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M Kroger, R Schlickeiser,
Analytical solution of the SIR-model for the temporal evolution of epidemics. Part A: time-independent reproduction factor
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL English 53 (2020) 505601
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We revisit the susceptible-infectious-recovered/removed (SIR) model which is one of the simplest compartmental models. Many epidemological models are derivatives of this basic form. While an analytic solution to the SIR model is known in parametric form for the case of a time-independent infection rate, we derive an analytic solution for the more general case of a time-dependent infection rate, that is not limited to a certain range of parameter values. Our approach allows us to derive several exact analytic results characterizing all quantities, and moreover explicit, non-parametric, and accurate analytic approximants for the solution of the SIR model for time-independent infection rates. We relate all parameters of the SIR model to a measurable, usually reported quantity, namely the cumulated number of infected population and its first and second derivatives at an initial time t = 0, where data is assumed to be available. We address the question of how well the differential rate of infections is captured by the Gauss model (GM). To this end we calculate the peak height, width, and position of the bell-shaped rate analytically. We find that the SIR is captured by the GM within a range of times, which we discuss in detail. We prove that the SIR model exhibits an asymptotic behavior at large times that is different from the logistic model, while the difference between the two models still decreases with increasing reproduction factor. This part A of our work treats the original SIR model to hold at all times, while this assumption will be relaxed in part B. Relaxing this assumption allows us to formulate initial conditions incompatible with the original SIR model. [Kroger, M.] Swiss Fed Inst Technol, Polymer Phys, Dept Mat, CH-8093 Zurich, Switzerland. [Schlickeiser, R.] Ruhr Univ Bochum, Lehrstuhl Weltraum & Astrophys 4, Inst Theoret Phys, D-44780 Bochum, Germany. [Schlickeiser, R.] Univ Kiel, Inst Theoret Phys & Astrophys, Kiel Leibnizstr 15, D-24118 Kiel, Germany. Kroger, M (corresponding author), Swiss Fed Inst Technol, Polymer Phys, Dept Mat, CH-8093 Zurich, Switzerland.; Schlickeiser, R (corresponding author), Ruhr Univ Bochum, Lehrstuhl Weltraum & Astrophys 4, Inst Theoret Phys, D-44780 Bochum, Germany.; Schlickeiser, R (corresponding author), Univ Kiel, Inst Theoret Phys & Astrophys, Kiel Leibnizstr 15, D-24118 Kiel, Germany. mk@matetz.ch; rsch@tp4.rub.de [hide]
Principal Investigators
Argyrios Karatrantos (PI)
Institute of Science and Technology, Luxembourg ►
Martin Kröger (PI)
Polymer Physics, ETH Zurich, Switzerland ►
Project Partners
Clement Mugemana
Institute of Science and Technology, Luxembourg ►
Jeremy Odent
Laboratory of polymeric and composite materials, Mons University, Belgium ►
Scientific Staff
Ahmad Moghimikheirabadi
Polymer Physics, ETH Zurich, Switzerland ►
Secretary
Patricia Horn
Polymer Physics, ETH Zurich, Switzerland ►
Enjoy your reading
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A Moghimikheirabadi, M Kroger, AV Karatrantos,
Insights from modeling into structure, entanglements, and dynamics in attractive polymer nanocomposites
SOFT MATTER English 17 (2021) 6362
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ZQ Shen, HL Ye, QM Wang, M Kroger, Y Li,
Sticky Rouse Time Features the Self-Adhesion of Supramolecular Polymer Networks
MACROMOLECULES English 54 (2021) 5053
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M Pourali, M Kroger, J Vermant, PD Anderson, NO Jaensson,
Drag on a spherical particle at the air-liquid interface: Interplay between compressibility, Marangoni flow, and surface viscosities
PHYSICS OF FLUIDS English 33 (2021) 062103
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R Schlickeiser, M Kroger,
Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations
PHYSICS English 3 (2021) 386
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YR Sliozberg, M Kroger, TC Henry, S Datta, BD Lawrence, AJ Hall, A Chattopadhyay,
Computational design of shape memory polymer nanocomposites
POLYMER English 217 (2021) 123476
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R Schlickeiser, M Kroger,
Epidemics Forecast From SIR-Modeling, Verification and Calculated Effects of Lockdown and Lifting of Interventions
FRONTIERS IN PHYSICS English 8 (2021) 593421
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M Kroger,
Top Cited 2018-2019 Papers in the Section "Polymer Theory and Simulation"
POLYMERS English 13 (2021) 43
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AV Karatrantos, T Ohba, Q Cai,
Diffusion of ions and solvent in propylene carbonate solutions for lithium-ion battery applications
JOURNAL OF MOLECULAR LIQUIDS English 320 (2020) 114351
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XC Shang, M Kroger,
Time Correlation Functions of Equilibrium and Nonequilibrium Langevin Dynamics: Derivations and Numerics Using Random Numbers
SIAM REVIEW English 62 (2020) 901
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A Moghimikheirabadi, C Mugemana, M Kroger, AV Karatrantos,
Polymer Conformations, Entanglements and Dynamics in Ionic Nanocomposites: A Molecular Dynamics Study
POLYMERS English 12 (2020) 2591
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P Ilg, M Kroger,
Dynamics of interacting magnetic nanoparticles: effective behavior from competition between Brownian and Neel relaxation
PHYSICAL CHEMISTRY CHEMICAL PHYSICS English 22 (2020) 22244
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M Sadeghi, MH Saidi, A Moosavi, M Kroger,
Tuning Electrokinetic Flow, Ionic Conductance, and Selectivity in a Solid-State Nanopore Modified with a pH-Responsive Polyelectrolyte Brush: A Molecular Theory Approach
JOURNAL OF PHYSICAL CHEMISTRY C English 124 (2020) 18513
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M Kroger, R Schlickeiser,
Gaussian Doubling Times and Reproduction Factors of the COVID-19 Pandemic Disease
FRONTIERS IN PHYSICS English 8 (2020) 276
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R Ranganathan, V Kumar, AL Brayton, M Kroger, GC Rutledge,
Atomistic Modeling of Plastic Deformation in Semicrystalline Polyethylene: Role of Interphase Topology, Entanglements, and Chain Dynamics
MACROMOLECULES English 53 (2020) 4605
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J Schuttler, R Schlickeiser, F Schlickeiser, M Kroger,
Covid-19 Predictions Using a Gauss Model, Based on Data from April 2
PHYSICS English 2 (2020) 197
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N Gheczy, K Sasaki, M Yoshimoto, S Pour-Esmaeil, M Kroger, P Stano, P Walde,
A two-enzyme cascade reaction consisting of two reaction pathways. Studies in bulk solution for understanding the performance of a flow-through device with immobilised enzymes
RSC ADVANCES English 10 (2020) 18655
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RS Hoy, M Kroger,
Unified Analytic Expressions for the Entanglement Length, Tube Diameter, and Plateau Modulus of Polymer Melts
PHYSICAL REVIEW LETTERS English 124 (2020) 147801
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A Moghimikheirabadi, P Ilg, LMC Sagis, M Kroger,
Surface Rheology and Structure of Model Triblock Copolymers at a Liquid-Vapor Interface: A Molecular Dynamics Study
MACROMOLECULES English 53 (2020) 1245
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M Kroger,
Developments in Polymer Theory and Simulation
POLYMERS English 12 (2020) 30
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ZQ Shen, DT Loe, A Fisher, M Kroger, JL Rouge, Y Li,
Polymer stiffness governs template mediated self-assembly of liposome-like nanoparticles: simulation, theory and experiment
NANOSCALE English 11 (2019) 20179
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MS Khan, AV Karatrantos, T Ohba, Q Cai,
The effect of different organic solvents and anion salts on sodium ion storage in cylindrical carbon nanopores
PHYSICAL CHEMISTRY CHEMICAL PHYSICS English 21 (2019) 22722
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A Moghimikheirabadi, P Fischer, M Kroger, LMC Sagis,
Relaxation Behavior and Nonlinear Surface Rheology of PEO-PPO-PEO Triblock Copolymers at the Air-Water Interface
LANGMUIR English 35 (2019) 14388
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S Costanzo, L Scherz, G Floudas, R Pasquino, M Kroger, AD Schluter, D Vlassopoulos,
Hybrid Dendronized Polymers as Molecular Objects: Viscoelastic Properties in the Melt
MACROMOLECULES English 52 (2019) 7331
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ZQ Shen, HL Ye, M Kroger, S Tang, Y Li,
Interplay between ligand mobility and nanoparticle geometry during cellular uptake of PEGylated liposomes and bicelles
NANOSCALE English 11 (2019) 15971
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D Messmer, A Sanchez-Ferrer, S Tacke, H Yu, H Nusse, J Klingauf, R Wepf, M Kroger, A Halperin, R Mezzenga, AD Schluter,
Can one determine the density of an individual synthetic macromolecule?
SOFT MATTER English 15 (2019) 6547
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M Kroger,
Efficient hybrid algorithm for the dynamic creation of wormlike chains in solutions, brushes, melts and glasses
COMPUTER PHYSICS COMMUNICATIONS English 241 (2019) 178
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W Wang, F Shao, M Kroger, R Zenobi, AD Schluter,
Structure Elucidation of 2D Polymer Monolayers Based on Crystallization Estimates Derived from Tip-Enhanced Raman Spectroscopy (TERS) Polymerization Conversion Data
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY English 141 (2019) 9867
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M Colangeli, C Giberti, C Vernia, M Kroger,
Emergence of stationary uphill currents in 2D Ising models: the role of reservoirs and boundary conditions
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS English 228 (2019) 69
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A Karatrantos, RJ Composto, KI Winey, M Kroger, N Clarke,
Modeling of Entangled Polymer Diffusion in Melts and Nanocomposites: A Review
POLYMERS English 11 (2019) 876
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A Karatrantos, RJ Composto, KI Winey, N Clarke,
Nanorod Diffusion in Polymer Nanocomposites by Molecular Dynamics Simulations
MACROMOLECULES English 52 (2019) 2513
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D Messmer, C Bottcher, H Yu, A Halperin, K Binder, M Kroger, AD Schlutert,
3D Conformations of Thick Synthetic Polymer Chains Observed by Cryogenic Electron Microscopy
ACS NANO English 13 (2019) 3466
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LMC Sagis, BX Liu, Y Li, J Essers, J Yang, A Moghimikheirabadi, E Hinderink, C Berton-Carabin, K Schroen,
Dynamic heterogeneity in complex interfaces of soft interface-dominated materials
SCIENTIFIC REPORTS English 9 (2019) 2938
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A Moghimikheirabadi, LMC Sagis, M Kroger, P Ilg,
Gas-liquid phase equilibrium of a model Langmuir monolayer captured by a multiscale approach
PHYSICAL CHEMISTRY CHEMICAL PHYSICS English 21 (2019) 2295
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PS Stephanou, M Kroger,
Assessment of the Tumbling-Snake Model against Linear and Nonlinear Rheological Data of Bidisperse Polymer Blends
POLYMERS English 11 (2019) 376
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T Weber, G Hofer, A Simonov, M Kroger, D Schluter,
UNDERSTANDING TWO-DIMENSIONAL POLYMERISATION USING BRAGG AND DIFFUSE X-RAY SCATTERING
ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES English 75 MS27-03 (2019) E427
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Selected conferences (co-)organized by project members3rd Global Summit Nanotechnology & Nanomedicine
Sep 2019, 3rd Global Summit Nanotechnology & Nanomedicine, Barcelona, Spain ►5th International Conference on Biopolymers & Polymer Chemistry
Jul 2020, 5th International Conference on Biopolymers & Polymer Chemistry, Houston, USA ►
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About this project
Fundamentally important to the processability and the material properties of polymer nanocomposites is the underlying interaction between polymer and nanoparticles, the resulting structure and dynamics. A high degree of nanoparticle dispersion is necessary for an effective reinforcement in a polymer matrix. A recent experimental approach to distributing nanoparticles into a polymer matrix is to let the interaction between nanoparticles and polymer chains to be of ionic nature.
Ionic nanoparticles can impart charged polymers with unique mechanical and functional properties such as self-healing and shape memory. Upon studying a single model nanocomposite via molecular simulation, we found that nanoparticle dispersion can indeed be achieved due to the insertion of electrostatic charge, that nanoparticle diffusion slows down due to this electrostatic charge, and that the ionic nanoparticles move according to a hopping mechanism.
These recent findings have the potential to spur new studies in modelling ionic polymer nanocomposites containing ionic functionalized silica nanoparticles.
We hereby propose to focus in a more detailed and conclusive fashion on four combined experimental/theoretical research objectives:
Investigate the role of ionic interactions and calculate viscoelastic properties (viscosity, storage modulus, loss modulus) with nanoparticle loading, for differently charged and sequenced polymers.
Quantify the lifetime of dynamic crosslinks between nanoparticles and polymers, formed in ionic nanocomposites, during deformation processes.
Calculate the dynamics and structure of polymers and their entanglements for differently charged and filled polymer ionic nanocomposite models,
Resolve the role of nanosilica surface confinement on polymer entanglements and dynamics.
The novelty of the proposed work stems from the combination of experiments, simulation and theoretical models to capture the interactions and polymer structural/dynamical, as well as rheological phenomena present in these ionic nanocomposites, who seem to offer qualitatively new properties worth being quantified and supplemented with an informed microscopic picture.
Lay-Summary (German only, as required by SNF)
Hintergrund:
Polymer-Nanokomposite (PNCs) stellen eine zunehmend wichtige Hybrid-Materialklasse dar. Das fehlende Verständnis der chemischen und physikalischen Mechanismen stellt seit Jahrzehnten ein Hindernis bei der weiteren Entwicklung dar. Für die Verarbeitung und die Eigenschaften von PNCs ist die Wechselwirkung zwischen Polymer und Nanoteilchen, sowie die resultierende Struktur und Dynamik von fundamentalem Interesse. Eine gute Dispersion der Nanoteilchen wird für die effiziente Verst&aauml;rkung von Polymer-Muttergewebe benötigt. Einer der neueren Ansätze, die diese Eigenschaft bewerkstelligen soll, ist die Verwendung von ionischen PNCs. Ionische Nanoteilchen können den ionischen Polymeren zudem neuartige mechanische und funktionelle Eigenschaften verleihen.
Inhalt und Ziel des Forschungsprojekts
ist ein besseres Verstädnis der ionischen PNCs. Dazu untersuchen wir die (i) Rolle von ionischen Wechselwirkungen und berechnen viskoelastische/mechanische Eigenschaften und ihre Abhäigkeit von System-Parametern (Konzentration, Ladungen, Ladungs-Sequenzen); (ii) Lebensdauer von Vernetzungspunkten in PNCs, isbesondere während Deformationsprozessen; (iii) Dynamik und Struktur der Polymere und deren Verschlaufungs-Netzwerke in Abhängigkeit der Ladungs-Sequenz; (iv) Rolle der Oberflächen-Beschaffenheit von Nano-Silikaten.
Wissenschaftlicher und gesellschaftlicher Kontext des Forschungsprojekts.
Wir möchten neuen Technologien für PNCs den Weg bereiten, die benötigt werden, um leichte, hoch-qualitative, und multifunktionelle Materialien weiter zu entwickeln. Ionische PNCs verprechen nicht nur die genannten mechanischen Eigenschaften, sondern auch ein Potential für Selstheilung, ionische Leitfähigkeit, und selektive Permeabilitä Simulationsmodelle erlauben uns, die genannten Abhäigkeiten im Detail zu untersuchen, und öffnen eue Horizonte für das Design ionischer PNCs für Anwendungen etwa in der Biomedizin, Biotechnologie, Energiespeicherung, Gastrennung.
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mk