Der Linear Chain Trick in der epidemiologischen Modellierung als Kompromiss zwischen gewöhnlichen und Integro-Differentialgleichungen

Das vorrangige Ziel dieser Arbeit besteht in der Herleitung der Modelle, die auf dem Linear Chain Trick basieren, sowie in der Analyse ihrer Eigenschaften. Dazu orientieren wir uns vor allem an den Ausarbeitungen zum Linear Chain Trick von Hurtado et al. [44, 45] und Feng et al. [31, 32]. Im Vordergrund steht zudem die Frage, ob die Modelle als Kompromiss zwischen den unkomplizierten, jedoch unrealistischen Modellen auf der Basis von gewöhnlichen Differentialgleichungen und den komplexen, jedoch flexiblen Modellen basierend auf Integro-Differentialgleichungen fungieren können. Zur Beantwortung dieser Frage stellen wir die Modelle basierend auf dem Linear Chain Trick den anderen beiden Modellklassen gegenüber und analysieren Vor- und Nachteile. Die theoretische Einleitung und Untersuchung erfolgt anhand von Modellen, welche die Ausbreitung einer Krankheit durch die Verwendung von lediglich drei Kompartimenten darstellen. Dieser Ansatz ermöglicht eine klare Darstellung der Konzepte anhand von einfachen Beispielen. In der praktischen Anwendung wird üblicherweise eine größere Anzahl von Kompartimenten verwendet und eine feinere Unterteilung der Bevölkerung nach dem Krankheitszustand definiert, um die verschiedenen Aspekte der Erkrankung genauer zu erfassen. Zur Bewertung der Modelle in Übereinstimmung mit praxisnahen Bedingungen führen wir für die drei Klassen Modelle mit einer größeren Anzahl von Kompartimenten ein. Darüber hinaus prüfen wir das Verhalten in Simulationen, indem wir alle Modellarten in der Form mit mehr Kompartimenten implementieren. Zur Simulation verwenden wir Charakteristiken der Erkrankung COVID-19, um die Modelle unter realitätsnahen Rahmenbedingungen zu erproben

Chiral symmetry restoration and the string picture of hadrons

QCD string picture of highly excited hadrons very naturally explains parity doubling once the chiral symmetry is restored high in the spectrum. In particular, the spin-orbit and tensor interactions of quarks at the ends of the string, related to dynamics of the string, vanish. High in the spectrum there appears higher degree of degeneracy, namely parity doublets with different angular momentum cluster around energy of the string in the given quantum state.Comment: 7 pages, LaTeX, 2 figs. The paper has been further expanded in order to make the point and physics more clear. To appear in Phys. Lett.

Probing the structure of Nucleons in Electromagbetic Interactions

Open problems in the study of the nucleon structure using electromagnetic probes are discussed. The focus is on experimental aspects in the regime of strong interaction QCD. Significant progress in our understanding of the nucleon structure in this domain of QCD may be expected in the first decade of the next millenium. This is due to major experimental and theoretical efforts currently underway in this field.Comment: 9 pages, 6 figures, plenary talk at PANIC9

Gluons and the eta' nucleon coupling constant

We derive the effective chiral Lagrangian for low energy eta--nucleon and eta'--nucleon interactions and show that gluonic degrees of freedom, via the axial anomaly, induce a contact term in the pp -> pp eta and pp -> pp eta' reactions. We then discuss the consequences for the extraction of g_{eta'NN} from experimental data.Comment: 10 pages, LaTe

Do parity doublets in the baryon spectrum reflect restoration of chiral symmetry?

We discuss the mass spectrum of highly-excited nucleon and $\Delta^*$ resonances. The spectrum exhibits parity doublets, pairs of resonances of identical total angular momentum J but of opposite parity. It has been proposed that the parity doublets evidence restoration of chiral symmetry at large baryon excitation energies. We compare this conjecture with the possibility that high-mass states are organized into $(L,S)$-multiplets with defined intrinsic quark spins and orbital angular momenta. Indeed, the latter interpretation results in a better description of the data. There is however a small and statisticially not very significant trend of the data which might indicate that chiral symmetry is not yet restored but does influence the masses of highly excited states.Comment: 10 pages, 1 fi

Radiative η′\eta' Decays, the Topological Susceptibility and the Witten-Veneziano Mass Formula

The formulae describing the radiative decays \eta'(\eta)\rta\c\c in QCD beyond the chiral limit are derived. The modifications of the conventional PCAC formulae due to the gluonic contribution to the axial anomaly in the flavour singlet channel are precisely described. The decay constants are found to satisfy a modified Dashen formula which generalises the Witten--Veneziano formula for the mass of the $\eta'$. Combining these results, it is shown how the topological susceptibility in QCD with massive, dynamical quarks may be extracted from measurements of \eta'(\eta)\rta\c\c.Comment: TeX, 21 pages, no figures, uses harvma

An infectious disease model considering the age of infection

Development of a model based on integro-differential equations to improve the prediction od disease dynamics at change points

An infectious disease model considering the age of infection

Development of a model based on integro-differential equations to improve the prediction od disease dynamics at change points

Eta and eta-prime meson production in the reaction pn -> dM near threshold

The two-step model with pi-, rho- and omega- exchanges taken into account is applied to investigate the reactions pn -> d eta and pn -> d eta-prime. The existing experimental data on the reaction pn -> d eta are analysed and predictions for the cross section of the reaction pn -> d eta-prime are presented. It is found that pi- as well as rho exchange yield significant contributions in both reactions. The effect of the final state interaction is also studied.Comment: 15 pages, 4 figure