Modeling a Smallpox Terrorist Attack
William J. Bicknell, MD, MPH
School of Public Health
June 21, 2002
You will probably find it easier to print out these instructions and read from them as you use the model on your computer.
You will need a recent version of Excel from Microsoft in order to use this model.
This model is presented as a working draft for you to use and, if you wish, to critique and send suggestions to me.
It is easy to put in your own assumptions about a terrorist attack and see what happens in terms of when different events take place, when control begins, the number of cities and towns affected and, of most importance, the cases of smallpox and smallpox deaths. Remember too, that those who recover often have permanent, disfiguring scarring on their face and wherever else the smallpox rash occurred.
All models simplify reality. The greater the simplifications, the less real and the less valuable the model. However, too much detail and the model becomes too difficult to understand and is no longer useful. This model, like most, tries to strike a middle ground. However, the user must remember the model, at best, shows some interrelationships and gives a rough approximation of the consequences that flow from varying assumptions. Please keep these caveats in mind as you use the model.
This model is in Excel and uses only simple arithmetic. All formulas can be seen in the formula bar. If you wish to see which cells feed a particular formula or which cells feed other cells, I suggest you go to "toolbars" under the "View" option on the menu bar, choose "customize" and select "auditing."
You will see a small red mark in the upper right hand corner of some cells. This indicates there is a cell note that further explains the content or meaning of that particular cell. Highlight the cell and the note should become visible. If not, highlight the cell and click on the cell note icon in the "auditing" toolbar (see below).
The model is locked and the only cells you can changes are the cells in column G, rows 5 to 15. These have a dark blue background and yellow type.
The initial values in the column labeled "VARY these numbers" have been set to reflect my estimate of a moderate attack. I have chosen neither a very bad case scenario nor a scenario that I feel is unrealistically benign. Rather I've selected numbers that I think represent a plausible middle ground. Once you download the model, you may make your own assumptions and vary these figures as you wish and see what happens.
Row A, Number of Terrorists: Insert how many terrorists you think would be involved in an attack.
Row B, Mortality from Smallpox: Most experts would place the overall mortality somewhere between 20% and 30%. I suggest you choose a number within this range.
Row C, Cities visited per Terrorist: How many different cities do you think each terrorist can visit in the 3 to 4 days available before he or she is either too sick or too visible to continue? Insert a number.
Row D, Terrorist(s) reveals how many cities visited: Do you think a terrorist would say how many cities he had visited? If so insert up to the number of cities the terrorist actually visited. If not, insert 1 as, if discovered, we will know the terrorist has at least been to the city where he or she is discovered.
Row E, Close contacts at each site: How many people in each city or town do you think a terrorist could approach within 6 or 7 feet and stay close for more than just a transitory moment. Insert your number. Remember terrorists will likely chose very crowded places like subway stations at rush hour, crowded buses, airport terminals and aircraft.
Row F, % close contacts infected: A close contact is usually considered someone within 6 to 7 feet of an infectious person. The longer the infectious person and the uninfected person are close together, the more likely it is that the uninfected person will become infected. Persons have become infected by simply walking by an open window with a smallpox patient inside or by putting their head briefly in the door of a smallpox ward. It is also possible to be close to an infectious person and not become infected. It is reasonable to assume that somewhere between 10% and 50% of susceptible (non-immune) people who come in close contact with an infectious terrorist will themselves become infected with smallpox. I suggest you select a number between 10% and 50%.
Row G, % infected close contacts traveling to different cities: What percent of persons
who are actually infected do you think would travel to another city or town within the next 10 to 12 days? Insert that percent here.
Row H, Each 1st round US case infects: Once someone in the US is infected with smallpox, they will become infectious in 11 to 12 days and are usually not visibly ill with a rash that looks like smallpox until the around day 15 or 16. From days 11 or 12 to 15 or 16 some patients will not feel very ill, others will feel more ill. They will be traveling to and from the doctor or clinic and some may also go to work, however, briefly. They may travel by car or public transport and will almost certainly be sitting in waiting rooms. For the first round of infected patients, how many other people do you think they may come into sufficiently close contact to actually transmit the infection? Different experts have suggested numbers from as low as 2 to more than 10 and possibly 20 or more. A range between 4 and 10 is reasonable and higher than 10 is not out of the question.
Row I, Each 2nd round US case infects: By now it will be known that smallpox is in the community. It is very likely that the rate of transmission will drop. People will isolate themselves. People will avoid contact with persons who have fever without a rash as is the case for smallpox patients before they become infectious. Control measures and vaccination will have begun. Some number less than 10 but not less than 2 to 5 is reasonable. Insert your choice.
Row J, Each 3rd round US case infects: Now the number should be quite small for all the reason stated just above. I would say under 5 and as low as 1 or 2 are reasonable choices. Insert your choice.
Row K, % of 2ary & 3ary cases going to new cities & towns: What percent of cases infected after the first round of cases directly infected by the terrorist(s) will travel to other cities and towns? This percent may be smaller than the percent you chose for Row G as these infected people are not deliberately targeting people in crowded places associated with travel. A figure somewhere between 1% and 10% is probably reasonable. Insert your choice.
Now you are done. The quantitative results are shown in the red boxes with white type.
You can now vary your assumptions and see what happens as you change one or more variables.
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