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Mathematical Models and Inverse Algorithms for Childhood Infectious Diseases with Vaccination - Case Studies in Measles

  • Author / Creator
    Jin, Chaochao
  • Children are at a high risk of infection since they have not yet developed mature immunity. Childhood infectious diseases, such as measles, chicken pox and mumps, remain epidemic and endemic around the world. Yet, their dynamics are still not fully understood. SIR-type models have been proposed and widely applied to understand and control infectious diseases, and the SEIR model has been frequently applied to study childhood infectious diseases. In this thesis, we improve the classic SEIR model by separating the juvenile group and the adult group to better describe the dynamics of childhood infectious diseases. We perform stability analysis to study the asymptotic dynamics of the new model, and perform sensitivity analysis to uncover the relative importance of the parameters on infection. The transmission rate is a key parameter in controlling the spread of an infectious disease as it directly determines the disease incidence. However, it is essentially impossible to measure the transmission rate due to ethical reasons. We introduce an inverse method for our new model, which can extract the time-dependent transmission rate from either prevalence data or incidence data in existing open databases. Pre- and post-vaccination measles data sets from Liverpool and London are applied to estimate the time-varying transmission rate. The effectiveness of vaccination has been widely discussed and studied in epidemiology. Outbreaks can still occur if the percentage of susceptible individuals who take the vaccination is low or the vaccination itself is not sufficiently effective. We further extend our model by adding a vaccination term for all children to predict the date and the infection number of a possible measles outbreak peak in the Province of Alberta.

  • Subjects / Keywords
  • Graduation date
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
  • Institution
    University of Alberta
  • Degree level
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Applied Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Wang, Hao (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Han, Bin (Mathematical and Statistical Sciences)
    • Li, Michael (Mathematical and Statistical Sciences)
    • Frei, Christoph (Mathematical and Statistical Sciences)