On a modification of a discrete epidemic model

AbstractIn this paper under some conditions on the constants A,B∈(0,∞) we study the existence of positive solutions, the existence of a unique nonnegative equilibrium and the convergence of the positive solutions to the nonnegative equilibrium of the system of difference equations xn+1=(1−yn−yn−1)(1−e−Ayn),yn+1=(1−xn−xn−1)(1−e−Bxn) where A,B∈(0,∞) and the initial values x−1,x0,y−1,y0 are positive numbers which satisfy the relations x0+x−1<1,y0+y−1<1,1−y0>(1−x0−x−1)(1−e−Bx0),1−x0>(1−y0−y−1)(1−e−Ay0)

Asymptotic behavior of the solutions of a class of rational difference equations

Abstract In this paper we study the asymptotic behavior of the positive solutions of certain rational difference equations

Behavior of the positive solutions of fuzzy max-difference equations

We extend some results obtained in 1998 and 1999 by studying the periodicity of the solutions of the fuzzy difference equations xn+1=max{A/xn,A/xn−1,…,A/xn−k}, xn+1=max{A0/xn,A1/xn−1}, where k is a positive integer, A, Ai, i=0,1, are positive fuzzy numbers, and the initial values xi, i=−k,−k+1,…,0 (resp., i=−1,0) of the first (resp., second) equation are positive fuzzy numbers

Seismic Risk of Inter-urban Transportation Networks

AbstractThe paper presents a holistic approach for assessing and managing the seismic risk and potential loss in inter-urban highway networks in earthquake-prone areas. The vulnerability of all elements of the intercity transportation system (i.e., roads, bridges, abutments, retaining walls, and tunnels) is assessed considering the interdependency among the structural, transportational and geotechnical components of the network under different seismic scenarios. Both the direct earthquake-induced damage, as well as the indirect socio-economic loss attributed to reduced network functionality are taken into account in an explicit and transparent formulation that is then displayed in space through an ad-hoc developed GIS-based software. The methodology and the decision-making tools developed are adequately modular, for them to be utilized after appropriate adaptation by local authorities in identifying, prior to a major earthquake event, those vulnerable components of their network whose failure may have a disproportional socio-economic impact. In this way, a rational and effective emergency plan can be deployed to minimize potential human, social and financial loss after a future earthquake. The outline of a foreseen application is also presented for the case of the road network of the Region of Western Macedonia in Greece. Through this pilot application, the methodology is to be optimized in real conditions before being cast in the form of a fully parameterised seismic risk tool, to be used in other earthquake prone areas as well

Bridge-specific fragility analysis: when is it really necessary?

In seismic assessment of bridges the research focus has recently shifted on the derivation of bridge-specific fragility curves that account for the effect of different geometry, structural system, component and soil properties, on the seismic behaviour. In this context, a new, component-based methodology for the derivation of bridge-specific fragility curves has been recently proposed by the authors, with a view to overcoming the inherent difficulties in assessing all bridges of a road network and the drawbacks of existing methodologies, which use the same group of fragility curves for bridges within the same typological class. The main objective of this paper is to critically assess the necessity of bridge-specific fragility analysis, starting from the effect of structure-specific parameters on component capacity (limit state thresholds), seismic demand, and fragility curves. The aforementioned methodology is used to derive fragility curves for all bridges within an actual road network, with a view to investigating the consistency of adopting generic fragility curves for bridges that fall within the same class and quantifying the degree of over- or under-estimation of the probability of damage when generic bridge classes are considered. Moreover, fragility curves for all representative bridges of the analysed concrete bridge classes are presented to illustrate the differentiation in bridge fragility for varying structural systems, bridge geometry, total bridge length and maximum pier height. Based on the above, the relevance of bridge-specific fragility analysis is assessed, and pertinent conclusions are drawn

Multi-hazard fragility assessment of bridges: Methodology and case study application

Reliability of road systems and their critical components exposed to multiple natural hazards is on the frontline of engineering research during the last three decades since potential damage of infrastructure is strongly related to important direct and indirect economic losses. In this context, the research project INFRARES (www.infrares.gr) aims at delivering a comprehensive methodology towards a more efficient risk and resilience assessment of roadway networks in Greece subjected to various natural hazards. In this context, an analytical framework for the fragility assessment of bridges subjected to independent and/or multiple subsequent natural hazards, is proposed herein and applied to a case study bridge. The proposed methodology includes the estimation of seismic and flood fragility and the development of multihazard fragility curves. The proposed approach considers multiple structural components for the development of fragility curves, which are generated based on case-specific estimation of limit state thresholds accounting for multiple failure modes and SSI effects. A probabilistic framework is introduced to account for the uncertainties in the demand and capacity in case of single hazards, which is then extended for multiple -separate and/or subsequent- hazards, highlighting the effect of cumulative damage on the fragility assessment. The proposed methodology is applied to a case study bridge in Greece, considering multiple hazards, separate in time (i.e. two subsequent flood events). The results in terms of flood fragility curves are discussed with a view to evaluate the effect of damage accumulation in multiple hazard analysis; the probability of damage was found to drastically increase for all limit states considered

Recent Advances in Seismic Vulnerability Assessment of Tunnels and Underground Structures

Tunnels and underground structures are constructed at an increasing rate in seismic prone areas to facilitate expanding transportation needs. The importance of these types of structures in modern societies, as well as the significant downtimes associated with seismically induced damage on them, led to an increasing interest of the scientific community and practitioners on the vulnerability assessment of this infrastructure against seismic hazard. Various methodologies have been recently proposed to estimate the vulnerability of bored tunnels in rock or alluvial and cut and cover or underground structures, e.g., subways, in alluvial, against ground seismic shaking and earthquake induced ground failures. This paper discusses critical aspects of these methodologies, based on a thorough review of relevant state-of-the art, carried out in the frame of research project INFRARES (www.infrares.gr). Emphasis is placed on the numerical tools employed to estimate analytically the fragility of examined structures in relevant studies, the constitutive models used to simulate the seismic response of ground and structures, the determination of the capacity of examined structures, the selection of appropriate seismic intensity measures, methods used to develop rational probabilistic seismic demand models, the estimation of uncertainties related to seismic vulnerability of underground structures, as well as the methods for selecting fragility functions from existing ones in assessment studies of actual case studies. Through the discussion, acknowledged gaps in the literature are highlighted and topics calling for further investigation are presented. In addition, an up-to-date database of available fragility functions for tunnels and underground structures developed within INFRARES is presented

Selection of earthquake ground motions for multiple objectives using genetic algorithms

Existing earthquake ground motion (GM) selection methods for the seismic assessment of structural systems focus on spectral compatibility in terms of either only central values or both central values and variability. In this way, important selection criteria related to the seismology of the region, local soil conditions, strong GM intensity and duration as well as the magnitude of scale factors are considered only indirectly by setting them as constraints in the pre-processing phase in the form of permissible ranges. In this study, a novel framework for the optimum selection of earthquake GMs is presented, where the aforementioned criteria are treated explicitly as selection objectives. The framework is based on the principles of multi-objective optimization that is addressed with the aid of the Weighted Sum Method, which supports decision making both in the pre-processing and post-processing phase of the GM selection procedure. The solution of the derived equivalent single-objective optimization problem is performed by the application of a mixed-integer Genetic Algorithm and the effects of its parameters on the efficiency of the selection procedure are investigated. Application of the proposed framework shows that it is able to track GM sets that not only provide excellent spectral matching but they are also able to simultaneously consider more explicitly a set of additional criteria

Soil-structure interaction effects in analysis of seismic fragility of bridges using an intensity-based ground motion selection procedure

The paper focuses on the effects of Soil-Structure Interaction (SSI) in seismic fragility analysis of reinforced concrete (RC) bridges, considering the vulnerability of multiple critical components of the bridge and different modelling approaches for soil-foundation and bridge-embankment interactions. A two-step procedure, based on the introduction of springs and dashpots at the pier foundations and the abutment to account for inertial and kinematic SSI effects, is incorporated into a component-based methodology for the derivation of bridge-specific fragility curves. The proposed methodology is applied for quantifying the fragility of a typical highway overpass at both the component and system level, while the effect of alternative procedures (of varying complexity) for modelling foundation and abutment boundary conditions is critically assessed. The rigorous SSI modelling method is compared with simpler methods and the results show that consideration of SSI may only slightly affect the probability of system failure, depending on the modelling assumptions made. However, soil-structure interaction may have a notable effect on component fragility, especially for the more critical damage states. This is an observation that is commonly overlooked when assessing the structural performance at the system level and can be particularly important when component fragility is an issue, e.g. when designing a retrofit scheme