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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Coevolution Of Hosts And Pathogens In The Presence Of Multiple Types Of Hosts, Evan J. Mitchell
Coevolution Of Hosts And Pathogens In The Presence Of Multiple Types Of Hosts, Evan J. Mitchell
Electronic Thesis and Dissertation Repository
How will hosts and pathogens coevolve in response to multiple types of hosts? I study this question from three different perspectives. First, I model a scenario in which hosts are categorized as female or male. Hosts invest resources in maintaining their immune system at a cost to their reproductive success, while pathogens face a trade-off between transmission and duration of infection. Importantly, female hosts are also able to vertically transmit an infection to their newborn offspring. The main result is that as the rate of vertical transmission increases, female hosts will have a greater incentive to pay the cost to …
Mathematical Modelling Of Prophage Dynamics, Tyler Pattenden
Mathematical Modelling Of Prophage Dynamics, Tyler Pattenden
Electronic Thesis and Dissertation Repository
We use mathematical models to study prophages, viral genetic sequences carried by bacterial genomes. In this work, we first examine the role that plasmid prophage play in the survival of de novo beneficial mutations for the associated temperate bacteriophage. Through the use of a life-history model, we determine that mutations first occurring in a plasmid prophage are far more likely to survive drift than those first occurring in a free phage. We then analyse the equilibria and stability of a system of ordinary differential equations that describe temperate phage-host dynamics. We elucidate conditions on dimensionless parameters to determine a parameter …
Phage-Bacteria Interaction And Prophage Sequences In Bacterial Genomes, Amjad Khan
Phage-Bacteria Interaction And Prophage Sequences In Bacterial Genomes, Amjad Khan
Electronic Thesis and Dissertation Repository
In this investigation, we examined the interaction of phages and bacteria in bacterial biofilm colonies, the evolution of prophages (viral genetic material inserted into the bacterial genome) and their genetic repertoire. To study the synergistic effects of lytic phages and antibiotics on bacterial biofilm colonies, we have developed a mathematical model of ordinary differential equations (ODEs). We have also presented a mathematical model consisting of a partial differential equation (PDEs), to study evolutionary forces acting on prophages. We fitted the PDE model to three publicly available databases and were able to show that induction is the prominent fate of intact …
Mathematical Modeling Of The American Lobster Cardiac Muscle Cell: An Investigation Of Calcium Ion Permeability And Force Of Contractions, Lauren A. Skerritt
Mathematical Modeling Of The American Lobster Cardiac Muscle Cell: An Investigation Of Calcium Ion Permeability And Force Of Contractions, Lauren A. Skerritt
Honors Projects
In the American lobster (Homarus americanus), neurogenic stimulation of the heart drives fluxes of calcium (Ca2+) into the cytoplasm of a muscle cell resulting in heart muscle contraction. The heartbeat is completed by the active transport of calcium out of the cytoplasm into extracellular and intracellular spaces. An increase in the frequency of calcium release is expected to increase amplitude and duration of muscle contraction. This makes sense because an increase in cytoplasmic calcium should increase the activation of the muscle contractile elements (actin and myosin). Since calcium cycling is a reaction-diffusion process, the extent to …