# Mathematical Biology

## A cross-scale approach to determining measures of vaccine efficacy

## Vaccination Against Genital Herpes

## Rapid Localized Spread and Immunologic Containment Defines Herpes Simplex Virus-2 Reactivation in the Human Genital Trac

## The effect of vaccination on influenza’s rate of antigenic drift

## Optimizing Influenza Vaccine Allocation

## Mathematical Modeling: The View from Public Health Practice

## Disease Dynamics 2013 (Photos)

## Alan Turing and the Patterns of Life

## 2012 IGTC Summit: Prof. Steve Krone (Part II)

There are many examples in nature where a system goes through a succession of states that are cyclically related. Examples include ecological succession in a forest and SIRS models of epidemics. When such populations are spatially arranged (as are *all* populations to some degree), these cyclic dynamics can sometimes lead to the spontaneous formation of spatial patterns such as spiral waves. We will explore this phenomenon via interacting particle system models and related differential equations.

## 2012 IGTC Summit: Prof. Steve Krone (Part I)

These talks will provide an introduction to individual-based stochastic spatial models (sometimes called interacting particle systems or stochastic cellular automata). We will proceed from very simple basic models to more elaborate ones, illustrating the ideas with examples of spatial biological population dynamics. We will compare these models and results with analogous differential equations (ODE and PDE) and see how they are connected. Biological topics will include spatial population growth and spread, epidemics, evolution of pathogens, and antibiotic resistance plasmids. Throughout, we will point out situations in which spatial structure can dramatically influence the ecology and evolution of populations.