Laws of large numbers for epidemic models with countably many types

DOI10.1214/08-AAP521zbMath1197.92039arXiv0802.1478OpenAlexW3104469908MaRDI QIDQ2378630

Malwina J. Luczak, Andrew David Barbour

Publication date: 13 January 2009

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.1478

zbMATH Keywords

infinitely many typesepidemic modelsquantitative law of large numbers

Mathematics Subject Classification ID

Epidemiology (92D30) Strong limit theorems (60F15) Continuous-time Markov processes on discrete state spaces (60J27) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (6)

Contact processes with random connection weights on regular graphs ⋮ Connecting deterministic and stochastic metapopulation models ⋮ Normal approximations for discrete-time occupancy processes ⋮ Linear-fractional branching processes with countably many types ⋮ Individual and patch behaviour in structured metapopulation models ⋮ A law of large numbers approximation for Markov population processes with countably many types

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Denumerable Markov processes and the associated contraction semigroups on l
• Semigroups of linear operators and applications to partial differential equations
• A host-parasite model yielding heterogeneous parasite loads
• Comparison of an infinite dimensional model for parasitic diseases with a related 2-dimensional system
• Stochastic interacting particle systems and nonlinear kinetic equations
• Concentration Inequalities and Martingale Inequalities: A Survey
• Deterministic approximation of a stochastic metapopulation model
• A perturbation approximation to the simple stochastic epidemic in a large population
• Extensions of a Limit Theorem of Everett, Ulam and Harris on Multitype Branching Processes to a Branching Process with Countably Many Types
• A Limit Theorem for Multidimensional Galton-Watson Processes
• Branching processes in biology
• Stochastic models of a parasitic infection, exhibiting three basic reproduction ratios
• Approximating the long-term behaviour of a model for parasitic infection

This page was built for publication: Laws of large numbers for epidemic models with countably many types