Predicting epidemics on directed contact networks

TLDR: Methods from percolation theory are used to develop a mathematical framework for predicting disease transmission through semi-directed contact networks in which some contacts are undirected-the probability of transmission is symmetric between individuals-and others are directed-transmission is possible only in one direction.

About: This article is published in Journal of Theoretical Biology.The article was published on 2006-06-07 and is currently open access. It has received 305 citations till now. The article focuses on the topics: Communicable disease transmission & Contact tracing.

Figures

Fig. 6. Epidemiological predictions on undirected and semi-directed contact networks. This graph shows the expected size of small outbreaks below the epidemic threshold (left), and the probability and expected size of a large-scale epidemic above the epidemic threshold (rate) for diseases with various transmission rates (T) spreading through an urban contact network. The predictions for the semi-directed and undirected networks are shown in black and gray, respectively.

Fig. 1. Contact networks: (A) undirected network; (B) bipartite network; and (C) semi-directed network.

Fig. 3. Simple semi-directed network. (A) The expected size of a small outbreak as a function of Td and Tu for a Poisson semi-directed network with Poisson parameters zd ¼ 2 and zu ¼ 3. (B) The epidemic threshold for a Poisson semi-directed network with Poisson parameters zd and zu.

Fig. 5. Epidemiological predictions for undirected, directed and semi-directed networks. The probability of an epidemic and expected fraction of the population infected during an epidemic for three classes networks: (N1) a completely undirected Poisson network with mean degree z; (N2) a semi-directed network with Poisson undirected and in-degree distributions of mean degree z=2, and with every vertex having an out-degree of exactly z=2; and (N3) a completely directed network with a Poisson in-degree distribution of mean degree z, and with every vertex having an out-degree of exactly z. For each of these networks, we plot the predicted probability and size of an epidemic (S) as a function of the average transmissibility of the disease (T). SN1 is both the expected magnitude and probability of an epidemic in network N1 and SN2size and SN2prob (SN3size and SN3prob ) are the expected magnitude and probability of an epidemic in N2 (N3). The left and right three lines correspond to networks with z ¼ 8 and 4, respectively.

Fig. 4. Structure of a semi-directed network. The largest set of vertices for which you can move between any two by following edges in the correct direction is the giant strongly connected component (GSCC). The set of vertices not contained in the GSCC that can be reached by following edges in the correct direction from the GSCC is called the giant out-component (GOUT). The set of vertices not contained in the GSCC from which the GSCC can be reached by following edges in the correct direction is called the giant in-component (GIN). Vertices that are not in the GSCC, GIN, or GOUT but can either be reached from the GIN or can reach the GOUT are in the tendrils of the network.

Fig. 8. Individual precautions. An individual can lower the probability that he or she will become infected during an epidemic by taking measures that limit transmission. The x-axis gives the percent reduction in transmissibility between the individual and all of his or her directed and undirected contacts for a disease originally above the epidemic threshold, Td ¼ Tu ¼ 0:1. The average likelihood of infection across the entire population is shown in black bars. The benefit of intervention is much greater for members of the general public (gray bars) than for HCWs (white bars).

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Q1. What contributions have the authors mentioned in the paper "Predicting epidemics on directed contact networks" ?

This is true for some sexually transmitted diseases that are more easily caught by women than men during heterosexual encounters ; and for severe infectious diseases that cause an average person to seek medical attention and thereby potentially infect health care workers ( HCWs ) who would not, in turn, have an opportunity to infect that average person. The authors furthermore demonstrate that these methods more accurately predict the vulnerability of HCWs and the efficacy of various hospital-based containment strategies during outbreaks of severe respiratory diseases. The authors find that the probability of an epidemic and the expected fraction of a population infected during an epidemic can be different in semi-directed networks, in contrast to the routine assumption that these two quantities are equal.