Dengue virus has shown a complex pattern of transmission across Latin America over the last two decades. In an attempt to explain the permanence of the disease in regions subjected to drought seasons lasting over six months, various hypotheses have been proposed. These include transovarial transmission, forest reservoirs and asymptomatic human virus carriers. Dengue virus is endemic in Mexico, a country in which half of the population is seropositive. Seropositivity is a risk factor for Dengue Hemorrhagic Fever upon a second encounter with the dengue virus. Since Dengue Hemorrhagic Fever can cause death, it is important to develop epidemiological mathematical tools that enable policy makers to predict regions potentially at risk for a dengue epidemic. We formulated a mathematical model of dengue transmission, considering both human behavior and environmental conditions pertinent to the transmission of the disease. When data on past human population density, temperature and rainfall were entered into this model, it provided an accurate picture of the actual spread of dengue over recent years in four states (representing two climactic conditions) in Mexico.

We consider the quantum harmonic oscillator in contact with a finite-temperature bath, modeled by the Caldeira-Leggett master equation. Applying periodic kicks to the oscillator, we study the system in different dynamical regimes between classical integrability and chaos, on the one hand, and ballistic or diffusive energy absorption, on the other. We then investigate the influence of the heat bath on the oscillator in each case. Phase-space techniques allow us to simulate the evolution of the system efficiently. In this way, we calculate high-resolution Wigner functions at long times, where the system approaches a quasistationary cyclic evolution. Thereby, we perform an accurate study of the thermodynamic properties of a nonintegrable, quantum chaotic system in contact with a heat bath at finite temperature. In particular, we find that the heat transfer between harmonic oscillator and heat bath is governed by Fourier's law

We investigate the possibility to monitor the dynamics of an open quantum system with the help of a small probe system, coupled via dephasing coupling to the open system of interest. As an example, we consider a dissipative harmonic oscillator and a single qubit as probe system. Qubit plus oscillator are described by a finite temperature quantum master equation, where the dynamics of the whole system can be obtained analytically. We find that the short time behavior of the reduced qubit state (its coherence) provides exhaustive information on the dissipative dynamics of the oscillator. Observing this coherence for two initial states with different out-of-equilibrium temperatures, one can determine all coupling constants and the equilibrium temperature fixed by the external heat bath. In addition, the dephasing coupling to the qubit probe, may be considered as a perturbation of the dissipative oscillator. The corresponding quantum fidelity can be calculated analytically, also. Hence, we find the precise relation between the behavior of the reduced qubit state (its coherence) and that fidelity.

An approximation to the description of the dynamics of a quantum planar rotor coupled to a finite temperature bath is derived by considering a microscopic model of interaction based on an angular momentum exchange with two different environments coupled independently to the positive and negative angular momentum spectrum. A non-Lindblad master equation is derived for this microscopic model by using the Born-Markov approximation in the weak coupling limit. We show that under this approximation the rotor dynamics presents the correct damping behavior of the motion and the thermal state reached by the rotor is in the form of Boltzmann distribution. The case of the quantum rotor in an external uniform field and the quantum kicked rotor are briefly discussed as exemplification.

We develop in the weak coupling approximation a quasi-non-Markovian master equation and study the phenomenon of decoherence during the operation of a controlled-not (CNOT) quantum gate in a quantum computer model formed by a linear chain of three nuclear spins system with second neighbor Ising interaction between them. We compare with the behavior of the Markovian counterpart for temperature different from zero (thermalization) and at zero temperature for low and high dissipation rates. At high dissipation there is a very small difference between Markovian and quasi no-Markovian at any temperature which is unlikely to be measured, and at low dissipation there is a difference which is likely to be measured at any temperature.

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Based on an exact analytical approach to describe scattering fidelity experiments [Köber et al., Phys. Rev. E 82, 036207 (2010)], we obtain an expression for the fidelity amplitude decay of quantum chaotic or diffusive systems under arbitrary Hermitian perturbations. This allows us to rederive previous separately obtained results in a simpler and unified manner, as is shown explicitly for the case of a global perturbation. The general expression is also used to derive a so far unpublished exact analytical formula for the case of a moving S-wave scatterer. In the second part of the paper, we extend a relation between fidelity decay and parametric level correlations from the universal case of global perturbations to an arbitrary combination of global and local perturbations. Thereby, the relation becomes a versatile tool for the analysis of unknown perturbations.

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