Author:
Sharkey K. J.,Kiss I. Z.,Wilkinson R. R.,Simon P. L.
Abstract
Abstract
We consider Markovian susceptible-infectious-removed (SIR) dynamics on time-invariant weighted contact networks where the infection and removal processes are Poisson and where network links may be directed or undirected. We prove that a particular pair-based moment closure representation generates the expected infectious time series for networks with no cycles in the underlying graph. Moreover, this “deterministic” representation of the expected behaviour of a complex heterogeneous and finite Markovian system is straightforward to evaluate numerically.
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,General Agricultural and Biological Sciences,Pharmacology,General Environmental Science,General Biochemistry, Genetics and Molecular Biology,General Mathematics,Immunology,General Neuroscience
Reference33 articles.
1. Anderson, R. M., & May, R. M. (1991). Infectious diseases of humans. London: Oxford University Press.
2. Bailey, N. T. J. (1975). The mathematical theory of infectious diseases. London: Griffin.
3. Baker, R. E., & Simpson, M. J. (2010). Correcting mean-field approximations for birth–death-movement processes. Phys. Rev. E, 82, 041905.
4. Ball, F., & Neal, P. (2008). Network epidemic models with two levels of mixing. Math. Biosci., 212, 69–87.
5. Bartlett, M. S. (1956). Deterministic and stochastic models for recurrent epidemics. In Proc. third Berkley symp. math. statist. prob. (Vol. 4, pp. 81–108).
Cited by
34 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献