Nikolas Popper

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.

Interdisciplinary Strategies for Simulation-Based Optimization of Energy Efficiency in Production Facilities

This paper presents an approach for interdisciplinary optimization of energy efficiency in production plants. Domain-specific areas of action are discussed as well as the integration into a dynamic co-simulation that helps predicting the impact and financial benefit of selected energy saving measures by comparing and quantifying different scenarios. This should help giving incentives and creating impulses for strategic investment decisions. In a comprehensive methodological approach, optimization potential of both the production process itself as well as the production infrastructure is combined. The technical implementation involves several simulation environments and a framework for synchronization and data exchange in terms of co-simulation. The paper concludes with a discussion of some exemplary simulation results.

Love emotions between Laura and Petrarca —an approach by mathematics and system dynamics

Laura, a very beautiful but also mysterious lady, inspired the famous poet Petrarch for poems, which express ecstatic love as well as deep despair. F. J. Jones - a scientist for literary - recognised in these changes between love and despair an oscillating behaviour - from 1328 to 1350 -, which he called Petrarchs emotional cycle. The mathematician S .Rinaldi investigated this cycle and established a mathematical model based on ordinary differential equation: two coupled nonlinear ODEs, reflecting Lauras and Petrarchs emotion for each other, drive an inspiration variable, which coincides with Petrarch s emotional cycle. These ODEs were starting point for the investigations in two directions: mapping the mathematical model to a suitable modelling concept, and trying to extend the model for love dynamics in modern times (F Breitenecker et al). This contribution introduces and investigates a modelling approach for love dynamics and inspiration by means of System Dynamics, as well as for Lauras and Petrarchs emotions as well as for a modern couple in love. In principal, emotions and inspiration emerge from a source, and are fading into a sink. But the controlling parameters for increase and decrease of emotion create a broad variety of emotional behaviour and of degree of inspiration, because of the nonlinearities. Experiments with an implementation of this model approach and selected simulations provide interesting case studies for different kind of love dynamics - attraction, rejection and neglect, - stable equilibriums and chaotic cycles.

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.

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

Comparison of a microscopic and a macroscopic age-dependent SIR model

ABSTRACT In this work, we compare two structurally different modelling approaches for the simulation of an age-dependent SIR (susceptible, infected, recovered)-type epidemic spread: a microscopic agent-based model and a macroscopic integro-partial differential equation model. Doing so, we put a newly derived mean-field theorem for mixed state-spaces (continuous and discrete) to the test, analytically proving the asymptotic equivalence of the results of both simulations on the aggregate level. Afterwards, both models are executed and compared for abstract scenarios to affirm the derived equivalence. As both models are hereby proven to deliver (asymptotically) the same results, they can be used to supplement each other in terms of structural knowledge of the model, identification and determination of parameters and their values, as well as finally verification and validation.

Mean-field based comparison of two age-dependent sir models

In this work we compare two structurally different modeling approaches for the simulation of an age-dependent SIR (susceptible, infected, recovered) type epidemic spread: a microscopic agent-based model and a macroscopic integro-partial differential equation model. Doing so we put a newly derived Mean-Field Theorem for mixed state-spaces (continuous and discrete) to the test. Afterwards both models are executed and compared for two abstract scenarios to confirm the derived asymptotic equivalence.

About an Alternative Method of Numerical Iteration for State Event Finding and Handling in System Simulation of Hybrid Dynamical Systems

This Paper is about an alternative iteration method to find state events in a hybrid dynamical system simulation. A method introduced in context of numerical computation of Poincare maps can be used to iterate a state event in some special scenarios. Classical ODE solver can be used for this task so no additional algorithms are needed only the mathematical framework has to be adapted. The paper will show this usage in system simulation and establish the context to standard numerical procedures. In the end of the contribution the implementation of this method on a simple example out of ARGESIM Benchmark will be demonstrated.

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