion of females vaccinated has a large impact on the proportion of females infected. We show that it is cost-effective to vaccinate males and females. Our results support current government policy for age of vaccination [2].We conclude that potential waning immunity will impact the success of the vaccine.We broadly support government policy for vaccination but recommend including male vaccination to most cost-effectively eradicate the disease.
Date of Award28 Feb 2010
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorJane White (Supervisor)


  • mathematical modelling
  • HPV
  • optimal control

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