Stochastic effects in a seasonally forced epidemic model

The interplay of seasonality, the system's nonlinearities and intrinsic stochasticity, is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that corresponds to childhood infectious diseases such as measles. The power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes. Size effects are studied through additional simulations. Other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated. The main conclusion is that stochastic amplification, rather than these effects, is the key ingredient to understand the observed incidence patterns.

Genus and Braid Index Associated to Sequences of Renormalizable Lorenz Maps

We describe the Lorenz links generated by renormalizable Lorenz maps with reducible kneading invariant (K(f)(-), = K(f)(+)) = (X, Y) * (S, W) in terms of the links corresponding to each factor. This gives one new kind of operation that permits us to generate new knots and links from the ones corresponding to the factors of the *-product. Using this result we obtain explicit formulas for the genus and the braid index of this renormalizable Lorenz knots and links. Then we obtain explicit formulas for sequences of these invariants, associated to sequences of renormalizable Lorenz maps with kneading invariant (X, Y) * (S,W)*(n), concluding that both grow exponentially. This is specially relevant, since it is known that topological entropy is constant on the archipelagoes of renormalization.

Spinning reserve and emission unit commitment through stochastic optimization

This paper proposes a stochastic mixed-integer linear approach to deal with a short-term unit commitment problem with uncertainty on a deregulated electricity market that includes day-ahead bidding and bilateral contracts. The proposed approach considers the typically operation constraints on the thermal units and a spinning reserve. The uncertainty is due to the electricity prices, which are modeled by a scenario set, allowing an acceptable computation. Moreover, emission allowances are considered in a manner to allow for the consideration of environmental constraints. A case study to illustrate the usefulness of the proposed approach is presented and an assessment of the cost for the spinning reserve is obtained by a comparison between the situation with and without spinning reserve.

Spinning reserve and emission unit commitment through stochastic optimization

This paper proposes a stochastic mixed-integer linear approach to deal with a short-term unit commitment problem with uncertainty on a deregulated electricity market that includes day-ahead bidding and bilateral contracts. The proposed approach considers the typically operation constraints on the thermal units and a spinning reserve. The uncertainty is due to the electricity prices, which are modeled by a scenario set, allowing an acceptable computation. Moreover, emission allowances are considered in a manner to allow for the consideration of environmental constraints. A case study to illustrate the usefulness of the proposed approach is presented and an assessment of the cost for the spinning reserve is obtained by a comparison between the situation with and without spinning reserve.

A stochastic programming approach for the development of offering strategies for a wind power producer

A stochastic programming approach is proposed in this paper for the development of offering strategies for a wind power producer. The optimization model is characterized by making the analysis of several scenarios and treating simultaneously two kinds of uncertainty: wind power and electricity market prices. The approach developed allows evaluating alternative production and offers strategies to submit to the electricity market with the ultimate goal of maximizing profits. An innovative comparative study is provided, where the imbalances are treated differently. Also, an application to two new realistic case studies is presented. Finally, conclusions are duly drawn.

Self-scheduling and bidding strategies of thermal units with stochastic emission constraints

This paper is on the self-scheduling problem for a thermal power producer taking part in a pool-based electricity market as a price-taker, having bilateral contracts and emission-constrained. An approach based on stochastic mixed-integer linear programming approach is proposed for solving the self-scheduling problem. Uncertainty regarding electricity price is considered through a set of scenarios computed by simulation and scenario-reduction. Thermal units are modelled by variable costs, start-up costs and technical operating constraints, such as: forbidden operating zones, ramp up/down limits and minimum up/down time limits. A requirement on emission allowances to mitigate carbon footprint is modelled by a stochastic constraint. Supply functions for different emission allowance levels are accessed in order to establish the optimal bidding strategy. A case study is presented to illustrate the usefulness and the proficiency of the proposed approach in supporting biding strategies. (C) 2014 Elsevier Ltd. All rights reserved.

Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach

In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems – the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression.