On the Dynamics of an Eco-Epidemiological System Incorporating a Vertically Transmitted Infectious Disease

An eco-epidemiological system incorporating a vertically transmitted infectious disease is proposed and investigated. Micheal-Mentence type of harvesting is utilized to study the harvesting effort imposed on the predator. All the properties of the solution of the system are discussed. The dynamical behaviour of the system, involving local stability, global stability, and local bifurcation, is investigated. The work is finalized with the numerical simulation to observe the global behaviour of the solution.

Evaluating structural edge importance in temporal networks

To monitor risk in temporal financial networks, we need to understand how individual behaviours affect the global evolution of networks. Here we define a structural importance metric—which we denote as $l_{e}$ l e —for the edges of a network. The metric is based on perturbing the adjacency matrix and observing the resultant change in its largest eigenvalues. We then propose a model of network evolution where this metric controls the probabilities of subsequent edge changes. We show using synthetic data how the parameters of the model are related to the capability of predicting whether an edge will change from its value of $l_{e}$ l e . We then estimate the model parameters associated with five real financial and social networks, and we study their predictability. These methods have applications in financial regulation whereby it is important to understand how individual changes to financial networks will impact their global behaviour. It also provides fundamental insights into spectral predictability in networks, and it demonstrates how spectral perturbations can be a useful tool in understanding the interplay between micro and macro features of networks.

The Organisational Structure of an Agent-Based Model for the Management of Wastewater Systems

Water managers have to deal with complex problems due to the intertwined characteristics of processes, in particular those that occur in wastewater systems. Existing modelling approaches are usually centred in the physical, chemical and biological aspects of the individual processes, excluding the social and organisational context that will generate the global behaviour. These also include the responsibilities and decision making of different actors in the system. This paper proposes an agent-based model with the novelty to integrate the social and organisational structure of the wastewater system from which emerges the global behaviour of the system. The modelling process allows considering the legal regulations and the technical limits that would drive the decision making. The instantiation of the model, implementing a small system, evidenced the usefulness of this approach to manage the complexity of wastewater systems and its possible contribution to prevent environmental problems.

Traffic Networks: Wardrop Equilibrium and Braess’ Paradox

The well-known Braess’ paradox illustrates situations when adding a new link to a transport network might lead to an equilibrium state in which travel times of users will increase. Here, Braess’ paradox and the equilibrium state are analysed in the classical network configuration introduced by Braess in 1968. This network configuration is of fundamental significance because Valiant and Roughgarden showed in 2006 that ‘the “global” behaviour of an equilibrium flow in a large random network is similar to that in Braess’ original four-node example. Moreover, the probability of Braess’ paradox occurring in the classical network configuration will be studied, with particular emphasis on the Erlang distribution of parameters of the travel time function. This distribution is important in the context of traffic networks. However, other distributions will be analysed as well because Braess’ paradox can be observed in various applied contexts such as telecommunication networks and power transmission networks.

On Local Convergence of Stochastic Global Optimization Algorithms

In engineering optimization with continuous variables, the use of Stochastic Global Optimization (SGO) algorithms is popular due to the easy availability of codes. All algorithms have a global and local search character, where the global behaviour tries to avoid getting trapped in local optima and the local behaviour intends to reach the lowest objective function values. As the algorithm parameter set includes a final convergence criterion, the algorithm might be running for a while around a reached minimum point. Our question deals with the local search behaviour after the algorithm reached the final stage. How fast do practical SGO algorithms actually converge to the minimum point? To investigate this question, we run implementations of well known SGO algorithms in a final local phase stage.