Existence of periodic solutions for seasonal epidemic models with quarantine

In this work, we establish the existence of periodic orbits for a seasonal saturated epidemiological model of a population consisting of susceptible, infectious and quarantined individuals (an SIQS model). To do so, we use Leray-Schauder degree theory. We also provide numerical examples of these solutions

Bifurcation analysis and optimal control of a network-based SIR model with the impact of medical resources

A new network-based SIR epidemic model, which incorporates the individual medical resource factor and public medical resource factor is proposed. It is verified that the larger the public medical resource factor, the smaller the control reproduction number, and the larger individual medical resource factor can weaken the spread of diseases. We found that the control reproduction number below unity is not enough to ensure global asymptotic stability of the disease-free equilibrium. When the number of hospital beds or the individual medical resource factor is small enough, the system will undergoes backward bifurcation. Moreover, the existence and uniqueness of the optimal control and two time-varying variables’s optimal solutions are obtained. On the scale-free network, the level of optimal control is also proved to be different for different degrees. Finally, the theoretical results are illustrated by numerical simulations. This study suggests that maintaining sufficient both public medical resources and individual medical resources is crucial for the control of infectious diseases

Epidemic transmission on SEIR stochastic models with nonlinear incidence rate

Our interest is to quantify the spread of an infective process with latency period and generic incidence rate that takes place in a Önite and homogeneous population. Within a stochastic framework, two random variables are deÖned to describe the variations of the number of secondary cases produced by an index case inside of a closed population. Computational algorithms are presented in order to characterize both random variables. Finally, theoretical and algorithmic results are illustrated by several numerical examples

Modeling and analysis of SIR epidemic dynamics in immunization and cross-infection environments: Insights from a stochastic model

We propose a stochastic SIR model with two different diseases cross-infection and immunization. The model incorporates the effects of stochasticity, cross-infection rate and immunization. By using stochastic analysis and Khasminski ergodicity theory, the existence and boundedness of the global positive solution about the epidemic model are firstly proved. Subsequently, we theoretically carry out the sufficient conditions of stochastic extinction and persistence of the diseases. Thirdly, the existence of ergodic stationary distribution is proved. The results reveal that white noise can affect the dynamics of the system significantly. Finally, the numerical simulation is made and consistent with the theoretical results

Global dynamics of an endemic disease model with vaccination: Analysis of the asymptomatic and symptomatic groups in complex networks

In this paper, we analyze the global dynamics of an endemic mathematical model that incorporates direct immunity by vaccination, as well as the shift from the asymptomatic to the symptomatic group in complex networks. By analyzing the Jacobian matrix and constructing suitable Lyapunov functionals, the stability of the disease-free equilibrium and the endemic equilibrium is determined with respect to the basic reproduction number $R_0$. Numerical simulations in scale-free and Poisson network environments are presented. The results validate the correctness of our theoretical analyses

Dynamics of a stochastic epidemic model with quarantine and non-monotone incidence

In this paper, a stochastic SIQR epidemic model with non-monotone incidence is investigated. First of all, we consider the disease-free equilibrium of the deterministic model is globally asymptotically stable by using the Lyapunov method. Secondly, the existence and uniqueness of positive solution to the stochastic model is obtained. Then, the sufficient condition for extinction of the stochastic model is established. Furthermore, a unique stationary distribution to stochastic model will exist by constructing proper Lyapunov function. Finally, numerical examples are carried out to illustrate the theoretical results, with the help of numerical simulations, we can see that the higher intensities of the white noise or the bigger of the quarantine rate can accelerate the extinction of the disease. This theoretically explains the significance of quarantine strength (or isolation measures) when an epidemic erupts

Global stability of multi-group SEIQR epidemic models with stochastic perturbation in computer network

In this paper, a class of multi-group SEIQR models with random perturbation in computer network is investigated. The existence and uniqueness of global positive solution with any positive initial value are obtained. The sufficient conditions on the asymptotic behavior of solutions around the disease-free equilibrium and endemic equilibrium of the corresponding deterministic model are established. Furthermore, the existence and uniqueness of stationary distribution are also obtained. Lastly, the analytical results are illustrated by the numerical simulations

Analysis of Environmental Influences on Dressed Stone Decay: a Case Study of Tafoni Development on a Hewn Djinn Block in Petra, Jordan

Petra, Jordan captivates tourists and researchers with its dramatic sandstone cliffs, Nabatean, Roman, Byzantine and Roman architecture, and rich cultural heritage. However, increasing tourism in the valley is exacerbating stone degradation and complicating heritage management. This research analyzed environmental influences on dressed stone decay via tafoni development and evaluating cell evolution on an isolated hewn feature, known as Djinn Block X. Resembling other sandstone blocks found in the area, this irregular sandstone monument exhibits faces ranging in size from 2.5m by 3.5m to 3.9m to 4.2m (29m perimeter). Protruding features, incisions along the top, and a large platform attached to the northern face suggests this monument was ritualistic or unfinished. Over twenty morphometric and micrometeorologic variables were measured for the ten largest and smallest tafoni cells per face. Data were examined and analyzed statistically, photographically, and cartographically. A mirrored-value-aspect matrix was created to reveal statistical relationships between aspect and detailed measurements including cell depth, average diameter, estimated volume, surface temperatures, ambient temperature, and humidity. Results supported field observations displaying greatest decay on the southern and northern faces with r2 values as high as 0.157 at 144˚N for cell volume (total material lost). Moreover, morphometric data exhibited episodic spikes in cell growth, both by depth and diameter, supporting a possible threshold response explanation. These findings challenge steady-rate decay models and represent major implications for rock decay and tafoni research, as well as cultural stone assessment. Furthermore, Geomorphologic research such as this provides policy-makers information necessary to improve conservation efficacy for crucially sensitive heritage sites

Precision bounds in noisy quantum metrology

In an idealistic setting, quantum metrology protocols allow to sense physical parameters with mean squared error that scales as $1/N^2$ with the number of particles involved---substantially surpassing the $1/N$-scaling characteristic to classical statistics. A natural question arises, whether such an impressive enhancement persists when one takes into account the decoherence effects that are unavoidable in any real-life implementation. In this thesis, we resolve a major part of this issue by describing general techniques that allow to quantify the attainable precision in metrological schemes in the presence of uncorrelated noise. We show that the abstract geometrical structure of a quantum channel describing the noisy evolution of a single particle dictates then critical bounds on the ultimate quantum enhancement. Our results prove that an infinitesimal amount of noise is enough to restrict the precision to scale classically in the asymptotic $N$ limit, and thus constrain the maximal improvement to a constant factor. Although for low numbers of particles the decoherence may be ignored, for large $N$ the presence of noise heavily alters the form of both optimal states and measurements attaining the ultimate resolution. However, the established bounds are then typically achievable with use of techniques natural to current experiments. In this work, we thoroughly introduce the necessary concepts and mathematical tools lying behind metrological tasks, including both frequentist and Bayesian estimation theory frameworks. We provide examples of applications of the methods presented to typical qubit noise models, yet we also discuss in detail the phase estimation tasks in Mach-Zehnder interferometry both in the classical and quantum setting---with particular emphasis given to photonic losses while analysing the impact of decoherence.Comment: PhD Thesis (defended 22.09.2014). 138 pages, 6 chapters (+10 appendices), 20 figures, 6 tables. Final version containing modifications suggested by the referees: Dariusz Chruscinski and Andrzej Grudka. Incorporates and extends the material of arXiv:1006.0734, arXiv:1201.3940, arXiv:1303.7271 and arXiv:1405.770