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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
An Agent-Based Modeling Approach To Determine Winter Survival Rates Of American Robins And Eastern Bluebirds, Samuel Iselin, Shannon Segin, Alex Capaldi
An Agent-Based Modeling Approach To Determine Winter Survival Rates Of American Robins And Eastern Bluebirds, Samuel Iselin, Shannon Segin, Alex Capaldi
Alex Capaldi
American Robins (Turdus migratorius) and Eastern Bluebirds (Sialia sialis) are two species of migratory thrushes that breed in Northwest Indiana but historically are uncommon during the winter season. These trends have changed recently, and both species are seen more abundantly during the winter. Recently invaded non-native fruiting plants continue to provide nutrients for the birds throughout the winter and may contribute to the increased avian populations during that time. To measure the effect these food sources contribute to thrush wintering habits, we created an agent-based computer model to simulate the birds' movement in Northwest Indiana along …
Multistrain Infections In Metapopulations, Sydney Garmer, Rachel Lynn, Dan Rossi, Alex Capaldi
Multistrain Infections In Metapopulations, Sydney Garmer, Rachel Lynn, Dan Rossi, Alex Capaldi
Alex Capaldi
Viruses and bacteria responsible for infectious diseases often mutate and are carried between geographical regions. We consider a mathematical model which begins to account for these factors. We assume two disjoint populations that only occasionally co-mingle and two strains of a disease present in these populations. Of interest are the equations describing the dynamics of this system, the conditions under which epidemics will occur, and the long term behavior of the system under various initial conditions. We fi#12;nd general conditions
under which a state of disease-free equilibrium is stable. Additionally, we #12;find existence of a biologically relevant equilibrium where two …
Investigating Anthropogenic Mammoth Extinction With Mathematical Models, Michael Frank, Anneliese Slaton, Teresa Tinta, Alex Capaldi
Investigating Anthropogenic Mammoth Extinction With Mathematical Models, Michael Frank, Anneliese Slaton, Teresa Tinta, Alex Capaldi
Alex Capaldi
One extinction hypothesis of the Columbian mammoth (Mammuthus columbi), called overkill, theorizes that early humans overhunted the animal. We employ two different approaches to test this hypothesis mathematically: analyze the stability of the equilibria of a 2D ordinary differential equations (ODE) system and develop a metapopulation differential equations model. The 2D ODE system is a modified predator-prey model that also includes migration. The metapopulation model is a spatial expansion of the first model on a rectangular grid. Using this metapopulation system, we model the migration of humans into North America and the response in the mammoth population. These approaches show …