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Supplementary Information for:

Controlling smallpox: Strategies in a Virtual City Built from Empirical Data

The Episims Team
James P Smith
Tel: 505.667.3733




1) Evolution of smallpox epidemics


    

    

CAPTION: Above are four frames of a movie showing a side-by-side comparison of a baseline case (on the left) with a targeted vaccination and quarantine strategy, in which symptomatic people are interviewed, most of their recent contacts identified, and the contacts and their households are vaccinated and sent to quarantine.

The full movie below shows 6 frames per day at 4 hour intervals for 70 days. The bars represent number infected at each location, and the color represents the fraction of infected people who are infectious.

The attack is presumed to be covert, so until people become symptomatic around day 10 they continue with their normal activities. (And there is no difference between the two movies until the ring response is implemented.) The attack site, a university, is readily visible as a very large spike in the downtown area which grows and decays every day as students gather on campus and disperse throughout the city.

Above the views of a sample generic city are strip charts displaying the cumulative number of people infected and dead as a function of time, and for the ring response, the number vaccinated and quarantined, which are important for determining feasibility of the response. These are not labelled, but the color coding corresponds to the labelled text below the charts.

Note that the scale on the leftmost chart is a factor of a hundred different from the rightmost.







smallpox propagation Movie (250 MB!)

Download here ---250 MB avi file








2) Degree dynamics according to activity types


    

    

    

    

CAPTION: Each location in EpiSims is associated with several activities. We consider the primary activity for each location (namely the activity done by the majority of people visiting that location) and observe the number of people with this activity at the location (i.e.,/ temporal degree/), as time progresses.

The figures above show the temporal degrees of a few locations with different activity types. Each plot shows the temporal degree of 5 randomly chosen locations. The X-axis shows time over a 24 hour period with 0 being approximately 11.00 p.m. The primary activity is indicated in the figure. The Y-axis represents the number of individuals at that location as the day progresses.

The temporal degrees are according to our expectations. For example, the a) figure, shows 5 different randomly chosen location blocks labeled homes: the degree decreases considerable during mid-day when people leave for work then it goes back up when they start returning home (some people do not return home working night shifts and leading to a small difference compared to the early morning hours). The locations where the primary activity is work, fill up with people during mid-day, to get emptied again by night when they leave, see the b) figure . The little dips around noon correspond to people leaving workplaces for lunch. Similarly, for schools, figure e) and colleges figure f) there is a mid-day fill up, with the difference that in colleges the evening classes create a second peak.v All these data are result of the people mobility generated by the TRANSIMs simulation engine, and thus they are not inputs to the simulation. The fact that these curves follow our expectations, is a validation of the simulation.



3) Demographics and mixing of the EpiSims population


CAPTION: Age distribution of the population

    

    

    

    

    

    

    

    

CAPTION: Demographics are likely to play a very important role in determining the efficacy of any strategies for disease control. We study different properties like distribution of age, and contact patterns for different demographic groups.

Figures a) - o) show the average number of contacts that a particular age group has with the rest of the population. Each graph corresponds to a specific age group (say A). The x-axis corresponds to all the age groups. For a particular age group (say B) on the x-axis, the (corresponding) value of the y-axis corresponds to the average number of contacts group A make with group B. The particular age (A) for which results are plotted is stated above the plot. The empirical observations agree quite well with our intuition. It also shows the degree of mixing among parts of population with that belong to various age groups.

From the pictures a) - g) it follows that youngsters typically have meetings with youngsters (syblings, schools, etc.). Figures i) - o) show that adults spend most contact with other adults (work places). The very high peaks in i), f) and g) show that teenagers have most contacts among other teenagers of the same age (16-18), and have little mixing with others.

One reason for studying these distributions is to see if it is possible to design targeted vaccination strategies that are derived from the demographic attributes of a population. Mixing properties among various age-groups help specialize the targeting methodology.



4) small portions of the social network


    

    

CAPTION: These figures display different representations of a same small part of the person-person contact graph, rendered using a graph drawing program. Vertices represent individual people, and edges are present if the two people came into contact for at least an hour during the day. Vertices are colored by their shortest path distance in the graph from one of a few individuals. Edges are colored corresponding to the color of vertices at either end.

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