My Research Interests

I am interested in the effects of spatial heterogeneity on biological processes, specifically epidemiology. I use mathematical models and computer simulations to evaluate the impact of including space as a variable. I have worked on a variety of biological problems during graduate school and my subsequent postdoctoral positions. Listed here are brief descriptions of these projects.

Current Work

Optimal control
- Optimal control of integro-difference equation
  - Gaff, H., H.R. Joshi and S.Lenhart, Optimal Harvesting in an Integro-difference Population Model, In preparation.
- Optimal control of tick-borne disease model
  - Gaff, H. D., L. J. Gross, R. Gerhardt, and C. Morris, Application of a tick-borne disease patch model to spatially varying habitats, In preparation.

Previous Work

Mathematical Epidemiology:
- Tick-borne diseases
  Based on data from an outbreak of Ehrlichiosis and the subsequent attempts at controling the tick population, a differential equation model was developed. This model was used to evaluate the relative effectiveness of different control strategies. The preliminary results indicate that the habitat of the location where a control device is implemented can impact the reduction in tick populations and thus the risk of disease.
  - Gaff, H. D. and L. J. Gross, Analysis of a tick-borne disease model with varying population sizes in various habitats, In preparation.
- HIV/HSV-2
  I very briefly began work looking at the potential reduction of HIV transmission that could be achieved by controling HSV-2.
Mathematical Ecology:
- ATLSS - ALFISH
  I have done extensive work on the fish model for the ATLSS project. ATLSS, Across Trophic Level System Simulation, is a project comprised of a set of models which are integrated into a multimodel for the South Florida Everglades ecosystem. My role was to develop and analyze a model for the freshwater fish populations present in the Everglades. ATLSS is currently part of the Central and Southern Florida Comprehensive Study Review with the goal of aiding plans for major changes to the hydrologic control systems over the next 30 years.
  - Gaff, H. D., D. L. DeAngelis, L. J. Gross, R. Salinas and M. Shorrosh, A dynamic landscape model for fish in the Everglades and its application to restoration, Ecological Modelling (2000) 127:33-52.
  - Gaff, H. D., J. Chick, D. L. DeAngelis, L. J. Gross, J. Trexler and R. Salinas, Evaluation of and insights from ALFISH: a spatially-explicit, landscape-level simulation of fish populations in the Everglades, Submitted.
- ATLSS - Fish SESI
  Additionally as part of the ATLSS project, I have started work on a spatially-explicit species index (SESI) model for the fish populations in the Everglades. This is a simplified model based on the empirical work of Joel Trexler et al.
- Nutrient flow in riparian zones
  Using data from the Ward Creek basin in the Lake Tahoe area, I started work investigating the impact of spatial structure on the release and uptake of nutrients.

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