病毒变异在小世界网络中的传播
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Epidemics with Pathogen Mutation on
Small-World Networks
1
Zhi-Gang Shao, Zhi-Jie Tan, Xian-Wu Zou, and Zhun-Zhi Jin
Department of Physics, Wuhan University
Wuhan, P. R. China 430072
xwzou@whu.edu.cn
Abstract
We study the dynamical behavior of the epidemiological model with pathogen mu-
tation on small-world networks, and discuss the influence of the immunity duration
τ
R
, the cross-immunity threshold h
thr
, and system size N on epidemic dynamics. A
decaying oscillation occurs because of the interplay between the immune response
and the pathogen mutation. These results have implications for the interpretation
of longitudinal epidemiological data on strain abundance, and they will be helpful to
assess the threat posed by deliberate release of mutable virus.
Keywords: Small-World Networks; Epidemics; Mutation
1 Introduction
Events of recent years have heightened awareness of the potential threat of bioterrorism [1]. Math-
ematical models of viral transmission and control are important tools for assessing the threat posed
by deliberate release of the virus and the best means of containing an outbreak, because they can
integrate epidemiological and biological data to give quantitative insights into patterns of disease
spread [2]. Examples include the design and evaluation of childhood disease immunization pro-
grammes [3, 4], predicting the demographic impact of the HIV epidemic in different regions [5], and
analyzing the spread and control of the 2001 foot-and-mouth epidemic in Britain [6, 7, 8, 9].
Following this philosophy, a lots of mathematical epidemiological model for the spread of disease
are researched [10, 11, 12, 13, 14, 15, 16, 17]. However, most mathematical models for spread of
disease have not incorporated the pathogen mutation, which is an important issue in epidemiology.
The interplay between the memory immune response and pathogen mutation affects epidemic dy-
namics. Recently, Girvan et al. proposed a simple model of epidemics with pathogen mutation [18].
This model is based on the uniform mixing assumption, but this assumption is unrealistic. In fact,
individuals tend to make contact with household members, workplace colleagues and friends at a
much higher rate than random strangers. Hence socio-spatial structure has an important impact
on transmission dynamics [19]. This kind of socio-spatial structure can be described by small-world
networks [19, 20]. Behavior of epidemics also shows characteristics of small-world networks [14].
1
Supported by the Specialized Research Fund for the Doctoral Program of Higher Education No. 20020486009.
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