WO2013089809A2 - Connectivity of rapidly disseminating epidemics - Google Patents

Abstract

Disclosed is a method for detecting epidemic connectors, geographically explicit structures that possess high influence on the dissemination of epidemic diseases, which prevent epidemic dissemination if promptly intervened after an epidemic is detected. The method that identifies epidemic connectors provides metrics that allow users to estimate where and when the epidemic is likely to disseminate, if not controlled, and the costs and/or benefits associated with decisions based on this method. The epidemic connectors method can be implemented earlier and at lower costs than was heretofor possible, with substantial health- and economic-related impacts, which include saving lives, and reduced duration of diseases affecting people or animals.

Description

CONNECTIVITY OF RAPIDLY DISSEMINATING EPIDEMICS

CROSS REFERENCE TO RELATED APPLICATIONS

This Application claims Priority to Provisional Patent Application Serial Number 61 / 576760, filed on December 16, 2011.

BACKGROUD OF THE INVENTION

1. Field of the Invention

The present invention relates to epidemic outbreaks and, in particular, to rapidly, effectively, and at a low cost, prevent epidemic dissemination. 'Epidemic' refers to any infectious disease, caused by any type of pathogen, which, once any susceptible host species is reached (infected), may disseminate over time and space. The invention identifies and differentiates geographically explicit sites or small regions with

unambiguous (measurable) connecting attributes which, if selectively and promptly intervened, prevent the invading pathogen to further disseminate. For brevity,

CONNECTIVITY OF RAPIDLY DISSEMINATING EPIDEMICS are here referred to as 'epidemic connectors.

2. Description of the Prior Art

Classic approaches used in epidemic control are characterized by one or more of the following features: (i) the use of aggregate data (data associated with rather large geographic surfaces, such as counties or states), (ii) insufficient data when decisions meant to control epidemics (when epidemics start) need to be made, and (iii) the use of data points assumed to be independent from one another [1-3]. However, it is known that (i) aggregate data ignore the precise location of individuals, which result in imprecise predictions, and lead to costly and slowly implemented, if not also ineffective decisions because such decisions should be applied to rather large geographical regions; (ii) to be effective, control measures should be conducted as early as possible (when the number of epidemic cases is very low); and (iii) in true epidemics, all epidemic cases are inter-dependent (all secondary case[s] can only be generated by some of the primary case[s], all tertiary case[s] can only be generated by some of the primary or secondary case[s], and so on [3-5]) Consequently, classic epidemic control approaches result in one or more of these undesirable consequences: (i) lack of precision as to where and when interventions should be implemented, (ii) slow and costly interventions, and (iii) sub-optimal or ineffective interventions. Such deficiencies result in loss of life, as well as damages to the economy.

Under the phrase 'epidemic control', the US PTO currently lists 14 patents. All of them are here analyzed. None of them describes, uses, or applies, simultaneously, (i) geographically explicit data, (ii) bio-temporal variables, and (iii) a method that considers dissemination mechanisms.

For instance, Niazi (US Patent 8,183,035); Wolff & Schuster (US Patent 7,680,757), Ratnakar (US Patent 8,183,035), and Humphreys et al (US Patent

7,179,645) neither consider geographically explicit data nor assess epidemic dissemination. These inventions refer to containers of samples (Niazi), election data analysis (Wolff & Schuster), a medicine container with a dispenser (Ratnakar), or biologic materials (Humphreys et al).

Because none of the previously described inventions measures geographically specific sites or areas, they cannot be used to prevent epidemic dissemination.

Kanevsky et al. (US Patent 6,993,442) refers to a mobile measurement device that neither considers geographically explicit data associated with infectious diseases nor epidemic dissemination mechanisms.

Both Dittmann et al. (US Patent 6,659,338) and Brem (US Patent 6,509,187) refer to devices for collection of biological samples. None of them considers

geographically explicit epidemiologic data or epidemic dissemination mechanisms.

Furthermore, Giroir et al. (US Patents 6,596,691 ; 6,242,418; 5,990,086; and 5,888,977), refer to therapeutical products applied to specific diseases, which neither consider geographically explicit epidemiologic data nor epidemic dissemination mechanisms.

Similarly, Phatak et al. (US Patent 4,731 ,104) and Harford et al. (US Patent 4,666,837) refer to treatments for specific diseases, which neither consider geographically explicit epidemiologic data nor epidemic dissemination mechanisms.

Finally, Affonso (US Patent 4,370,305) refers to a sterilization process, not to geographically explicit epidemiologic data or epidemic dissemination mechanisms.

In addition, the peer-reviewed literature on the spatial-temporal dissemination of infectious diseases ('epidemics') has not yet provided a method that demonstrates its validity and generalizabiility across diseases, and is based on geographically explicit sites or areas with early and large influence on epidemic dissemination. The literature on epidemic control can be viewed as composed of five major sets: (i) mathematical epidemiology, (ii) social structures, (iii) Network Theory, (iv) social network analysis (SNA), and (v) medical geography.

Mathematical epidemiology focuses on hosts. It asks who is in contact with whom [6, 7]. The calculation of the basic reproductive number (R₀) is one of its pillars [2]. Ro is the ratio of secondary cases generated per primary case: when >1 , the epidemic will disseminate; when it is <1 , the epidemic will soon die out [4]. R₀-based models -which, typically, lack low-scale geographical data- have overestimated some epidemics [8-15].

Social structure models [2] consider sub-populations suspected to be the target of the epidemic, such as families, which could be under-estimated if no stratification is conducted [16]. Typically, these models do not consider geographical data.

A third group of models explores networks. They consider the relative location of each individual (a 'node', which may be represented by a circle or point), and contacts between individuals ('links', e.g., a line that connects two nodes [17-201). While network models are usually labeled 'spatial', typically, they lack geographic data [22].

One subset partially related to both social structure and Network models is that known as Social Network Analysis (SNA). This approach may include geographically explicit data. It determines the location of individuals ('nodes') and the time and duration of contacts [23]. However, like all other models, SNA has been reported to: 1) risk missing data on connections [24], and 2) be sensitive to dynamic changes [25].

Medical geography addresses some of the limitations described above. This approach is based on disease maps, today generated with geographical information systems. Such maps may reveal geographical data patterns likely to be missed when only tabular data are considered [26-28]. Geographical models are frequently coupled with spatial statistical analysis. Potential limitations of this approach include: 1) dependence on a relatively large sample size (rarely available in the early epidemic phase), and 2) dependence on static processes (a rare event in epidemics, which, typically, are dynamic, that is, they change over time and space).

To address the limitations described above, functional (network theory-based), geographically explicit models that measure both dynamics and connectivity are needed [29-33]. While calls to study both global and local dynamics -which occur at high and low scales, respectively- have been expressed [12, 33], the simple combination of the previous models will not generate what is needed because all the described methods focus on contacts (people or animals) and, at the earliest epidemic phase, the number of infected individuals is very low. Consequently, classic approaches result in several consequences: (i) poor estimates (due to the low number of pieces of information available when decisions are most needed), and (ii) nation-wide or population-based control or preventive measures (such as vaccinations), which are costly, do not induce immediate protection, and are inherently slow in their implementation.

Furthermore, one reason why epidemic connectivity has not yet been addressed with an objective and reproducible method is that nature does not offer bio-geo- temporal equivalents of 'nodes' and 'edges': no map shows where, when, or why an 'epidemic node' emerges or is situated. To measure epidemic connectors, if, indeed, they exist (and then apply them to control epidemics), new metrics should be created and validated. Such metrics should include geographically measurable entities and capture biological dynamics.

Epidemic connectivity relates to, but differs from distance [34, 35]. For instance, two pairs of points, separated by the same (straight-line or Euclidean) distance, will differ in connectivity if a mountain or lake is located between one pair of points.

Connectivity may also be modified by time: different geographical sites may behave as nodes at some times but not at other times; e. g., a factory may act as a node on week days, losing that condition on weekends, when a park may become a node. None of the inventions described above addresses these considerations.

BRIEF SUMMARY OF THE INVENTION

The present invention unambiguously determines, in any geographical context (whether a town or a larger geographical region), a connecting structure (such as a road segment) coupled with a small area, which can prevent epidemic dissemination, if interventions are promptly implemented upon.

In one embodiment, the invention generates two outcomes: (i) it defines, with geographically explicit data, the sites or areas which, in the event of an epidemic, are likely to act as 'epidemic nodes' (connecting centers from which epidemic flows emerge) and (b) it differentiates the most influential of such 'nodes' (those more likely to be activated first, in an epidemic process).

Such gee—temporal information allows users to identify the epidemic node(s) that should be prioritized when interventions are implemented, providing its/their

geographical coordinates as well as estimates as to when (how early or late) such node(s) is/are likely to disseminate epidemics.

In another embodiment of the present invention, those skilled in this art are provided with a method that estimates the costs and/or benefits associated with this method, which can be compared against those of alternative methods.

In another embodiment of the present invention, it provides those skilled in this art with information on factors measurable before epidemics occur, thereby facilitating not only targeted responses after epidemics start but also preventive measures, ascribed to geographically specific sites.

In another embodiment of the present invention, it provides those skilled in this art with metrics usable to compare the costs and benefits associated with particular decisions, such as blanket vaccination vs. targeted and transient disruption of connecting structures.

In another embodiment, this invention provides a tool to monitor the efficacy of interventions implemented. By determining the geographical center of epidemic cases at particular time units (such as the replication or transmission cycle of the invading pathogen [the time required by the pathogen to multiply and disseminate'), it determines whether the epidemic 'moves' and, if so, in what direction(s) and at what speed.

These and other objects of the present invention will become apparent to those skilled in this art upon reading the accompanying description, drawings, and claims set forth herein. The headings provided herein are for the convenience of the reader only. No headings should be construed to limiting upon the content in any way. BRIEF DESCRIPTION OF THE DRAWINGS

Figures 1a and b depict both geographically and numerically how the radius of an 'epidemic node' is determined, using data of the 2006 Nigerian Avian Influenza H5N1 epidemic, which infected chickens.

Figures 2a and b depict how infective links (Euclidean distance between epidemic cases) are identified, both at large and small scales.

Figure 3 shows the number of cases per ranked epidemic node (REN) vs.

epidemic time (weeks).

Figure 4 shows how to conduct cost-benefit analyses, which can then be compared: (i) the number of cases potentially prevented by this method (Fig. 4a) vs. the number of cases potentially prevented by the classic approach (Fig. 4b); (ii) the degree of continuity (number of non-fragmented road segments); and (iii) the road length (non- Euclidean distance, expressed in km) generated by this method (Fig. 4c) and the road length associated with the classic approach (Fig. 4d).

Figure 5 evaluates the repeatability of the results generated by the invention: by assessing a different epidemic, generated by a different pathogen, which infected a different host species in a different country at a different time, the same analysis and data presentation described in Fig. 4 is repeated with data of the 2001 Foot-and-Mouth epidemic, which infected cows, in Uruguay. Figure 6 shows a triple cost-benefit comparison, which includes three alternatives (a classic spatial statistical approach, a classic Network Theory-based cluster, and the solution generated by this invention), demonstrating that this method produces greater benefits than either of the alternatives which either do not inform on directionality or create larger areas to be controlled, i.e. they are more expensive and/or less effective.

DETAILED DESCRIPTION OF THE INVENTION

1. Definitions

An epidemic case is any geo-referenced site (such as a farm or a town) where at least one individual is infected or susceptible to be infected.

Epidemic day (or week) refers to the day (or week) an epidemic case is reported, after epidemic start.

Epidemic node is the smallest geo-referenced circle or polygon that includes: 1) >50% of all cases reported per replication or transmission cycle (TC) of the infecting pathogen, except TC I, and 2) a highway intersection. Alternatively, the epidemic node is the smallest circle or polygon that includes a highway intersection (or an alternative, also geographically measurable, connecting structure, such as a railroad station) and >50% susceptible individuals within such circle or polygon than within a circle or polygon with a twice longer diameter or a twice larger size. [0038] Infective link is any segment of an Euclidean graph that connects pairs of epidemic cases. Depending on the location of such cases and/or the relative location of epidemic nodes, infective links estimated long-range connectivity. When cases are outside epidemic nodes and there is no epidemic node between cases, infective links do not involve epidemic nodes. However, when either epidemic cases are

located within epidemic nodes or such nodes are located between pairs of cases, infective links cross epidemic nodes: in such situations, the number of infective links crossing a node's surface estimates long-range node degrees.

Road segment is the length of the road network located within or between epidemic nodes or epidemic cases.

Continuity is the number of breaks (fragmented road segments) that may be found within a road network subset.

Ranked epidemic node (REN) is defined as the number of infective links that cross an epidemic node, where the most influential node is that crossed by the largest number of infective links (REN #1), and the node crossed by the smallest number of links is REN n. Therefore, epidemic nodes are characterized in terms of short- range connectivity (road segments) and long-range connectivity {infective links). 2. Best Mode of the Invention

FIGS. 1-5 show graphic representations of the best mode contemplated by the inventor of the epidemic connectors according to the concepts of the present invention. Briefly, the method consists of four steps, conducted in the following sequence: (i) determination of the critical radius of the 'epidemic node', (ii) creation of the 'infective link' matrix, (iii) calculation of the number of 'infective links' reaching or crossing every 'epidemic node'; and (iv) estimation of the geo-temporal epidemic progression, based on the plot that includes within-ranked-node cases vs. cases per temporal unit (e.g., weekly cases). Applied originally to study geo-referenced data from past epidemics, such information can then be fed into the method, and applied to estimate future epidemic disseminations. Alternatively, it can be applied together with covariates preexisting any epidemic, such as highway intersections, tows and cities, markets, schools, factories.

3. How to Make the Invention

As can be amply seen from the drawings, epidemic connectors is both a detection and a decision-making method that identifies specific geographical sites or areas with high and early influence on epidemic dissemination and, consequently, such sites or areas can lead to epidemic cessation, if promptly intervened upon.

Using geo-referenced data (data with latitude and longitude values) as well as, whenever possible, temporal data on a few variables (such as location and time of epidemic case occurrence, and location of atemporal [pre-epidemic] variables, such as the local road and demographic structures), three basic metrics are calculated, namely, 'epidemic nodes', 'infective links', and 'ranked epidemic nodes.'

The method begins with the insertion, within a geographically explicit context, of point data ('epidemic cases'), which may associated with several attributes such as time of occurrence (date), and the replication or transmission cycle corresponding to the infecting pathogen (e.g., 2 days per cycle, for some viruses, that is, the biological expression of time becomes 'cycle , 'cycle ΙΓ, ,,,'cycle n').

The second step is to add connectivity data (expressed as lines, such as the road/railroad/river netwon ).

Additional variables may possess any type of data (points, lines, or surfaces), such as the location of tows or cities, lakes, mountains, etc.

By inserting circles centered on particular locations with obvious connecting potential (such as highway intersections), creating circles or several radii, and then superimposing epidemic case points, 'epidemic nodes' are empirically determined.

By linking every pair of points of interest (such as epidemic cases) with Euclidean (straight) lines, the 'infective link' matrix is generated.

By partially or totally superimposing various geographic layers (as when the 'infective link' layer is superimposed on the layer of 'epidemic nodes'), additional (secondary variables) are generated, such as the number of lines ('infective links') that intersect 'epidemic nodes.' This operation produces a table with the number of lines that reach or cross each epidemic node (ranked epidemic nodes).

Similarly, by linking point and surface layers, such as the population of a town and the surface of a county, densities (surfaces) can be generated.

After the basic metrics are generated, partially overlapping 'epidemic nodes' are merged, if so observed, and alternative measures are generated, such as 'infective links' calculated on the basis of non-Euclidean ('along-read') distances between pairs of a variety of points (towns, cities, farms, epidemic cases).

4. How to use the invention

The problems identified in the Prior Art (imprecise estimates as to where/when epidemics disseminate, at what speed and into what direction; delayed implementation of control measures, and/or costly control measures that cover extended areas) are solved by epidemic connectors, which are applicable to any epidemic, regardless of the infecting pathogen, infected host species, place, or time; and may facilitate point- specific epidemic control measures, which may be implemented rapidly, at low cost, even when the available information (number of epidemic cases) is very low.

When Epidemic nodes and infective links are simultaneously used, the combination generates ranked epidemic nodes, that is, the number of infective links that reach or cross each epidemic node, whereby the epidemic node crossed by the highest number of infective links is regarded as the epidemic node with the # 1 rank, and the epidemic node crossed by the lowest number of infective links receives the lowest rank (e.g., the n rank or highest number). The epidemic node with the highest rank (that crossed by the highest number of infective links) is assumed to be the first (the earliest) engaged in an epidemic dissemination process (epidemic node #1 includes epidemic cases earlier than nodes of lower rank (epidemic nodes # 2, 3, 4, ...n). Epidemic node rank # 1 is also the node associated with the highest number of epidemic cases. Because this method also identifies the precise geo-referenced location of every ranked epidemic node, the invention allows those skilled in this art to implement epidemic control measures (of their election) at a precise geo-referenced location and also know when (at what time) such measures may or may not be effective. Depending on the amount of time available to implement control measures, when less than one replication or transmission cycle of the infecting pathogen has taken place (e.g., less than 2 days since epidemic start, when the replication or transmission cycle is assumed to be up to 2 days), the priority is to control epidemic node #1 (the most influential epidemic node). If, instead, 3 days have elapsed since epidemic start, in this example, the priority is to implement control measures on epidemic node # 2 or higher because, by that time (when a second replication or transmission cycle is already in progress), the epidemic may have reached epidemic nodes with higher rank numbers; i.e., controlling only epidemic node #1 may already be too late. When the initiation of the epidemic start is unknown, then epidemic nodes of two or more consecutive ranks should be controlled, e.g., epidemic nodes with rank #2 and 3.

The information provided by epidemic connectors can lead to numerous applications, which include prevention of disease dissemination and reduction of economic losses.

Some of the variables epidemic connectors measure may be adapted to local conditions. For instance, when road density is low, simple Euclidean (straight-line) distances may suffice to identify and calculate infective links. However, when road or demographic density is high, non-Euclidean ('along-road') distance measurements may result in better estimates.

While classic temporal units (days, weeks) can be used with epidemic

connectors, more precise estimates are expected to be achieved when time is expressed in biological terms, i.e., replication or transmission cycles of the infecting pathogen (e.g., the first, second, third,...n transmission cycle since epidemic start).

Because epidemic connectors are inherently based on high-resolution (low geographic scale) data, ceteris paribus provided, its solutions are likely to result in enhanced epidemic control measures (faster, earlier, less costly measures, associated with smaller surfaces to be controlled). The cost-benefit capabilities of this method can be estimated in various ways. One example is to compare the number of cases prevented, as shown in Figs. 4a, b and Figs. 5a, b. Another example involves measuring the degree of continuity of the connecting structure generated by the method (e.g., the total length of road segments captured by the invention, Figs. 4c, d; Figs. 5c, d). A third example is to compare its estimates with those generated by classic spatial statistics (which tend to result in small areas to be controlled) as well as those generated by Network Theory-based methods (which identify the most influential node). Such comparisons provide quantitative data on the limitations of classic methods (lack of directionality, in clusters determined by spatial statistics; excessively large control areas, in Network Theory), as described in Fig. 6.

When applied, epidemic connectors can generate cost-benefit estimates, which may also include, for comparison, estimates associated with other methods, such as those generated by classic spatial statistical methods and Network Theory-based algorithms.

Epidemic connectors can further shorten the 'critical time to respond' (the time within which an intervention has to be conducted and completed at a particular geographical site) if used as an information tool: this invention can identify where, exactly, resources and specialized personnel can be located in order to achieve the lowest cost or highest impact.

While the application of this method is likely to require large computers, because the primary variables that feed epidemic connectors are known or can be rapidly known for every country, a worldwide application is likely, which may save lives, mitigate disease, and reduce economic losses.

5. Examples of the invention

That it will be appreciated by those skilled in the art that the present invention is not restricted to the particular preferred embodiments described with reference to the drawings, and that variations may be made therein without departing from the scope of the present invention as defined in the appended claims and equivalents thereof.

DETAILED DESCRIPTION OF THE DRAWINGS

Figure 1 describes how epidemic nodes (the smallest circles that included one or more highway intersections^] and >50 % of all epidemic cases, at each replication cycle of the infecting pathogen [estimated to be 2 days]) are empirically identified: 4 circles of different radii (betweenIO and 34 km) were compared for the number of cases found inside or outside such circles, at each time point. (A) The 31 -km radius circle was the smallest that included >50% of all cases reported at each time point (solid symbols, B). Figures A and B show the same data, expressed in geographical or numerical terms, respectively. 'Cases' refer to the number of infected individuals (chickens infected with Avian Influenza H5N1), reported in 2006, in Nigeria.

Figure 2 describes the first step used to assess the importance of each epidemic node. After merging those epidemic nodes that overlapped, an additional geographic layer is superimposed, which includes infective links. An infective link is the straight line that connects every pair of epidemic cases. An enlarged view of one epidemic node (red box, A) is shown in B.

Figure 3 describes the second step used to assess the importance of each epidemic node. That is determined according to the number of infective links that cross their surfaces (see Figure 2a, b). The number of infective links that reach or cross each epidemic node is used to rank such nodes: the node with the highest number of infective links is ranked node # 1. The node receiving the smallest number of infective links is node n. This figure demonstrates the practical significance of node

differentiation: the plot of weekly cases vs. ranked epidemic nodes (REN) shows that the node of highest influence on epidemic dissemination (REN #1) was involved first and generated most cases. Later, RENs # 2 and 3 were involved, generating the second highest number of cases, and so on.

Figure 4 evaluates the efficacy of this invention with two metrics: (i) comparing the number of epidemic cases captured by the method at the end of the epidemic, based on information available at the second replication cycle of the infecting pathogen; and (ii) comparing the total length of road segments included in each solution. While 62 cases were found within the solution generated by this invention (A), the alternative method (B) captured approximately less than half (30) of the cases, in the same time. The alternative method considers both the same information used by this invention, and utilizes circles of equal radius than that of an epidemic node. However, the circles of the alternative method are centered on 'contacts' (neighbors), i.e., the location of sites infected at the time. Hence, the higher efficacy of this invention, in terms of cases potentially prevented, is associated with its focus on measuring epidemic connectors (circles that include an explicit connecting structure, such as highway intersections, in addition to cases, i.e., the definition of epidemic nodes). Similarly, this invention generated a road network almost three longer (C) than that of the alternative method (D), i.e., epidemic connectors (A, C) are more continuous or less fragmented than classic approaches (B, D).

Figure 5 evaluates the reproducibility of this invention by conducting the same analysis described in Fig. 4, now applied to a different epidemic (a different virus [Foot- and-Mouth Disease virus]), which infected a different species [cows], and took place in a different place, at a different time [Uruguay, 2001]). It shown that this invention captured almost twice as many cases as the alternative method did (360 vs. 181 cases, respectively, A, B). Similarly, this invention generated a road network much longer (C) than that of the alternative method (D).

Figure 6 documents additional (beneficial) differences generated by this invention. Based on the same data, three possible solutions are shown. If classic spatial statistical approaches are utilized (which regard each epidemic node as a cluster of epidemic cases because, by definition, there are more cases inside than outside epidemic nodes), because such method does not consider connectivity (it does not consider, in this example, the road network), the solution would require to conduct control measures on each of the 6 epidemic nodes (of which two pairs partially overlapped) shown within the red pentagon. That translates as an overall surface of 21 ,303 sq km to be controlled. If, instead, a classic Network Theory-based analysis is applied (which includes nodes and links [in this case represented by road segments]), the solution would be to control the single cluster represented by the whole surface of the red pentagon, which is equal to 32,970 sq km). However, if this invention is applied, both the advantages of classic spatial statistics (a small area) and those of Network theory (identification of the most influential node) could be considered, but a much better solution would be generated: controlling REN # 1 (node #1) only involves 3019 sq km (lower cost, earlier completion, and greater efficacy than the alternatives).

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Claims

What is claimed is:

1. A method to prevent epidemic dissemination, comprising the steps of:

i. building a geo-referenced dataset on the spatial-temporal dissemination of an infectious disease;

ii. inclusion, in said dataset, of information on one or more connecting

structure(s), which should be unambiguously measurable before the epidemic start, such as the road / railroad / river network;

iii. inclusion, in said dataset, of information on the number and/or location of the population susceptible to be infected;

iv. identification of geographically explicit sites or areas more (or less)

influential on epidemic dissemination; and

v. generation of metrics that facilitate cost-benefit assessments. A method to prevent epidemic dissemination according to claim 1 , wherein said

method includes a process for identifying 'epidemic nodes' (the smallest explicitly measurable, connecting structures that, most of the time, include >50 % of all epidemic cases reported per time unit), comprising:

i. building circles of different radii and/or polygons of different sizes, ii. centering said circles or polygons on an explicit connecting structure, such as a highway intersection, and

iii. selecting the smallest structures (circles or polygons) that, most

of the time, include >50 % of all epidemic cases reported per time unit.

3. A method to prevent epidemic dissemination according to claim 1 , wherein

said method includes a process for constructing an 'infective link' matrix,

comprising:

i. building straight lines ('Euclidean infective links') and/or 'along-road'

segments ('non-Euclidean infective links'), of which each connects a pair of points of interest, and

ii. selecting points of interest from the group consisting of: epidemic

cases, cities, neighborhoods, or farms.

4. A method meant to prevent epidemic dissemination according to claim 1 ,

wherein said method includes a process for ranking epidemic nodes ('ranked

epidemic nodes'), comprising:

i. determination of the number of (Euclidean and/or non-Euclidean)

'infective links' that cross or reach each epidemic node, and ii. hierarchical classification of epidemic nodes, according to the number of (Euclidean and/or non-Euclidean) 'infective links' that cross or reach each epidemic node, so rank # 1 is assigned to the epidemic node crossed or reached by the highest number of infective links, and the last rank (rank n) is assigned to the epidemic node crossed or reached by the lowest number of infective links.

5. A method that characterizes all ranked epidemic nodes identified by epidemic connectors according to claim 1 , comprising:

i. a plot that, simultaneously, describes two or more variables, and

identifies (with distinct symbols) the rank assigned to each epidemic node,

ii. reveals epidemic directionality (it reveals from which epidemic node[s] (that/those infected earlier) the epidemic was transmitted to which epidemic node[s] (that/those infected later), and/or

iii. if present, reveals epidemic synchronicity (it shows whether two or more epidemic nodes were infected at the same time).

6. A method to monitor the efficacy of measures implemented to prevent or control epidemic dissemination, comprising the steps of:

i. building a geo-referenced dataset on the spatial-temporal dissemination of an infectious disease;

ii. inclusion, in said dataset, of information on one or more connecting

structure(s), which should be unambiguously measurable before the epidemic start, such as the road / railroad / river network;

iii. inclusion, in said dataset, of information on the number and/or location of the population susceptible to be infected;

iv. identification of geographically explicit sites or areas more (or less)

influential on epidemic dissemination; and

v. generation of metrics that facilitate cost-benefit assessments.

7. A method that monitors the efficacy of measures implemented to prevent or control epidemic dissemination according to claim 6, wherein said method includes a process for evaluating the costs and/or benefits associated with decision-making, comprising: i. the number of cases expected to be prevented,

ii. the extension of the surface to be controlled,

iii. the length of the connecting structure included in the method's output, and/or

iv. the selection of the location(s) (where) interventions should be

implemented, according to the time elapsed since epidemic start.

8. A method to determine the center of, the direction it moves toward, and/or the speed of epidemic processes, comprising the steps of:

i. building a geo-referenced dataset on the spatial-temporal dissemination of an infectious disease;

ii. inclusion, in said dataset, of information on one or more connecting

structure(s), which should be unambiguously measurable before the epidemic start, such as the road / railroad / river network;

iii. inclusion, in said dataset, of information on the number and/or location of the population susceptible to be infected;

vi. identification of geographically explicit sites or areas more (or less)

influential on epidemic dissemination; and

vii. generation of metrics that facilitate cost-benefit assessments.

9. A method that determines the center of, the direction it moves toward, and/or the speed of epidemic processes according to claim 8, wherein said method includes a process for identifying 'epidemic nodes' (the smallest explicitly measurable, connecting structures that, most of the time, include >50 % of all epidemic cases reported per time unit), comprising :

i. building circles of different radii and/or polygons of different sizes, ii. centering said circles or polygons on an explicit connecting structure, such as a highway intersection, and

iv. selecting the smallest structures (circles or polygons) that, most of the time, include >50 % of all epidemic cases reported per time unit.

10. A method that determines the center of, the direction it moves toward, and/or the speed of epidemic processes according to claim 8, wherein said method includes a process for constructing an 'infective link' matrix, comprising:

i. building straight lines ('Euclidean infective links') and/or 'along-road' segments ('non-Euclidean infective links'), of which each connects a pair of points of interest, and

ii. selecting points of interest from the group consisting of: epidemic cases, cities, neighborhoods, or farms.

11. A method that determines the center of, the direction it moves toward, and/or the speed of epidemic processes according to claim 8, wherein said method includes a process for ranking epidemic nodes ('ranked epidemic nodes'), comprising: i. determination of the number of (Euclidean and/or non-Euclidean)

'infective links' that cross or reach each epidemic node, and ii. hierarchical classification of epidemic nodes, according to the number of

(Euclidean and/or non-Euclidean) 'infective links' that cross or reach each epidemic node, so rank # 1 is assigned to the epidemic node crossed or reached by the highest number of infective links, and the last rank (rank n) is assigned to the epidemic node crossed or reached by the lowest number of infective links.

A method to facilitate the study of properties associated with epidemic

dissemination, comprising the steps of:

i. building a geo-referenced dataset on the spatial-temporal dissemination of an infectious disease;

ii. inclusion, in said dataset, of information on one or more connecting

structure(s), which should be unambiguously measurable before the epidemic start, such as the road / railroad / river network;

iii. inclusion, in said dataset, of information on the number and/or location of the population susceptible to be infected;

iv. identification of geographically explicit sites or areas more (or less)

influential on epidemic dissemination; and

v. generation of metrics that facilitate cost-benefit assessments.

13. A method that facilitates the study of properties associated with epidemic dissemination according to claim 12, wherein said method includes a process for identifying 'epidemic nodes' (the smallest explicitly measurable, connecting structures that, most of the time, include >50 % of all epidemic cases reported per time unit), comprising:

i. building circles of different radii and/or polygons of different sizes, ii. centering said circles or polygons on an explicit connecting structure, such as a highway intersection, and

iii. electing the smallest structures (circles or polygons) that, most of the time, include >50 % of all epidemic cases reported per time unit.

14. A method that facilitates the study of properties associated with epidemic dissemination according to claim 12, wherein said method includes a process for constructing an 'infective link' matrix, comprising:

i. building straight lines ('Euclidean infective links') and/or 'along-road' segments ('non-Euclidean infective links'), of which each connects a pair of points of interest, and

ii. selecting points of interest from the group consisting of: epidemic cases, cities, neighborhoods, or farms.

15. A method that facilitates the study of properties associated with epidemic dissemination according to claim 12, for ranking epidemic nodes ('ranked epidemic nodes'), comprising: determination of the number of (Euclidean and/or non-Euclidean) 'infective links' that cross or reach each epidemic node, and

hierarchical classification of epidemic nodes, according to the number of (Euclidean and/or non-Euclidean) 'infective links' that cross or reach each epidemic node, so rank # 1 is assigned to the epidemic node crossed or reached by the highest number of infective links, and the last rank (rank n) is assigned to the epidemic node crossed or reached by the lowest number of infective links.