OSCILLATIONS AND PHASE TRANSITION IN THE MEAN INFECTION RATE OF A FINITE POPULATION

Qingchu Wu (), Xinchu Fu, Haifeng Zhang and Michael Small
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Qingchu Wu: Department of Mathematics, Shanghai University, Shanghai, China;
Xinchu Fu: Department of Mathematics, Shanghai University, Shanghai, China
Haifeng Zhang: Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, P. R. China;
Michael Small: Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, P. R. China

International Journal of Modern Physics C (IJMPC), 2010, vol. 21, issue 10, 1207-1215

Abstract: We consider epidemic transmission in a finite population with both scale-free network structure and heterogeneous infection rates related to both susceptibility and infectiousness of individuals. The restriction to a finite population size and heterogeneity are included so that the model more closely matches reality. In particular, the arithmetic average behavior of heterogeneous infection rates with node-degree correlation is discussed. Through numerical simulations, we find that the average infection rate presents robust small-amplitude oscillations. Based on this property, we propose a statistical measure of the system dynamics — the epidemic spreading efficiency (ESE) — and discuss its phase transitions as a function of the various system parameters. The results show that the ESE presents a non-continuous phase transition and the ESE threshold is an extension of the epidemic threshold from the case of homogeneous infection rate (for homogeneous populations, the two quantities exhibit the same behavior). By comparing the ESE threshold and the epidemic threshold, we find that ESE threshold is larger than epidemic threshold for a sufficiently large network size. This implies that the traditional homogeneous assumption of infection rates in many epidemiological models overestimates the likelihood of epidemic disease survival.

Keywords: Complex networks; susceptibility and infectiousness; epidemic dynamics; 89.75.-k; 87.23.Ge; 05.70.Ln (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0129183110015774

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