Complete hierarchies of SIR models on arbitrary networks with exact and approximate moment closure

Mathematical Biosciences

Volumn 264, Issue 1, 2015, Pages 74-85

  Sharkey, Kieran J ^a   Wilkinson, Robert R ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

BBGKY; Dimensional reduction; Epidemic; Moment closure; Network; SIR

Indexed keywords

DIFFERENTIAL EQUATIONS; DYNAMIC MODELS; DYNAMICS; GRAPH THEORY; NETWORKS (CIRCUITS); STOCHASTIC SYSTEMS;

BBGKY; DIMENSIONAL REDUCTION; EPIDEMIC; MOMENT CLOSURE; SIR;

STOCHASTIC MODELS;

DISEASE TRANSMISSION; EPIDEMIC; INFECTIOUS DISEASE; PROBABILITY; STOCHASTICITY;

ACCURACY; ARBITRARY NETWORK; ARTICLE; BASIC REPRODUCTION NUMBER; DYNAMIC PARTITIONING; MATHEMATICAL MODEL; MOMENT CLOSURE MODEL; POISSON DISTRIBUTION; PROBABILITY; PROCESS OPTIMIZATION; SIMULATION; STATISTICAL DISTRIBUTION; STATISTICAL PARAMETERS; SUSCEPTIBLE INFECTIOUS REMOVED DYNAMICS MODEL; SYSTEM ANALYSIS; COMMUNICABLE DISEASE; EPIDEMIC; HUMAN; STATISTICS AND NUMERICAL DATA; THEORETICAL MODEL; TRANSMISSION;

COMMUNICABLE DISEASES; EPIDEMICS; HUMANS; MODELS, THEORETICAL;

EID: 84932626032     PISSN: 00255564     EISSN: 18793134     Source Type: Journal    
DOI: 10.1016/j.mbs.2015.03.008     Document Type: Article

References (16)

1. Newman M.E.J. The structure and function of complex networks. SIAM Rev. 2003, 45:167-256.
2. Matsuda H.N., et al. Statistical mechanics of population: the lattice Lotka-Volterra model. Prog. Theor. Phys. 1992, 88:1035-1049.
3. Sato K., et al. Pathogen invasion and host extinction in lattice structured populations. J. Math. Biol. 1994, 32:251-268.
4. Harada Y., Iwasa Y. Lattice population dynamics for plants with dispersing seeds and vegetative propagation. Res. Popul. Ecol. 1994, 36:237-249.
5. Keeling M.J. The effects of local spatial structure on epidemiological invasions. Proc. Biol. Sci. 1999, 266:859-867.
6. Bauch C. The spread of infectious diseases in spatially structured populations: an invasory pair approximation. Math. Biosci. 2005, 198:217-237.
7. House T., et al. A motif-based approach to network epidemics. Bull. Math. Biol. 2009, 71:1693-1706.
8. Sharkey K.J. Deterministic epidemiological models at the individual level. J. Math. Biol. 2008, 57:311-331.
9. Sharkey K.J. Deterministic epidemic models on contact networks: correlations and unbiological terms. Theor. Popul. Biol. 2011, 79:115-129.
10. Simpson M.J., Baker R.E. Correcting mean-field models for spatially dependent advection-diffusion-reaction phenomena. Phys. Rev. E 2011, 83:051922.
11. Sharkey K.J., et al. Exact equations for sir epidemics on tree graphs. Bull. Math. Biol. 2013, 10.1007/s11538-013-9923-5.
12. Kiss I.Z., et al. Exact deterministic representation of Markovian SIR epidemics on networks with and without loops. J. Math. Biol. 2015, 70:437-464.
13. Wilkinson R.R., Sharkey K.J. Message passing and moment closure for susceptible-infected-recovered epidemics on finite networks. Phys. Rev. E 2014, 89:022808.
14. Newman M.E.J. Networks, An Introduction 2010, Oxford University Press, Oxford, UK.
15. Ball F., Sirl D., Trapman P. Analysis of a stochastic SIR epidemic on a random network incorporating household structure. Math. Biosci. 2010, 224:53-73.
16. Karrer B., Newman M.E.J. A message passing approach for general epidemic models. Phys. Rev. E. 2010, 82:016101.