Hydrodynamical Limits For Epidemic Models

Hydrodynamical limits of a spatial epidemic model are studied through the representation of the process as a projection of a higher dimensional Poisson process. The standardized process (In(t)) of infected individuals in a box of volume one at time t converges to a deterministic process (I(t)). Moreover, there exists a Gaussian process V such that nd/2(In-I) converges to V weakly. Copyright © 1998 by Marcel Dekker, Inc.143497508Daley, D.J., Vere-Jones, D., (1988) An Introduction to the Theory of Point Processes, , Springer-Verlag, New York, NYDunford, N., Schwartz, J.T., (1957) Linear Operators. Part I: General Theory, , Interscience Publishers, Inc, New York, NYEthier, S.N., Kurtz, T.G., (1986) Markov Processes: Characterization and Convergence, , John Wiley & SonsGarcia, N.L., Birth and Death Processes as Projections of Higher Dimensional Poisson Processes (1995) Advances in Applied Probability, 27 (4), pp. 911-930Garcia, N.L., Large Population Results for Epidemic Models (1995) Stochastic Processes and Their Applications, 60 (1), pp. 147-160Kurtz, T.G., Approximation of Population Processes (1981) CBMS-NSF Regional Conference in Applied Mathematics, , SIAMKurtz, T.G., Gaussian approximations for Markov chains and counting processes (1983) Bulletin of the International Statistical Institute, Proceedings of the 44th Session, Invited Paper, 1, pp. 361-376Solomon, W., Representation and approximation of large population age distributions using Poisson random measures (1987) Stochastic Processes and Their Applications, 26, pp. 237-255Stute, W., On a generalization of the Glivenko-Cantelli theorem (1976) Z. Wahrsch. Verw. Geb., 35, pp. 167-175Van Den Bosch, F., Zadoks, J.C., Metz, J.A.J., Focus expansion in plant disease. I: The constant rate of focus expansion (1988) Phytopathology, 78, pp. 54-5