Super-spreaders and the rate of transmission of the SARS virus

Abstract

We describe a stochastic small-world network model of transmission of the SARS virus. Unlike the standard Susceptible-Infected-Removed models of disease transmission, our model exhibits both geographically localised outbreaks and "super-spreaders". Moreover, the combination of localised and long range links allows for more accurate modelling of partial isolation and various public health policies. From this model, we derive an expression for the probability of a widespread outbreak and a condition to ensure that the epidemic is controlled. Moreover, multiple simulations are used to make predictions of the likelihood of various eventual scenarios for fixed initial conditions. The main conclusions of this study are: (i) "super-spreaders" may occur even if the infectiousness of all infected individuals is constant; (ii) consistent with previous reports, extended exposure time beyond 3-5 days (i.e. significant nosocomial transmission) was the key factor in the severity of the SARS outbreak in Hong Kong; and, (iii) the spread of SARS can be effectively controlled by either limiting long range links (imposing a partial quarantine) or enforcing rapid hospitalisation and isolation of symptomatic individuals. In addition, the epidemiological data currently available for Hong Kong is far superior to that of the Chinese mainland. 1 Two characteristic features were observed during the SARS outbreak in Hong Kong in 2003 (see Fig. 1 E-mail address: ensmall@polyu.edu.hk (M. Small). 1 During the epidemic, mainland authorities classified information on SARS infections as a state secret. Moreover, bureaucracy caused much of the available information to be concealed. Despite this, subsequent official investigation indicates that the infection rate for the Chinese mainland was significantly overreported. The reliability of data from China is therefore uncertain. a large number of cases; and persistent transmission within the community. Two widely cited SSEs were observed early in the epidemic and have been the subject of much attention: at the Amoy Gardens housing estate and at the Prince of Wales hospital. Epidemiological studies [5,1] have found that in Hong Kong:• the fatality rate was approximately 17% (compared to 11% globally); • the mean incubation period was 6.4 days (range 2-10 days) [6]; • the duration between onset of symptoms and hospitalisation was 3-5 days; and, • the mean number of individuals infected by each case during the initial phase of the epidemic (excluding SSEs) was 2.7 [4]. Standard deterministic SIR (susceptible-infected-removed) models of the spread of infectious diseases [7] make several important assumptions. An alternative approach [8], particularly popular for the study of sexually transmitted diseases [9][10][11], is to build an explicit network and model 0167-2789/$ -see front matter c

Analyzing and modeling real-world phenomena with complex networks: a survey of applications

“…The model included as agents those who were infected but not yet infectious, and as the main result the authors found that outbreaks could be prevented if the patients with symptoms were isolated as soon as possible. Another model applied to SARS spreading of virus in Hong Kong can be found in [405]. In 2007, Small et al [406] studied the distribution of avian influenza virus among wild and domestic birds and obtained a network with scale-free topology with no epidemic threshold.…”

Staged progression model for epidemic spread on homogeneous and heterogeneous networks

“…The obtained results on heterogenous networks are based on the hypothesis that the larger the degree of an infected individual, the greater the capability for infection it has, i.e., hub=super −spreader [13] . However, in [6][7][8], Zhou, et al argued that this hypothesis is not always true.…”

On pinning control of some typical discrete-time dynamical networks

“…Recently, the study on dynamical behaviors of complex networks has become a focus of great interest in this research field, such as the synchronization and the pinning control of dynamical networks, the epidemic of disease [4][5][6][7][8][9][10][11][12][13][14][15][16], etc. Especially, there are attempts to control the dynamics of a complex network and drive the network to an desired state.…”