A model of dengue fever

BACKGROUND: Dengue is a disease which is now endemic in more than 100 countries of Africa, America, Asia and the Western Pacific. It is transmitted to the man by mosquitoes (Aedes) and exists in two forms: Dengue Fever and Dengue Haemorrhagic Fever. The disease can be contracted by one of the four different viruses. Moreover, immunity is acquired only to the serotype contracted and a contact with a second serotype becomes more dangerous. METHODS: The present paper deals with a succession of two epidemics caused by two different viruses. The dynamics of the disease is studied by a compartmental model involving ordinary differential equations for the human and the mosquito populations. RESULTS: Stability of the equilibrium points is given and a simulation is carried out with different values of the parameters. The epidemic dynamics is discussed and illustration is given by figures for different values of the parameters. CONCLUSION: The proposed model allows for better understanding of the disease dynamics. Environment and vaccination strategies are discussed especially in the case of the succession of two epidemics with two different viruses

A new quantum version of f-divergence

This paper proposes and studies new quantum version of $f$-divergences, a class of convex functionals of a pair of probability distributions including Kullback-Leibler divergence, Rnyi-type relative entropy and so on. There are several quantum versions so far, including the one by Petz. We introduce another quantum version ($\mathrm{D}_{f}^{\max}$, below), defined as the solution to an optimization problem, or the minimum classical $f$- divergence necessary to generate a given pair of quantum states. It turns out to be the largest quantum $f$-divergence. The closed formula of $\mathrm{D}_{f}^{\max}$ is given either if $f$ is operator convex, or if one of the state is a pure state. Also, concise representation of $\mathrm{D}_{f}^{\max}$ as a pointwise supremum of linear functionals is given and used for the clarification of various properties of the quality. Using the closed formula of $\mathrm{D}_{f}^{\max}$, we show: Suppose $f$ is operator convex. Then the\ maximum $f\,$- divergence of the probability distributions of a measurement under the state $\rho$ and $\sigma$ is strictly less than $\mathrm{D}_{f}^{\max}\left( \rho\Vert\sigma\right)$. This statement may seem intuitively trivial, but when $f$ is not operator convex, this is not always true. A counter example is $f\left( \lambda\right) =\left\vert 1-\lambda\right\vert$, which corresponds to total variation distance. We mostly work on finite dimensional Hilbert space, but some results are extended to infinite dimensional case.Comment: The proof of dual representation of the former version was misstated. An alternative proof is presente

Towards multiobjective optimization and control of smart grids

The rapid uptake of renewable energy sources in the electricity grid leads to a demand in load shaping and flexibility. Energy storage devices such as batteries are a key element to provide solutions to these tasks. However, typically a trade-off between the performance related goal of load shaping and the objective of having flexibility in store for auxiliary services, which is for example linked to robustness and resilience of the grid, can be observed. We propose to make use of the concept of Pareto optimality in order to resolve this issue in a multiobjective framework. In particular, we analyse the Pareto frontier and quantify the trade-off between the non-aligned objectives to properly balance them.Comment: 20 pages, 8 figures, journal pape

Mean-risk models using two risk measures: A multi-objective approach

This paper proposes a model for portfolio optimisation, in which distributions are characterised and compared on the basis of three statistics: the expected value, the variance and the CVaR at a specified confidence level. The problem is multi-objective and transformed into a single objective problem in which variance is minimised while constraints are imposed on the expected value and CVaR. In the case of discrete random variables, the problem is a quadratic program. The mean-variance (mean-CVaR) efficient solutions that are not dominated with respect to CVaR (variance) are particular efficient solutions of the proposed model. In addition, the model has efficient solutions that are discarded by both mean-variance and mean-CVaR models, although they may improve the return distribution. The model is tested on real data drawn from the FTSE 100 index. An analysis of the return distribution of the chosen portfolios is presented

Measuring the balance space sensitivity in vector optimization

Recent literature has shown that the balance space approach may be a significant a1ternative to address several topics concerning vector optimization. Although this new look also leads lo the eflicient set and, consequently, is equivalent to the classical viewpoint, it yields new results and a1gorithms, as well as new economic interpretations, that may be very useful in theoretical framevorks and practical applications. The present paper focuses on the sensitivity of The balance set. We prove a general envelope theorem that yields the sensitivity with respect to any parameter considered in the problem. Fulthermore, we provide a dual problem that characlerizes the primal balance space and its sensitivity. Finally, we a1so give the implications of our results with respect to the sensitivity of the efficient set

Optimal control of impulsive switched systems with minimum subsystem durations

This paper presents a new computational approach for solving optimal control problems governed by impulsive switched systems. Such systems consist of multiple subsystems operating in succession, with possible instantaneous state jumps occurring when the system switches from one subsystem to another. The control variables are the subsystem durations and a set of system parameters influencing the state jumps. In contrast with most other papers on the control of impulsive switched systems, we do not require every potential subsystem to be active during the time horizon (it may be optimal to delete certain subsystems, especially when the optimal number of switches is unknown). However, any active subsystem must be active for a minimum non-negligible duration of time. This restriction leads to a disjoint feasible region for the subsystem durations. The problem of choosing the subsystem durations and the system parameters to minimize a given cost function is a non-standard optimal control problem that cannot be solved using conventional techniques. By combining a time-scaling transformation and an exact penalty method, we develop a computational algorithm for solving this problem. We then demonstrate the effectiveness of this algorithm by considering a numerical example on the optimization of shrimp harvesting operations