Monte Carlo simulation and analytic approximation of epidemic processes on large networks

Central European Journal of Mathematics

Volumn 11, Issue 4, 2013, Pages 800-815

  Nagy, Noémi ^a   Simon, Péter L ^a  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

Author keywords

Network process; ODE approximation; SIS epidemic

Indexed keywords

EID: 84873108193     PISSN: 18951074     EISSN: 16443616     Source Type: Journal    
DOI: 10.2478/s11533-012-0162-z     Document Type: Article

References (11)

1. Barrat A., Barthélemy M., Vespignani A., Dynamical Processes on Complex Networks, Cambridge University Press, Cambridge, 2008.
2. Bollobás B., Random Graphs, 2nd ed., Cambridge Stud. Adv. Math., 73, Cambridge University Press, Cambridge, 2001.
3. Brauer F., van den Driessche P., Wu J. (Eds.), Mathematical Epidemiology, Lecture Notes in Math., 1945, Math. Biosci. Subser., Springer, Berlin-Heidelberg, 2008.
4. Danon L., Ford A. P., House T., Jewell C. P., Keeling M. J., Roberts G. O., Ross J. V., Vernon M. C., Networks and the epidemiology of infectious disease, Interdisciplinary Perspectives on Infectious Diseases, 2011, #284909.
5. Gleeson J. P., High-accuracy approximation of binary-state dynamics on networks, Phys. Rev. Lett., 2011, 107(6), #068701.
6. House T., Keeling M. J., Insights from unifying modern approximations to infections on networks, Journal of the Royal Society Interface, 2011, 8(54), 67-73.
7. Keeling M. J., Eames K. T. D., Networks and epidemic models, Journal of the Royal Society Interface, 2005, 2(4), 295-307.
8. Nåsell I., The quasi-stationary distribution of the closed endemic SIS model, Adv. in Appl. Probab., 1996, 28(3), 895-932.
9. Sharkey K. J., Deterministic epidemic models on contact networks: Correlations and unbiological terms, Theoretical Population Biology, 2011, 79(4), 115-129.
10. Simon P. L., Taylor M., Kiss I. Z., Exact epidemic models on graphs using graph-automorphism driven lumping, J. Math. Biol., 2010, 62(4), 479-508.
11. Taylor M., Simon P. L., Green D. M., House T., Kiss I. Z., From Markovian to pairwise epidemic models and the performance of moment closure approximations, J. Math. Biol., 2012, 646(6), 1021-1042.