Plenary Lecture

The Statistical Behavior of the Spread of Infection by the Contact Systems

Professor Jun Wang
College of Science
Beijing Jiaotong University
Beijing 100044, P. R. CHINA
E-mail: wangjun@bjtu.edu.cn

Abstract: We consider a contact system that describes the behavior of a process which has been used to model the spread of a disease or a biological population. The collection of individuals that may be infected at any given time is taken to be the set of vertices of a connected, undirected graph . For such a graph, the degree of a vertex is the number of vertices that are connected to by an edge. In the present paper, we consider the contact model on the dimensional integer lattice (in which the degree of each vertex is ). In -dimensional space, one point is stood by one individual. The virus infects one proximate individual at a rate equal to , where is an intensity of the contact model. And the individual infected recovers at rate one. Speaking concretely, contact model is a continuous time Markov process in the configuration . At some random time, one individual at the point is deemed to be infected when and the infected individual recovers at rate one; if , the individual at the point is healthy and will be infected at a rate equal to times the number of the infected neighbors. In this paper, applying the theory of the contact system, one kind of spread of infection model (which defined from the contact model) is analyzed and estimated by the theory of stochastic analysis, including the stopping time method. Further, we show the asymptotic behavior of probability distributions which describe the fluctuations for the spread of infection.

Brief Biography of the Speaker:
Professor and Dr. Jun Wang is a full professor at College of Science in Beijing Jiaotong University, P.R. China. He is also the Director of Institute of Financial Mathematics and Financial Engineering. Professor Wang received his Ph.D. from the Kobe University of Japan, and continued his research work in Kobe University as a researcher supported by Japan Society for the Promotion of Science. Recently, his research work is supported in part by the National Natural Science Foundation of China Grant No. 70471001 and No. 70771006, Ministry of Education of China Grant No. 406 (2003), BJTU Foundation No. 2006XM044.
Professor Wang has wide research interests, which include: Large Scale Interacting Systems, Stochastic Systems, Dynamical Systems, Statistical Physics Systems (Ising Dynamical Systems, Percolation Theory, Voter Systems and Contact Systems, Widom-Rowlinson Model, etc.), Non-linear Systems, Stochastic Control, Artificial Intelligence, Modeling and Computer Simulation, Ergodic Theory, Probability Theory and Statistics, Financial Mathematics and Financial Engineering (Risk Management and Risk Analysis, Marketing, Stock Fluctuations Analysis, Option, Contingent Claims, Valuation and Hedging, etc.).