Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mathematical Science


Dimitrova, Elena

Committee Member

Medlock, Jan


Dengue is one of the most rapidly spreading mosquito-borne viral diseases in the world and inflicts significant health, economic and social burdens on populations. In this dissertation, I studied different aspects of modeling of dengue and vector-borne diseases in general. Among various dengue models that have appeared in literature, some explicitly model the mosquito population, while others model them implicitly. In spite of extensive use of both modeling approaches, little guidance exists for which type of model should be preferred. I developed a Bayesian approach that uses a Markov chain Monte Carlo (MCMC) method to fit disease models to epidemiological data and used it to explore how well these models explain observed incidence and to find good estimates for the epidemiological parameters for dengue. I fitted dengue hemorrhagic fever data from Thailand to both type of models and found using Akaike Information Criterion that explicitly incorporating the mosquito population may not be necessary in modeling dengue transmission. On comparing my estimates of the basic reproduction number, R0, with other estimates in literature, I found a wide variability in R0 estimates among studies. This variability in R0 estimate for dengue transmission is not well understood. By fitting a simple dengue model to dengue incidence for varying R0 values, I found a logarithmic type relationship between population immunity levels and R0, which may be a reason for the variability in R0 estimates. The result also highlighted the importance of finding better estimates of population immunity level to help more accurately estimate R0 and other epidemiological parameters for dengue. Driven by the seasonality in mosquito abundance and complex dynamics of denuge, introducing a vaccine may induce a transient period immediately after vaccine introduction where prevalence can spike higher than in the pre-vaccine period. These transient spikes could lead to doubts about the vaccination program among the public and decision makers, possibly impeding the vaccination program. Using simple dengue-transmission models, I found that large transient spikes in prevalence are robust phenomena that occur when vaccine efficacy and vaccine coverage is not either both very high or both very low. Despite the presence of these spikes, vaccination always reduced total number of infections in the 15 years after vaccine introduction. Therefore, policy makers should prepare for spikes in prevalence after vaccine introduction to mitigate the burden of these spikes and to accurately measure the effectiveness of the vaccine program.

Included in

Mathematics Commons