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Outbreak of Infectious Diseases through the Weighted RandomConnection Model

Published online by Cambridge University Press:  24 April 2014

M. Bradonjić
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Abstract

When modeling the spread of infectious diseases, it is important to incorporate riskbehavior of individuals in a considered population. Not only risk behavior, but also thenetwork structure created by the relationships among these individuals as well as thedynamical rules that convey the spread of the disease are the key elements in predictingand better understanding the spread. In this work we propose the weighted randomconnection model, where each individual of the population is characterized by twoparameters: its position and risk behavior. A goal is to model the effect that theprobability of transmissions among individuals increases in the individual risk factors,and decays in their Euclidean distance. Moreover, the model incorporates a combined riskbehavior function for every pair of the individuals, through which the spread can bedirectly modeled or controlled. We derive conditions for the existence of an outbreak ofinfectious diseases in this model. Our main result is the almost sure existence of aninfinite component in the weighted random connection model. We use results on the randomconnection model and site percolation in Z2.

Keywords

epidemic modelingPoisson point processrandom connection modelinfinite componentpercolation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 2: Epidemics models on networks , 2014 , pp. 82 - 88
Copyright
© EDP Sciences, 2014

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References

L.J.S. Allen, C.T. Bauch, C. Castillo-Chavez, D. Earn, Z. Feng, M.A. Lewis, J. Li, M. Martcheva, M. Nuño, J. Watmough, M.J. Wonham. Mathematical Epidemiology (Lecture Notes in Mathematics / Mathematical Biosciences Subseries). F. Brauer, P. van den Driessche, J. Wu eds., Springer, 2008.
N. Alon, J. Spencer. The probabilistic method. John Wiley & Sons Inc., 2000.
H. Andersson, T. Britton. Stochastic epidemic models and their statistical analysis. Springer Lecture Notes in Statistics, 151. Springer-Verlag, New York, 2000.
Arriola, L., Hyman, M.. Being sensitive to uncertainty. Computing in Science and Engineering, 9 (2007), No. 2, 10–20. CrossRefGoogle Scholar
H.T. Banks, M. Davidian, J.R. Samuels Jr., K.L. Sutton. An inverse problem statistical methodology summary. Mathematical and statistical estimation approaches in epidemiology. G. Chowell, J.M. Hyman, L.M.A. Bettencourt, C. Castillo-Chavez eds., Springer, (2009), 249–302.
M. Franceschetti, R. Meester. Random Networks for Communication: From Statistical Physics to Information Systems. Cambridge University Press, 2007.
G. Grimmett. Percolation. Springer Verlag, 1999.
R. Meester, R. Roy. Continuum Percolation. Cambridge University Press, 1996.
M.D. Penrose. Random Geometric Graphs. Oxford. University Press, Oxford, 2003.