Günther Zauner

Modelling SIR-type epidemics by ODEs, PDEs, difference equations and cellular automata – A comparative study

Abstract The Kermack–McKendrick susceptible-infected-recovered (SIR) model describes the dynamics of epidemics in a cumulative way. This contribution compares different approaches for introducing spatial patterns into these dynamics. The applied techniques cover lattice gas cellular automata (LGCA), stochastic cellular automata (SCA) and partial differential equations (PDE). Even though these methods involve distinct types of spatial interaction, it can be shown, that consistent qualitative and quantitative model behaviour can be obtained by means of parameter adaptions and slight technical modifications. These modifications are motivated by stochastic analysis of distributed interaction (PDE, SCA) and diffusion dynamics (LGCA) as well as prevailing physical analogies. The law of large numbers permits to approximate stochastic contacts by distributed interaction. Diffusion of particles can be approximated through empiric adjustment of a Gaussian diffusion distribution.

Simulation of influenza epidemics with a hybrid model - combining cellular automata and agent based features

To understand and predict epidemic patterns ODEs and PDEs have been used since the beginning of the last century. But these approaches have a quite relevant shortcoming. Trying to model a multiply heterogeneous population (e.g. with individual characteristics, varying population densities) increases complexity beyond limits. To bring individual effects into epidemic models a new approach is necessary. Agent-based (AB) models as well as cellular automata (CA) represent tools which allow incorporating such influences. In this paper we shall present a hybrid model that combines the flexibility of an AB-framework with the computational efficiency of CAs. We will also look at the potential benefit of such a structure by taking a look at first (academic) results.

Introducing MATLAB into basic mathematic lectures using a custom e-learning system

To counter the decreasing interest and understanding in the basic mathematic lectures in geodesy, it was decided to supplement these lectures with MATLAB. Due to licence issues, the MATLAB Web server was used, changing the lecture to a blended learning course. A special interface for the Web server was created for a better separation of content and Web server, and the system has proven satisfactory.

A Flexible Agent-Based Framework for Infectious Disease Modeling

Agent-based modeling is a method to model a system by autonomous entities. The proposed framework models single persons with personal behavior, different health states and ability to spread the disease. Upon simulation, the epidemic emerges automatically. This approach is clear and easily understandable but requires extensive knowledge of the epidemic’s background. Such real-world model structures produce realistic epidemics, allowing detailed examination of the transmission process or testing and analyzing the outcome of interventions like vaccinations. Due to changed epidemic propagation, effects like herd immunity or serotype shift arise automatically. Beyond that, a modular structure splits the model into parts, which can be developed and validated separately. This approach makes development more efficient, increases credibility of the results and allows reusability and exchangeability of existing modules. Thus, knowledge and models can be easily and efficiently transferred, for example to compute scenarios for different countries and similar diseases.

BCP - A Benchmark for Teaching Structural Dynamical Systems

Abstract New object-oriented modelling techniques for physical systems along with more complex systems of interest lead to increasing requirements on modern simulators regarding performance and stability as well as state event modelling and event handling in combination with hybrid and structural dynamic systems. To see how modelling and simulation environments deal with such systems and to compare new approaches to hybrid modelling, a new benchmark is defined using three case studies with modelling and simulation tasks. The first case study investigates the classic bouncing ball example with some extensions. The second example discusses an electrical circuit - it can be used to compare the simulation results of different implementation techniques (e.g. physical modelling vs. classical DAE form) in one simulator. The third case study is a definition of a pendulum on a rope with free falling phase, representing another simple structural dynamic mechanical system. These three parts offer a spectrum of questions for testing basic features for handling hybrid and structural dynamic physical systems and they represent minimum requirements on hybrid simulators regarding state events.

Benchmarking of Simulation Systems--The ARGESIM Comparisons

Modelling and simulation has become the third pillar of gaining knowledge. Modelling and simulation of a process makes use of a simulation software, and quality of results and investigation time depend dramatically on the choice of the most appropriate simulator. Consequently, a basis for simulator choice or at least serious hints are necessary. This contribution first gives an overview about methods for comparing and benchmarking simulation systems. Then it introduces the ARGESIM benchmarks/comparisons on simulation software and gives details on some comparisons. The paper concludes with an outlook for further development of the ARGESIM benchmarks

Statistical methods and modelling techniques for analysing hospital readmission of discharged psychiatric patients: a systematic literature review

BackgroundPsychiatric services have undergone profound changes over the last decades. CEPHOS-LINK is an EU-funded study project with the aim to compare readmission of patients discharged with psychiatric diagnoses using a registry-based observational record linkage study design and to analyse differences in the findings for five different countries. A range of different approaches is available for analysis of the available data. Although there are some studies that compare selected methods for evaluating questions on readmission, there are to our knowledge no published systematic literature reviews on commonly used methods and their comparison. This work shall therefore provide an overview of the methods in use, their evolution throughout history and new developments which can further improve the research quality in this area.MethodsBased on systematic literature reviews realized in the course of the CEPHOS-LINK study, this work is a systematic evaluation of mathematical (statistical and modelling) methods used in studies examining psychiatric readmission. The starting point were 502 papers, of which 407 were analysed in detail; Methods used were assigned to one of five categories with subcategories and analysed accordingly. Our particular interest next to survival analysis and regression models is modelling and simulation.ResultsAs population sizes and follow-up times in the included studies varied widely, a range of methods was applied. Studies with bigger sample sizes conducted survival and regression analysis more often than studies with fewer patients did. These latter relied more on classical statistical tests (e.g. t-tests and Student Newman Keuls). Statistical strategies were often insufficiently described, posing a major problem for the evaluation. Almost all cases failed to provide and explanation of the rationale behind using certain methods.ConclusionThere is a discernible trend from classical parametric/nonparametric tests in older studies towards regression and survival analyses in more recent ones. Modelling and simulation were under-represented despite their high usability, as has been identified in other health applications and comparable research areas.

A modular simulation model for assessing interventions for abdominal aortic aneurysms

This paper discusses the development of an individual based simulation model for evaluation of interventions for better treatment of patients with abdominal aortic aneurysms (AAA). The interdisciplinary subject required collaboration of medical doctors, Health Technology Assessment (HTA) experts and modelers. The here presented modular model structure is flexible enough to allow adaptation on screening research questions for similar diseases. Another focus of the work was integration of risk factors and how it determines our model choice, especially because steadily increasing knowledge about or improved treatment of AAA could cause necessity of reevaluation. Through inclusion of several patient specific properties the model does not only provide comparison of current state with screening but also elaboration of alterations of population characteristics and its consequences on AAA cases.

DATA, METHODS, MODELS AND RESULT INTERPRETATION: A MODEL BASED COMBINATION OF VARIOUS SKILLS TO THE IFEDH FRAMEWORK

Abstract As health care systems in all countries have to deal with limited resources and upcoming new technologies, high quality decision support and HTA based on dynamic and static modeling is getting more and more essential. In Austria the research project Innovative Framework for Evidence based Decision support in Health care (IFEDH) founded by The Austrian Research Promotion Agency is developing a framework addressing HTA questions. Main focus of the project lies on the development of processes leading an interdisciplinary group of experts in the field of HTA, statistics, modeling, visualization and database analysts through the whole HTA production cycle. The modeling process and design of adequate modeling methods are one core part. In the context of IFEDH a model based framework has to be implemented using detailed knowledge of the partners from different domains. The first step in the project is the analysis of model and structure expertise as well as gathering the state of the art of modeling in HTA in Austria. Based on this information a specification of requirements regarding model structure and documentation of simulation outputs are set up. The core working task of the network is the development of reusable modeling structures and methods. Furthermore modular model parts are developed. The analysis of data sources and interface descriptions finalize this task. The development of modern modeling methods and setting up an interdisciplinary process, dealing with the rising questions in HTA especially for infectious diseases and vaccination strategy evaluation is realized. The description of the research project presented in the paper shows how different scientific domains can be joined to a joint overall approach in model based HTA. As decision support has to become faster, parameter sources and modular reusable model parts have to be developed in advance.

Long Term Behaviour of Agent based Epidemic Simulation of Streptococcus Pneumoniae - A Mathematical Status Report

SN E 2/2, A uust 2010 Long Term Behaviour of Agent based Epidemic Simulation of Streptococcus Pneumoniae A Mathematical Status Report Florian Miksch1, Nikolas Popper2, Günther Zauner2, Irmgard Schiller-Frühwirth3, Gottfried Endel3 1Vienna University of Technology, Institute for Analysis and Scientific Computing, Vienna, Austria; 2dwh Simulation Services, Vienna, Austria; 3Evidence Based Economic Healthcare, Hauptverband der Öst. Sozialversicherungsträger