Steve Krone

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  Antibiotic resistance plasmids and spatial structure
  Steve Krone
  Bacterial plasmids are circular extra-chromosomal genetic elements that code for simultaneous resistance to multiple antibiotics and are thought to be one of the most important factors in the alarmingly rapid loss of our arsenal of antimicrobial drugs. Plasmids propagate horizontally by infectious transfer, as well as vertically during cell division. Horizontal transfer requires contact between donor and recipient cells, and so spatial structure can play a key role in mediating the spread of antibiotic resistance genes. We will discuss ODE and stochastic spatial models of plasmid population dynamics, as well as empirical results. As an example of the effects of spatial structure, we will use the spatial model to evaluate the effectiveness of a commonly used estimate of plasmid transfer efficiency when applied to surface-associated populations.
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  Particle Systems and Reaction-Diffusion Equations: connecting micro and macro models
  Steve Krone
  This will be something of an introductory talk that considers two types of spatial models used in population biology, and connections between them. Interacting particle systems can be thought of as "microscopic" level descriptions of populations, including interactions between discrete individuals and stochasticity. Reaction-diffusion equations provide deterministic models that can be thought of as "macroscopic" versions of particle systems through scaling limits. We will discuss the basic ideas behind this connection, treat a few examples, and try to understand the extent to which the two types of models predict the same behavior.
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  Individual�based stochastic spatial models
  Steve Krone
  We will work through some of the basic ideas involved in modeling various types of interactions in spatial population biology using interacting particle systems (sometimes referred to as stochastic cellular automata). Some of the essential ingredients and behaviors come from simple models like the contact process and the voter model. These components can be combined and tweaked to obtain models with more biological detail, including epidemic behavior for host-pathogen systems, the spread of antibiotic resistance genes, etc. These models can be informative since real biological populations exhibit a high degree of spatial structure and this structure affects the interactions between individuals and species in ways that can dramatically alter dynamics compared to well-mixed systems. The computer exercises will allow students to alter some existing MATLAB code to simulate various processes. A preview of these models can be found in the WinSSS software that can be downloaded from Steve Krone's webpage.
• 
  Individual�based stochastic spatial models
  Steve Krone
  We will work through some of the basic ideas involved in modeling various types of interactions in spatial population biology using interacting particle systems (sometimes referred to as stochastic cellular automata). Some of the essential ingredients and behaviors come from simple models like the contact process and the voter model. These components can be combined and tweaked to obtain models with more biological detail, including epidemic behavior for host-pathogen systems, the spread of antibiotic resistance genes, etc. These models can be informative since real biological populations exhibit a high degree of spatial structure and this structure affects the interactions between individuals and species in ways that can dramatically alter dynamics compared to well-mixed systems. The computer exercises will allow students to alter some existing MATLAB code to simulate various processes. A preview of these models can be found in the WinSSS software that can be downloaded from Steve Krone's webpage.