The spread of coronavirus disease 2019 (COVID-19) in Italy prompted drastic measures for transmission containment. We examine the effects of these interventions, based on modeling of the unfolding epidemic. We test modeling options of the spatially explicit type, suggested by the wave of infections spreading from the initial foci to the rest of Italy. We estimate parameters of a metacommunity Susceptible-Exposed-Infected-Recovered (SEIR)like transmission model that includes a network of 107 provinces connected by mobility at high resolution, and the critical contribution of presymptomatic and asymptomatic transmission. We estimate a generalized reproduction number (R 0 = 3.60 [3.49 to 3.84]), the spectral radius of a suitable next-generation matrix that measures the potential spread in the absence of containment interventions. The model includes the implementation of progressive restrictions after the first case confirmed in Italy (February 21, 2020) and runs until March 25, 2020. We account for uncertainty in epidemiological reporting, and time dependence of human mobility matrices and awareness-dependent exposure probabilities. We draw scenarios of different containment measures and their impact. Results suggest that the sequence of restrictions posed to mobility and human-to-human interactions have reduced transmission by 45% (42 to 49%). Averted hospitalizations are measured by running scenarios obtained by selectively relaxing the imposed restrictions and total about 200,000 individuals (as of March 25, 2020). Although a number of assumptions need to be reexamined, like age structure in social mixing patterns and in the distribution of mobility, hospitalization, and fatality, we conclude that verifiable evidence exists to support the planning of emergency measures.

[1] The probability density functions (pdf's) of travel and residence times are key descriptors of the mechanisms through which catchments retain and release old and event water, transporting solutes to receiving water bodies. In this paper we analyze theoretically such pdf's, whose proper characterization reveals important conceptual and practical differences. A general stochastic framework applicable to arbitrary catchment control volumes is adopted, where time-variable precipitation, evapotranspiration and discharge are assumed to be the major hydrological drivers. The master equation for the residence time pdf is derived and solved analytically, providing expressions for travel and residence time pdf's as a function of input/output fluxes and of the relevant mixing. Our solutions suggest intrinsically time-variant travel and residence time pdf's through a direct dependence on hydrological forcings and soil-vegetation dynamics. The proposed framework integrates age-dating and tracer hydrology techniques, and provides a coherent framework for catchment transport models based on travel times. Citation: Botter, G., E. Bertuzzo, and A. Rinaldo (2011), Catchment residence and travel time distributions: The master equation, Geophys.

[1] We propose an ecomorphodynamic model which conceptualizes the chief land-forming processes operating on the intertwined, long-term evolution of marsh platforms and embedded tidal networks. The rapid network incision (previously addressed by the authors) is decoupled from the geomorphological dynamics of intertidal areas, governed by sediment erosion and deposition and crucially affected by the presence of vegetation. This allows us to investigate the response of tidal morphologies to different scenarios of sediment supply, colonization by halophytes, and changing sea level. Different morphological evolutionary regimes are shown to depend on marsh ecology. Marsh accretion rates, enhanced by vegetation growth, and the related platform elevations tend to decrease with distance from the creek, measured along suitably defined flow paths. The negative feedback between surface elevation and its inorganic accretion rate is reinforced by the relation between plant productivity and soil elevation in Spartina-dominated marshes and counteracted by positive feedbacks in multispecies-vegetated marshes. When evolving under constant sea level, unvegetated and Spartina-dominated marshes asymptotically tend to mean high water level (MHWL), different from multiple vegetation species marshes, which can make the evolutionary transition to upland. Equilibrium configurations below MHWL can be reached under constant rates of sea level rise, depending on sediment supply and vegetation productivity. Our analyses on marine regressions and transgressions show that when the system is in a supply-limited regime, network retreat and expansion (associated with regressions and transgressions, respectively) tend to be cyclic. Conversely, in a transport-limited regime, network reexpansion following a regression tends to take on a new configuration, showing a hysteretic behavior.Citation: D'Alpaos, A., S. Lanzoni, M. Marani, and A. Rinaldo (2007), Landscape evolution in tidal embayments: Modeling the interplay of erosion, sedimentation, and vegetation dynamics,

The hydrologic response of a channel network is defined by decomposing the process of runoff formation into two distinct contributions, one accounting for the mechanisms of travel time within individual reaches (hydrodynamic dispersion), and the other accounting for the morphology of the network structure (geomorphological dispersion). Exact Laplace transforms of first passage time distributions at the outlet of a network are obtained by a consistent approximation of travel time distributions through individual reaches. The moments of such distributions are obtained analytically in the general case. Closed-form first-passage distributions are obtained in the particular case of basin-constant hydrodynamic dispersion. The variance of the resulting travel time distributions is shown in this paper to be made up of two additive contributions corresponding to the two dispersion mechanisms considered. The geomorpho}ogic dispersion coefficient is shown to depend on the ratios of bifurcation, length and area of the network suggesting that, at the scale of an organized network, heterogeneities other than those related to the convection field shape the dispersive character of transport. In particular, a significant application of the general solution to Hortonian channel networks suggests that models based on accurate specification of the geometry and the topology of the network and a simplified dynamics capture the foremost features of the travel time distributions in a broad range of dispersivities within individual reaches. channel networks [e.g., Shreve, 1966; Smart, !972; Mandelbrot, 1983; Abrahams, 1984; Tarboton et al., 1988; La Barbera and Rosso, 1989; A. Marani et al., A note on fractal channel networks, Paper number 90WR02501, •3-t 397/91/90WR-0250 ! $05.00 1990 (hereinafter Marani et al. (submitted manuscript, 1990))]. Similar ideas have been explored with reference to random networks (modeling, somewhat arbitrarily, porous media as a random resistor network [De Arcangelis et al., 1986]), whereas we propose, in the framework of studies on transport by travel time distributions, the geomorpho!ogic analysis of channel networks. Recent contributions have provided new significant inroads toward a unifying approach for transport processes based on travel (first-passage, arrival or residence) time distributions. It is granted in this study that (1) the arrival time distribution at the outlet of a channel network after an instantaneous pulse is the geomorphologic unit hydrograph (GUH) which is the core of the hydrologic response [Rodriguez-!turbe and Valdes, 1979; Gupta et al., 1980; Gupta and Waymire, 1983]; and (2) travel time distributions may be related in a rational manner to approaches based on the solution of the mass and momentum balance equations in an Eulerian framework, are of general nature and robust in characterizing the transport process, and blend all sources of uncertainty into a unique curve [Rinaldo and Marani, 1987; Shapiro and Cvetkovic, 1988; Dagan and Nguyen, 1989; Rinaldo et al., 1989; Dagan, 198...