An impulsive differential equation model for Marek's disease

Many dynamical processes are subject to abrupt changes in state. Often these perturbations can be periodic and of short duration relative to the evolving process. These types of phenomena are described well by what are referred to as impulsive differential equations, systems of differential equations coupled with discrete mappings in state space. In this thesis we employ impulsive differential equations to model disease transmission within an industrial livestock barn. In particular we focus on the poultry industry and a viral disease of poultry called Marek's disease. This system lends itself well to impulsive differential equations. Entire cohorts of poultry are introduced and removed from a barn concurrently. Additionally, Marek's disease is transmitted indirectly and the viral particles can survive outside the host for weeks. Therefore, depopulating, cleaning, and restocking of the barn are integral factors in modelling disease transmission and can be completely captured by the impulsive component of the model. Our model allows us to investigate how modern broiler farm practices can make disease elimination difficult or impossible to achieve. It also enables us to investigate factors that may contribute to virulence evolution. Our model suggests that by decrease the cohort duration or by decreasing the flock density, Marek's disease can be eliminated from a barn with no increase in cleaning effort. Unfortunately our model also suggests that these practices will lead to disease evolution towards greater virulence. Additionally, our model suggests that if intensive cleaning between cohorts does not rid the barn of disease, it may drive evolution and cause the disease to become more virulent.

Differential contributions of the mIPS and PMd in the movement planning of reaches investigated through HD-tDCS

To reach for a target, we must formulate a movement plan - a difference vector of the target position with respect to the starting hand position. While it is known that the medial part of the intraparietal sulcus (mIPS) and the dorsal premotor (PMd) activity reflects aspects of a kinematic plan for a reaching movement, it is unclear whether or how the two regions may differ. We investigated the functional roles of the mIPS and PMd in the planning of reaching movements using high definition transcranial direct current stimulation (HD-tDCS) and examined changes in horizontal endpoint error when participants were subjected to anodal and cathodal stimulation. The left mIPS and PMd were functionally localized with fMRI in each participant using an interleaved center-out pointing and saccade task and mapped onto the scalp using Brainsight. We adopted a randomized, single-blind design and applied anodal and cathodal stimulation (2mA for 20 min; 3cm radius 4x1 electrode placement) during 4 separate visits scheduled at least a week apart. Each participant performed 250 baseline, stimulation, and post-stimulation memory-guided reaches starting from one of two initial hand positions (IHPs) to one of 4 briefly flashed targets (20 cm distant, 5 cm apart horizontally) while fixating on a straight-ahead cross located at the target line. Separate 2-way repeated measures ANOVAs of horizontal endpoint error difference after cathodal tDCS at each stimulation site revealed a significant IHP by target position interaction effect at the left mIPS, and significant IHP and target main effects at the left PMd. Behaviorally, these effects corresponded to IHP-dependent contractions after cathodal mIPS tDCS and IHP-independent contractions after cathodal PMd tDCS. These results suggest that the movement vector is not yet formed at the input level of mIPS, but is encoded at the input of PMd. These results also indicate that tDCS is a viable, useful method in investigating movement planning properties through temporary perturbations of the system.