Connecting network properties of rapidly disseminating epizoonotics

BACKGROUND: To effectively control the geographical dissemination of infectious diseases, their properties need to be determined. To test that rapid microbial dispersal requires not only susceptible hosts but also a pre-existing, connecting network, we explored constructs meant to reveal the network properties associated with disease spread, which included the road structure. METHODS: Using geo-temporal data collected from epizoonotics in which all hosts were susceptible (mammals infected by Foot-and-mouth disease virus, Uruguay, 2001; birds infected by Avian Influenza virus H5N1, Nigeria, 2006), two models were compared: 1) ‘connectivity’, a model that integrated bio-physical concepts (the agent’s transmission cycle, road topology) into indicators designed to measure networks (‘nodes’ or infected sites with short- and long-range links), and 2) ‘contacts’, which focused on infected individuals but did not assess connectivity. RESULTS: The connectivity model showed five network properties: 1) spatial aggregation of cases (disease clusters), 2) links among similar ‘nodes’ (assortativity), 3) simultaneous activation of similar nodes (synchronicity), 4) disease flows moving from highly to poorly connected nodes (directionality), and 5) a few nodes accounting for most cases (a ‘‘20:800 pattern). In both epizoonotics, 1) not all primary cases were connected but at least one primary case was connected, 2) highly connected, small areas (nodes) accounted for most cases, 3) several classes of nodes were distinguished, and 4) the contact model, which assumed all primary cases were identical, captured half the number of cases identified by the connectivity model. When assessed together, the synchronicity and directionality properties explained when and where an infectious disease spreads. CONCLUSIONS: Geo-temporal constructs of Network Theory’s nodes and links were retrospectively validated in rapidly disseminating infectious diseases. They distinguished classes of cases, nodes, and networks, generating information usable to revise theory and optimize control measures. Prospective studies that consider pre-outbreak predictors, such as connecting networks, are recommended.The National Veterinary Research Institute, Vom, Plateau, Nigeria; the Center for Non-Linear Studies of Los Alamos National Laboratory; and partially funded by Defense Threat Reduction Agency (DTRA) Grant CBT-09-IST-05-1-0092 (to JMF).http://www.plosone.orgab2012ab2013 (Author correction

Connecting Network Properties of Rapidly Disseminating Epizoonotics

To effectively control the geographical dissemination of infectious diseases, their properties need to be determined. To test that rapid microbial dispersal requires not only susceptible hosts but also a pre-existing, connecting network, we explored constructs meant to reveal the network properties associated with disease spread, which included the road structure.Using geo-temporal data collected from epizoonotics in which all hosts were susceptible (mammals infected by Foot-and-mouth disease virus, Uruguay, 2001; birds infected by Avian Influenza virus H5N1, Nigeria, 2006), two models were compared: 1) 'connectivity', a model that integrated bio-physical concepts (the agent's transmission cycle, road topology) into indicators designed to measure networks ('nodes' or infected sites with short- and long-range links), and 2) 'contacts', which focused on infected individuals but did not assess connectivity.THE CONNECTIVITY MODEL SHOWED FIVE NETWORK PROPERTIES: 1) spatial aggregation of cases (disease clusters), 2) links among similar 'nodes' (assortativity), 3) simultaneous activation of similar nodes (synchronicity), 4) disease flows moving from highly to poorly connected nodes (directionality), and 5) a few nodes accounting for most cases (a "20:80" pattern). In both epizoonotics, 1) not all primary cases were connected but at least one primary case was connected, 2) highly connected, small areas (nodes) accounted for most cases, 3) several classes of nodes were distinguished, and 4) the contact model, which assumed all primary cases were identical, captured half the number of cases identified by the connectivity model. When assessed together, the synchronicity and directionality properties explained when and where an infectious disease spreads.Geo-temporal constructs of Network Theory's nodes and links were retrospectively validated in rapidly disseminating infectious diseases. They distinguished classes of cases, nodes, and networks, generating information usable to revise theory and optimize control measures. Prospective studies that consider pre-outbreak predictors, such as connecting networks, are recommended

Detection of ‘along-road’ disease clusters and empirical determination of <i>epidemic nodes</i>.

<p>Maps show high-scale geographical data of the 2001 Uruguayan FMD (A) and the 2006 Nigerian AI H5N1 (B) epizoonotics. Low-scale data revealed that epidemic cases not only displayed spatial auto-correlation but also clustered along the road network (C, D).The radii of <i>epidemic nodes</i> (the smallest circles that included one or more highway intersections[s] and epidemic cases, at any viral transmission cycle [TC] except TC I) were 7.5 -km (FMD, E) and 31-km long (AI, F). In both epizoonotics, >57% of all cases occurred within epidemic nodes (A, B, E, F).</p

Comparison between connectivity and contact models–the AI epizoonotic.

<p>The AI dispersal process was similar to that of the FMD epidemic diffusion: after transmission cycle (TC) I, the connectivity model captured twice as many cases than the contact model (A, B). The length of road segments found within the area determined by the connectivity model was three times longer and less fragmented than the road structure captured by the contact model (C, D).</p

Differentiation of epidemic cases, detection of network properties, and estimation of long-range connectivity in the AI epizoonotic.

<p>Low-scale data revealed that one primary AI <i>case</i> was located close to but outside the connecting structure defined by <i>epidemic nodes</i> (A). In contrast, at or after TC II, most cases were found within epidemic nodes (B). Two <i>clusters</i> of <i>cases</i> were observed (red polygons, B). Some <i>epidemic nodes</i> displayed a much higher proportion of cases than average nodes, e.g., two nodes (nodes # 1 and 2, red pentagon, B) accounted for 46 (or 71%) of all within-node cases. Four <i>road intersection areas</i>, out of 16 (or 25%) included 80% (52/65) of all within-node <i>cases</i> (C). To estimate long-range connectivity, all pairs of epidemic cases were connected with Euclidean lines, conforming a graph of N * (N –1)/2 lines, where N = epidemic case (an infected farm), or (113 * 112)/2 = 6328 <i>infective links</i> (D).</p

Synchronicity and directionality of AI epidemic flows and interactions between pre- and post-outbreak variables.

<p>Based on the data reported in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0039778#pone-0039778-g006" target="_blank">Figure 6a</a>, <i>epidemic nodes</i> were ranked according to the number of <i>infective links</i> that crossed their surface, e. g., <i>ranked epidemic node</i> (REN) # 1 was crossed by the highest number of infective links (<b>A</b>). Both synchronicity and directionality were revealed when RENs were plotted against the weekly (log) number of <i>epidemic cases</i>, and several classes of epidemic nodes were distinguished. REN # 1 was engaged first, and later, it was followed by nodes of lower ranks The epidemic flow moved from high to low RENs (directionality was observed) and, at a given point in time, similar nodes were active (synchronicity was demonstrated). RENs #8 and 9 had no influence on epidemic dispersal: they only produced one case each (<b>A</b>). An additional graph, which linked the centroids of <i>epidemic nodes</i>, determined the distance between pairs of highway intersection areas that included epidemic cases (<b>B</b>). The median distance between such intersections was significantly shorter for high than for low RENs (<b>C</b>). Such finding supported the view that critical hubs –connecting node structures, which predate epidemic occurrence and are likely to act as epidemic nodes– may be identified even before microbial invasions occur.</p

Differentiation of AI epidemic nodes based on AI infective links.

<p>After overlapping <i>epidemic nodes</i> were merged, they were distinguished according to the number of <i>infective links</i> that crossed their surfaces (A). The <i>density of infective links/node</i> was so high in nodes # 1–4 that the color used to identify each node’s circle is not observed: only the color of the crossing (overlaying) <i>infective links</i> is noticed in such nodes. The density of <i>infective links/epidemic node</i> (infective links/sq km) decayed by a factor greater than 5 between node #1 and the following set of nodes (nodes # 2 to 4), by a factor of ∼3 between nodes # 2–4 and the set that included nodes #5 and 6, and by a factor of ∼2 between nodes # 5 and 6 and the remaining nodes. A significant positive correlation was found between the <i>infective link density/sq km</i> and the <i>case density/sq km</i> (<i>r</i> = .98, <i>P</i><0.001, B). An enlarged view of one AI epidemic node (red box, A), is shown in C.</p

Three cost-benefit perspectives.

<p>The AI data allowed the generation of three sets of metrics, potentially applicable in cost-benefit analyses. 1) While the <i>spatial statistical</i> (SS) model identified <i>6 disease clusters</i> (the 6 <i>epidemic nodes</i>, of which two partially overlapped, which are seen, within the red pentagon, as 4 circles or ovals, of different colors), because the SS approach does not offer information on directionality, control measures should consider every <i>epidemic node</i>, i.e., the overall ‘cost’ of an intervention would be equal to the sum of the areas of the 6 original epidemic nodes included in the red pentagon. 2) If a <i>Network Theory</i> (NT) perspective were considered, only a <i>single cluster</i> would be observed (the area included within the red pentagon, which is defined by nodes and edges [road segments]). The NT model may generate several cost-benefit metrics. 3) A <i>bio-geo-temporal</i> analysis can integrate both SS advantages (a small area) and NT advantages (identification of the most influential node, based on analysis of network properties). The bio-geo-temporal model can generate the lowest ‘cost’ (smallest area to be intervened per each prevented case). Calculations are reported in the text.</p

Differentiation of epidemic cases, detection of network properties, and estimation of long-range connectivity in the FMD epizoonotic.

<p>Not all primary FMD cases –those reported in the first transmission cycle or TC– were located within circles that included a highway intersection: only one the first 6 primary cases was connected (A). In contrast, at or after TC II, most cases were connected: they were within epidemic nodes. Some epidemic nodes included a much higher proportion of cases than average nodes, e.g., 8 epidemic nodes included 115 of all 402 within-node cases (B). Those 8 nodes were located in an area characterized by a high density of road segments (box, A). Such nodes revealed assortativity (selective connection among similar nodes) as well as Pareto’s “20∶80″ pattern: 8 of the 157 nodes connected at or after TC II (5% of all nodes) reported 23% of all cases (132/572), i. e., these nodes included 4.6 times (23/5) more cases than average nodes (B, C). To estimate long-range connectivity, a graph was made, which connected every pair of <i>epidemic cases</i> with Euclidean lines, here named <i>infective links</i> (D). A low-scale map shows <i>infective links</i> crossing 3 partially overlapping <i>epidemic nodes</i>, which include one <i>case</i> (E).</p

Relationships between pre- and post-outbreak variables in FMD.

<p>Because some TC I and TC II epidemic nodes overlapped, they were merged. Merging resulted in a total of 9 (one in TC I, 8 in TC II) node clusters (A). The hypothesis that the number of infective links crossing each node cluster preceded case occurrence was supported by the data: the correlation between <i>infective link density</i> (number of infective links crossing epidemic nodes, per sq km, observed at TC I and TC II) and within-node <i>case density</i> (cases reported by epidemic day 60, expressed on a per sq km basis) was positive and significant (<i>r</i> = .75, <i>P</i><0.02, B). <i>Early</i> variables (<i>infective links</i> observed in the first 10% of the epidemic progression [days 1–6] predicted <i>late</i> outcomes (within-node case density, observed in the last 90% of the epidemic [days 7–60]).</p