# [CT016]

• Session Time & Room
• CT016 (1/1) : 1E @G401 [Chair: Monika Joanna Piotrowska]
• Classification
• CT016 (1/1) : General theory for ordinary differential equations (34A) / Holomorphic functions of several complex variables (32A)

## [00551] Network suppression of the pathogen spread within the healthcare system

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : We consider an impulsive-differential-equation system, based on SIS model, to describe the spread of pathogens in healthcare systems accounting for patient mobility. We propose sufficient conditions guaranteeing network suppression of infection and an algorithm to indicate hospitals prone to high bacteria prevalence and ultimately to ensure the stability of a disease-free state. As an illustration, we present a model of hospital-acquired multidrug-resistant bacteria transmission based on hospital admission records provided by a German insurance company.
• Classification : 34A37, 65P40, 92D30
• Format : Talk at Waseda University
• Author(s) :
• Monika Joanna Piotrowska (Institute of Applied Mathematics and Mechanics, University of Warsaw)
• Aleksandra Puchalska (Institute of Applied Mathematics and Mechanics, University of Warsaw)
• Konrad Sakowski (Institute of Applied Mathematics and Mechanics, University of Warsaw and Institute of High Pressure Physics, Polish Academy of Sciences)

## [01010] Superconvergent Scheme for a System of Green Fredholm Integral Equations

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : In this study, we consider a system of second kind linear Fredholm integral equations with Green’s type kernel function. We propose a piecewise polynomial based Galerkin and iterated Galerkin methods to solve the integral model. We carry out the convergence and error analysis for the proposed methods and establish the superconvergence results for iterated Galerkin method. The theoretical results are supported by numerical tests.
• Classification : 34A12, 45F15
• Format : Talk at Waseda University
• Author(s) :
• Rakesh Kumar (Indian Institute of Technology, Kanpur (India))
• Kapil Kant (Indian Institute of Technology, Kanpur (India))
• B.V. Rathish Kumar (Indian Institute of Technology, Kanpur (India))

## [00501] Efficient numerical method for simulation of plasma

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : Understanding the dynamics of plasma is crucial in many concurrent applications. Those include astrophysics, space discovery, and designing fusion reactors. Numerical methods are a great tool for this purpose. In this talk, an efficient numerical method based on Galerkin approximations is presented. The method has high accuracy, capability of capturing shocks and turbulence, and consistency with thermodynamics. We show several interesting numerical simulations to demonstrate those properties.
• Classification : 34A45
• Format : Talk at Waseda University
• Author(s) :
• Tuan Anh Dao (Uppsala University)

## [00968] Modelling pathogen spreading in a network of hospitals

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : I will introduce an ODE model describing the spread of multidrug-resistant bacteria in a hospital network. I will present the mathematical properties of the model solutions, including the global stability of steady states. Based on simulations for real-life data, I will describe how the parameters affect the process dynamics at both network and hospital levels. Finally, the relations to other types of models describing similar processes will be discussed.
• Classification : 34Axx, 34Cxx, 34D23, 92D30
• Format : Talk at Waseda University
• Author(s) :
• Agata Lonc (University of Warsaw)
• Monika Joanna Piotrowska (Institute of Applied Mrsaathematics and Mechanics, University of Waw)
• Aleksandra Puchalska (Institute of Applied Mathematics and Mechanics, University of Warsaw)

## [00728] Descriptions of distribution function and hyperfunction using discretization

• Session Time & Room : 1E (Aug.21, 17:40-19:20) @G401
• Type : Contributed Talk
• Abstract : Nonlinear systems with singular solutions, such as vortices and vortex sequences, can be mathematically described using the distribution function (δ function). However, it is difficult to numerically analyze the singular solution. In this study, we have considered approaches to discretize the distribution function and discussed the usefulness of introducing it into numerical analysis. Furthermore, we have carried out some examples of applications to discrete distribution functions and Sato’s hyperfunction.
• Classification : 32A45, 46F15, 46F30, 46T30, 65E05
• Format : Talk at Waseda University
• Author(s) :
• Yuya Taki (Graduate School of Science and Engineering, SOKA University)
• Yoshio Ishii (Faculty of Science and Engineering, SOKA University)