Human history tells us of two great mass migrations- one out of Africa and into Asia and Europe, and one out of Asia into the Americas. Traditionally the particulars of these events have been in the scholarly domain of anthropologists and archeologists and of linguists. They used artifacts- teeth and bones, crania, tools, and ceramics, or historical comparative linguistics as the tools for investigation. These methods rely on intense field work and on luck to complete the picture.
More recently, genetics studies and modes of evolution are also being employed for the study of Home sapiens. For these studies, we are required to find individuals with the requisite genetic history and to develop an appropriate mathematical model of genetic evolution. Michael Hammer, an evolutionary biologist and statistician and Stephen Zigura, an anthropologist, have been working together to combine molecular and archelogical approaches to build models in population genetics and systematic biology. They have used the human Y chromosome [10] and mitochrondrial DNA to investigate these two mass migration of humans. Their two strategies provide independent predictions of the migration- the first based on paternal lines, the second on maternal lines.
In the study of human disease, biological, epidemiological, behavioral, and social science studies produce better projections and better understanding of the transmission dynamics of infectious diseases when they are coordinated with a credible mathematical model. A multidisciplinary research team based at the Los Alamos National Laboratory, with participation of two University of Arizona graduate students, is working to create a logical structure that organizes existing information on epidemics into coherent frameworks, suggesting new information that must be collected on a wide variety of diseases [11,12]. This research team has learned a variety of lessons on epidemiological models. Models that are founded on the transmission mechanisms can show how the early infections in an epidemic, behavioral changes, and future medical advances such as treatments and vaccines will affect the future course of the epidemic. Because effects will be highly nonlinear functions of the parameter values, they will at times lead to changes that are counter to both intuition simple extrapolated predictions. For the example of HIV, models by necessity must structure the population into a large number of groups, based on sexual preferences, gender, risk behavior level, age, and genetic susceptibility.
One former Flinn fellow, Cecelia Fosser, an Applied Mathematics doctoral student is developing and analyzing a cellular automata model for epidemics. Because her model is based on the mechanisms of the transmission process and the progression from the initial infection to the onset of the disease, it can lead to an improved understanding of the future spread of disease because explicit elements of biology and behavior are included in the models.