A Bayesian analysis for the seismic data on Taiwan

A Bayesian approach is used to analyze the seismic events with magnitudes at least 4.7 on Taiwan. Following the idea proposed by Ogata (1988,Journal of the American Statistical Association,83, 9–27), an epidemic model for the process of occurrence times given the observed magnitude values is considered, incorporated with gamma prior distributions for the parameters in the model, while the hyper-parameters of the prior are essentially determined by the seismic data in an earlier period. Bayesian inference is made on the conditional intensity function via Markov chain Monte Carlo method. The results yield acceptable accuracies in predicting large earthquake events within short time periods.     

一类含有非线性传染率的传染病模型的全局稳定性

讨论了一类带有非线性传染率的SIRS型传染病模型,得到了无病平衡点和地方病平衡点存在的阈值条件,借助构造Dulac函数和Liapunov函数,找到了两类平衡点全局渐近稳定的充要条件.     

A mathematical model for a distributed attack on targeted resources in a computer network

A mathematical model has been developed to analyze the spread of a distributed attack on critical targeted resources in a network. The model provides an epidemic framework with two sub-frameworks to consider the difference between the overall behavior of the attacking hosts and the targeted resources. The analysis focuses on obtaining threshold conditions that determine the success or failure of such attacks. Considering the criticality of the systems involved and the strength of the defence mechanism involved, a measure has been suggested that highlights the level of success that has been achieved by the attacker. To understand the overall dynamics of the system in the long run, its equilibrium points have been obtained and their stability has been analyzed, and conditions for their stability have been outlined.     

A new epidemic model of computer viruses

This paper addresses the epidemiological modeling of computer viruses. By incorporating the effect of removable storage media, considering the possibility of connecting infected computers to the Internet, and removing the conservative restriction on the total number of computers connected to the Internet, a new epidemic model is proposed. Unlike most previous models, the proposed model has no virus-free equilibrium and has a unique endemic equilibrium. With the aid of the theory of asymptotically autonomous systems as well as the generalized Poincare–Bendixson theorem, the endemic equilibrium is shown to be globally asymptotically stable. By analyzing the influence of different system parameters on the steady number of infected computers, a collection of policies is recommended to prohibit the virus prevalence.     

Epidemic spreading in a scale-free network of regular lattices

The susceptible-infected-susceptible (SIS) epidemics in a scale-free network in which each node is a square lattice itself is investigated through large-scale computer simulations. The model combines a local contact process among individuals in a node (or city) with stochastic long-range infections due to people traveling between cities interconnected by the national transportation scale-free network. A nonzero epidemic threshold is found and it is approached with a power-law behavior by the density of infected individuals, as observed in the small-world network of Watts and Strogatz. Also, the epidemic propagation follows a 1/f$1/f$, hierarchical dynamics from the highly connected square lattices to the smaller degree nodes in outbreaks with sizes distributed accordingly a Gaussian function.     

Effects of superspreaders in spread of epidemic

Within the standard SIR model with spatial structure, we propose two models for the superspreader. In one model, superspreaders have intrinsically strong infectiousness. In other model, they have many social connections. By Monte Carlo simulation, we obtain the percolation probability, the propagation speed, the epidemic curve, the distribution of secondary infected and the propagation path as functions of population and the density of superspreaders. By comparing the results with the data of SARS in Singapore 2003, we conclude that the latter model can explain the observation.     

On the use of the geometric approach to global stability for three dimensional ODE systems: A bilinear case

In this paper, we consider a general bilinear three dimensional ODE system, whose structure generalizes many mathematical models of biological interest, including many from epidemics. Our main goal is to find sufficient conditions, expressed in terms of the parameters of the system, ensuring that the geometric approach to global stability analysis, due to [M.Y. Li, J.S. Muldowney, A geometric approach to global-stability problems, SIAM J. Math. Anal. 27 (4) (1996) 1070-1083], may be successfully applied. We completely determine the dynamics of the general system, including thresholds and global stability of the nontrivial equilibrium. The obtained result is applied to several epidemic models. We further show how the role of new parameters on stability of well-established models may be emphasized.     

Multi-phase epidemic model by a Markov chain

In this paper we propose a continuous-time Markov chain to describe the spread of an infective and non-mortal disease into a community numerically limited and subjected to an external infection. We make a numerical simulation that shows tendencies for recurring epidemic outbreaks and for fade-out or extinction of the infection.     

Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient

We consider a multidimensional diffusion X$X$ with drift coefficient b(α,_Xt)$b(\alpha ,X_t)$ and diffusion coefficient ?σ(β,_Xt)$?\sigma (\beta ,X_t)$. The diffusion sample path is discretely observed at times _tk=kΔ$t_k=k\Delta$ for k=1…n$k=1\dots n$ on a fixed interval [0,T]$[0,T]$. We study minimum contrast estimators derived from the Gaussian process approximating X$X$ for small ?$?$. We obtain consistent and asymptotically normal estimators of α$\alpha$ for fixed Δ$\Delta$ and ?→0$?\to 0$ and of (α,β)$(\alpha ,\beta )$ for Δ→0$\Delta \to 0$ and ?→0$?\to 0$ without any condition linking ?$?$ and Δ$\Delta$. We compare the estimators obtained with various methods and for various magnitudes of Δ$\Delta$ and ?$?$ based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework.     

Threshold behaviour of a stochastic SIR model

In this paper, we investigate the threshold behaviour of a susceptible-infected-recovered (SIR) epidemic model with stochastic perturbation. When the noise is small, we show that the threshold determines the extinction and persistence of the epidemic. Compared with the corresponding deterministic system, this value is affected by white noise, which is less than the basic reproduction number of the deterministic system. On the other hand, we obtain that the large noise will also suppress the epidemic to prevail, which never happens in the deterministic system. These results are illustrated by computer simulations.