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


Other title
Transmission rate
Mathematical models
Type of item
Degree grantor
University of Alberta
Author or creator
Jin, Chaochao
Supervisor and department
Wang, Hao (Mathematical and Statistical Sciences)
Examining committee member and department
Han, Bin (Mathematical and Statistical Sciences)
Frei, Christoph (Mathematical and Statistical Sciences)
Li, Michael (Mathematical and Statistical Sciences)
Department of Mathematical and Statistical Sciences
Applied Mathematics
Date accepted
Graduation date
Master of Science
Degree level
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.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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