Overview of General Plan
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Many of the scientific challenges in Central America may be viewed in the general category of population dynamics. These include the spread of communicable diseases (e.g., malaria, tuberculosis and dengue fever), the growth and control of certain insect populations (e.g., the fly Cochliomyia hominivorax and mosquitos) which affect the human or the cattle population, and the levels of fish on the ocean coast, rivers and lakes. The understanding of the time evolution of these populations and, ultimately, the control of their sizes is of vital importance in the region since they have a marked effect on public health as well as a high social and economic impact in developing countries.

The goal of this Pan-American Advanced Studies Institute, which will take place July 17 - 28, 2006 at the National University of El Salvador (UES), is to build on previous collaborative activities among scientists in El Salvador, other Central American countries, Mexico and the U.S.A. by bringing together mathematical modelers, statisticians, and other scientists with intimate knowledge of available data on the type of problems described above. This will have the local benefit of bringing to the Central American region some of the leading U.S. mathematical modelers to provide expertise in the way that population dynamics can be approached based on the specific state of the science and available data in Central America. At the same time, the Institute will allow U.S. scientists to present ways to develop and apply existing models to the very real conditions in developing countries. The focus of the Institute is mathematical models of population dynamics, a project that is interdisciplinary in nature since the development of such models requires statistical analysis, data management, biological applications, computational methods, mathematical analysis, and close contact with personnel from agencies that can aid in the application of the models.

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Program Objectives
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The objectives of the Institute are to:

1. Promote the use of statistical and mathematical models for the study of the spread of diseases, insect and fish populations with the purpose of applying them to current social, economic and health problems in Central America.
2. Build on previous collaborative projects among scientists from the participating countries to stimulate new areas of collaboration and to explore mutually beneficial research and educational projects in the general area of mathematical modeling of population dynamics.
3. Promote the exchange of ideas and research in mathematical modeling.

The project will have as additional benefits the expansion of the realm of opportunities for Central American students to interact with researchers from the U.S.A. who can serve as outside thesis project advisors, and to set the stage for follow-up meetings and future collaborations between U.S. scientists and those in the Central American region.

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Program Motivation
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El Salvador has been chosen as the host country because there is already a history of collaboration between scientists at the UES and from the U.S.A. as well as with other Latin American countries. It is important to highlight that these collaborative projects are interdisciplinary and all of them seek the contributions of applied mathematics.

Recently the School of Mathematics of the UES and personnel from the Salvadoran Social Security Institute (ISSS) have established initial contact to explore possible collaborations. The ISSS collects data on levels of infections of certain diseases that a ect the general population. Much of the data now require analysis and management in order to extract significant trends related to the rates of incidence of infectious diseases and to determine the consequences of policies or other actions. The data management and analysis are also required for the inclusion of that information into mathematical models that can predict hypothetical outcomes of various courses of action. The contact between the ISSS and the UES is at an early stage and has been established specifically to understand the type of data available and the necessary statistical analyses that must be performed in order to combine the data with mathematical models, to determine the type of models that would be appropriate for different epidemics, and to suggest new possible data collection mechanisms. In addition, the possibility of academic activities that can bring students to this area is currently being assessed.

The UES has recently created the Institute of Sea Science and Limnology (ICMARES). This institute involves scientists from several disciplines, including faculty specializing in statistics, dynamical systems and biology in support of its projects. This institute seeks to understand the physical, biological and chemical processes that regulate the stability of ecological systems in marine and fresh water environments; to develop research and technology transfer in this area; to increase the understanding of environmental pollution on the coast and in fresh waters and investigate possible courses of action to reduce it; and to serve as an academic program at the undergraduate and graduate levels in Marine Ecology and related areas. As part of events related to this institute, scientists from Costa Rica, Mexico, Chile and the U.S.A. have visited the UES to give talks and explore various possibilities of collaboration. This project involves the processing and analysis ofavailable data, collaboration among ecologists, biologists and applied mathematicians for the development of population models. In addition, it requires computational methods for fluid flow capable of simulating rivers and streams and their interaction with the shrimp and fish populations.

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