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List of Minisessions
-Epidemiology Modeling
-Evolution of Pathogens
-Spatially-Explicit Models of Epidemics
-Theoretical Immunology
-Cell population models with spatial or hierarchical structures
-Employing biomathematical modelling in drug development and in the clinical practice: feasibility and concerns
-Metabolic Networks and Systems Biology
-Deterministic and Stochastic Factors in Biological Invasion: Matching Theory and Observations
-Modelling and managing metapopulations
-Recent advances in adaptive dynamics
-Control Problems in Population Dynamics and Epidemiology
-Complex Diffusive Systems in Mathematical Biology
-Interrelations between stochastic and deterministic modeling in population biology and harvesting
-Stochastic Modelling of Spatially Structured Biological Systems
Epidemiology Modeling
Herb Hethcote, Department of Mathematics, University of Iowa
Theoretical aspects of models for infectious diseases and applications of epidemiological modeling to specific diseases will be presented. Some papers will focus on vaccination-preventable diseases while others will examine control methods for emerging and re-emerging infectious diseases.
Evolution of Pathogens
Maia Martcheva, Department of Mathematics, University of Florida and Zhilan Feng, Department of Mathematics, Purdue University
This session will present research on evolution of pathogens - both within-a-host dynamics and dynamics on epidemiological level. The section will focus on modeling the complexity of multistrain interaction as well as the epidemiology of emerging diseases (like SARS).
Spatially-Explicit Individual-Based Models of Epidemics
Tanya Kostova, Center for Applied Scientific Computing, Livermore
Spatial individual-based simulation models have become very popular in ecological studies. This approach allows the formulation of models of high complexity, incorporating individual and environmental factors as well as a richness of interconnections.
Epidemic spread depends on various factors, often neglected by modelers. The duration of contact, distance to infectious individual, characteristics of pathogen (particle size for example) are measurable physical features that are included implicitly in the rate of infection of traditional models as lumped quantities. These factors are inherently spatial. Other important spatial issues are the factors of indirect contact, such as contaminated locations. Important factors in epidemic spread are the individual immune responses. These also can play role in the spatial spread of an epidemic, as a group of resistant individuals "in the right place at the right time" can alter the route of epidemic spread. Spatially-explicit individual-based simulation models provide a tool to capture the biocomplexity of epidemics. This session is meant to summarize the progress in this field.
Theoretical Immunology
Rob J De Boer, Univ. of Utrecht and Alan Perelson, Los Alamos National Laboratory
The immune system is a complicated and dynamic system, and understanding its functioning calls for a modeling approach. Possible topics to be addressed in this session are: interaction between host and pathogen, HIV and HCV dynamics, the (programmed) dynamic of a primary immune response, analysis of labeling data, affinity maturation in germinal centers, regulatory T cells, Th1/Th2 phenotype switches, etcetera.
Cell population models with spatial or hierarchical structures
Alberto Gandolfi and Alessandro Bertuzzi, Istituto di Analisi dei Sistemi ed Informatica del CNR, Italy
Structured models of cell populations are traditionally formulated in terms of cell age or cell size. Additional levels of structure appear to be of importance for an adequate description of cell populations such as those in tumours or in renewal normal tissues (e.g. epidermis, bone marrow, intestinal epithelia). In tumour, cells proliferate with different rates according to the concentration of oxygen and nutrients in their microenvironment, and thus according to their distance from the blood vessels. In renewal tissues, through rounds of proliferation, cells move along different maturation stages, from stem cells to fully differentiated cells. In some tissues, the different maturation stages are accompanied by different spatial location. The session is devoted to give a brief insight on these new models.
Employing biomathematical modelling in drug development and in the clinical practice: feasibility and concerns
Zvia Agur, Inst. for Medical BioMathematics
Aims of the session: a) To present the significance and achievements of biomathematics for rationalizing clinical treatment, with a special emphasis on potential pitfalls; b) "Good biomathematical practice" - a new paradigm of "applied biomathematics". Scope of the session: a) Areas of implementation of biomathematics in clinic, doctors' and pharma needs, achievements of modelling up to nowadays, feasibility and possible pitfalls; b) multidisciplinary approach to biomathematics, parameter/data-oriented modelling, parameter search/evaluation, retrospective validation, planning of prospective experiments.
Metabolic Networks and Systems Biology
Marek Kimmel, Rice Univ. and Vlastimil Krivan, Czech Acad. Sci.
This session should give an overview on mathematical modelling techniques applied to the study of biological systems from the molecular through the cellular to the behavioral level. This includes models at DNA level, gene interactions (gene networks, in particular), protein interactions, metabolic pathways etc. In particular, talks on conceptual mathematical approaches are welcomed.
Deterministic and Stochastic Factors in Biological Invasion: Matching Theory and Observations
Sergei Petrovskii, Shirshov Institute of Oceanology, Russian Academy of Science and Horst Malchow, Institute for Environmental Systems Research, Osnabrueck University.
The problem of biological invasion is an issue of major significance in contemporary ecology. Among many issues related to species invasions, a highly practical and theoretically important question is which environmental and biological factors can affect the pattern of spread and the rate of invasion either speeding up or slowing down spreading of invasive species. The heterogeneity of the environment is apparently one of them although its impact on the species spread is not always as obvious as it may seem to be. Another factor is identified in predation that can slow down or even reverse the invasion. The Allee effect has recently been shown to possibly affect the whole pattern of spread changing it from population fronts to patchy invasion. An issue of interest is the interplay of species invasion and other forms of species transport, one (but not the only) example being given by advection with the wind or water current. Environmental stochasticity is very important, although the impacts of deterministic and stochastic factors are not always easily distinguishable and their relative contribution still remains obscure.
This session will focus on (but will not be limited to) the issues mentioned above. A special attention will be paid to the scenarios of biological invasion resulting from an interplay between deterministic and stochastic processes. Both rigorous analytical results and results based on numerical simulations will be presented, as well as papers based on analysis of field data. The session is expected not only to highlight recent progress in theoretical/mathematical approaches to biological invasion but also to bring up new examples of species invasion that cannot be readily described by standard models, and thus to stimulate farther development in this field.
Modelling and managing metapopulations
Marino Gatto, Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milano, Italy and Andrea Pugliese, Dipartimento di Matematica, Università di Trento, Italy
Space-implicit and space-explicit models of metapopulations. The influence of disturbance and habitat loss. The design of reserves: location and shape. We,ll try to have a good mixture of theoretical, applied and field scientists.
Recent advances in adaptive dynamics
Ulf Dieckmann, International Institute for Applied Systems Analysis, Austria and Hans Metz, Leiden University
The theory of adaptive dynamics continues to be a lively field of research, integrating stochastic and deterministic approaches to describing phenotypic evolution at the level of populations and communities. This minisession will present a potpourri of recently obtained results.
Control Problems in Population Dynamics and Epidemiology
B.E. Ainseba, MAB Bordeaux, Université Victor Segalen Bordeaux 2, 146 Rue Léo Saignat 33076 Bordeaux Cedex.
The aim of this session is to present recent works and advances on control problems in population dynamics and epidemiology. Population control is the process of forcing a population in order to obtain a suitable behavior or shape. The intervention strategy constitutes the control. Some significant ecological applications are harvesting natural or farmed populations, regulating the density of individuals within a population, containing epidemics. The talks in the session will discuss both more technical and numerical problems related to the control of population and epidemic models, as well as some specific biological implications.
Complex Diffusive Systems in Mathematical Biology
W.E. Fitzgibbon (University of Houston) and M. Langlais (University of Bordeaux)
Complex diffusive systems arise in a variety of contexts in biological and ecological modeling including the dynamics of spatially dispersed interacting populations, the geographic spread of infectious diseases, epidemiological modeling, models of tumor growth, theoretical analysis biological pattern formation, biodegradation, genetics and pollutant production and transport. This session will focus upon the models and their theoretical analysis, approximation and simulation.
Interrelations between stochastic and deterministic modeling in population biology and harvesting
Carlos A. Braumann, Dept. Math., Univ. Évora, Portugal and Shay Gueron Department of Mathematics University of Haifa Haifa, 31905, Israel
Stochastic processes, particularly in the field of mathematical ecology and applications to harvesting, are often modelled by means of deterministic differential or difference equations, thus ignoring environmental or demographic random variations. These deterministic descriptions of the time evolution hope to approximate the underlying stochastic process, at least for large populations. However, various examples demonstrate that this is not always the case: discrepancies, inconsistencies and inaccuracies, emerge, merely as a result of the modelling approach. These differences may result in different predictions concerning population persistence or extinction and optimal harvesting strategies (possibly under conservation or social constraints).
This session will be devoted to the methodological study of the interrelations between stochastic and deterministic modelling approaches in population biology and its applications to harvesting. Possible scenarios for the presentations are:
A. Similarities and differences in the predictions made by different approaches.
B. Studies that show how and why the deterministic descriptions fail.
C. Studies that can prove the success of deterministic descriptions in various cases.
Stochastic Modelling of Spatially Structured Biological Systems
Vincenzo Capasso, Universita' di Milano
In biology there is a wide spectrum of examples which exhibit collective behavior, such as formation of patterns and clustering.
This may happen at any scale: from the cellular scale of embryonic tissue formation, wound healing or tumor growth, and vasculogenesis, the microscopic scale of life cycles of bacteria or social amoebae, to the larger scale of animal grouping.
Often it is suitable a multiscale approach: individual stochastic approach to the microscopic scale, Eulerian deterministic approach to the macroscopic scale.
Furthermore in many situations a strong coupling of the evolution equations for (stochastic) geometries with the evolution equations of the underlying fields of densities,concentrations, etc may be needed.
In this minisymposium we would like to exploit the mathematical tools of coupling multiscales arising in nature, via "laws of large numbers"
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