Metapopulation and Non-proportional Vaccination Models Overview

Influenza viruses are a major cause of morbidity and mortality worldwide. The 2009 influenza pandemic not only brought to our attention the strengths and weaknesses of the public health system but also changed their priorities. Vaccination still is themost powerful allay for preventing ormitigating influenza outbreaks or other diseases. In this article, we summarize our findings that arose from two different published research articles (see Cruz-Aponte et al. BMC Infect. Dis. 11(1), 207, (2011), [ 22], Herrera-Valdez et al. Math. Biosci. Eng. (MBE) 8(1), 21-48, (2011), [ 36]) that were presented at the Association ofWoman in Mathematics (AWM) 2015 symposium at the University of Maryland College Park. The first one is a metapop-ulation model we constructed using the data from Mexico's 2009 epidemic patterns characterized by three peaks. These peak patterns were theoretically investigated via models that incorporate Mexico's general trends of land transportation, public health measures, and the academic calendar trends of that year. After studying many mathematical models that incorporated vaccination into the modeling, we were not satisfied with the simplification approaches that usually took place. Vaccinating only the susceptible individuals or vaccinating a fraction of the population was not realistic when supplies or daily administration capacity was considered. Hence, in the second project we presented a SIR-like model that explicitly takes into account vaccine supply and the number of vaccines administered per day and places datain-formed limits on these parameters. The model that we refer to as non-proportional vaccination model is a theoretical improvement that provides more accurate predictions of the mitigating effects of vaccination than the typical proportional model. For some parameter regimes, proportional and non-proportional models behave the same, especially when the vaccination supplies were depleted but for others there were significant changes that predicted earlier or longer epidemics as we discuss further. Both of our models can be easily modified to be used by government and medical officials to create preparedness plans based on specific constraints.