Abstract: The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. Commonly used variations with multiple exponentially distributed variables are more flexible, yet do not allow for arbitrary distributions. We present a new formulation, focussing on the SEIR concept that allows to include general distributions of incubation and removal times. We compare the solution to two types of agent-based model simulations, a spatially homogeneous one where infection occurs by proximity, and a model on a scale-free network with varying clustering properties, where the infection between any two agents occurs via their link if it exists. We find good agreement in both cases. Furthermore a family of asymptotic solutions of the equations is found in terms of a logistic curve, which after a non-universal time shift, fits extremely well all the microdynamical simulations. The formulation allows for a simple numerical approach; software in Julia and Python is provided.

Abstract: We present a chiral (K) over barN interaction model that has been developed and optimized in order to account for the experimental data of inelastic (K) over barN reaction channels that open at higher energies. In particular, we study the effect of the higher partial waves, which originate directly from the chiral Lagrangian, as they could supersede the role of high-spin resonances employed in earlier phenomenological models to describe meson-baryon cross sections in the 2 GeV region. We present a detailed derivation of the partial wave amplitudes that emerge from the chiral SU(3) meson-baryon Lagrangian up to the d-waves and next-to-leading order in the chiral expansion. We implement a nonperturbative unitarization in coupled channels and optimize the model parameters to a large pool of experimental data in the relevant energy range where these new contributions are expected to be important. The obtained results are encouraging. They indicate the ability of the chiral higher partial waves to extend the description of the scattering data to higher energies and to account for structures in the reaction cross-sections that cannot be accommodated by theoretical models limited to the s-waves.

Abstract: Starting from a recent model of the eta'N interaction, we evaluate the eta'-nucleus optical potential, including the contribution of lowest order in density, t rho/2m(eta'), together with the second-order terms accounting for eta' absorption by two nucleons. We also calculate the formation cross section of the eta' bound states from (pi(+), p) reactions on nuclei. The eta'-nucleus potential suffers from uncertainties tied to the poorly known eta'N interaction, which can be partially constrained by the experimental modulus of the eta'N scattering length and/or the recently measured transparency ratios in eta' nuclear photoproduction. Assuming an attractive interaction and taking the claimed experimental value vertical bar a(eta'N)vertical bar = 0.1 fm, we obtain an eta' optical potential in nuclear matter at saturation density of V eta' = -(8.7 + 1.8i) MeV, not attractive enough to produce eta' bound states in light nuclei. Larger values of the scattering length give rise to deeper optical potentials, with moderate enough imaginary parts. For a value vertical bar a(eta'N)vertical bar = 0.3 fm, which can still be considered to lie within the uncertainties of the experimental constraints, the spectra of light and medium nuclei show clear structures associated to eta'-nuclear bound states and to threshold enhancements in the unbound region.