Introduction

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Modeling a Smallpox Outbreak

In order to assess the effectiveness of Trace Vaccination (TV), Mass Vaccination (MV), and an interim policy that switches from Trace Vaccination to Mass Vaccination, Kaplan et al. embed key features of these strategies in a disease transmission model.

The model incorporates the following key assumptions:

1. Each individual goes through four stages of infection:

    Stage 1. Duration - 3 days. Properties - asymptomatic, noninfectious, vaccine-sensitive.
    Stage 2. Duration - 8 days. Properties - asymptomatic, noninfectious, vaccine-insensitive.
    Stage 3. Duration - 3 days. Properties - asymptomatic, infectious.
    Stage 4. Duration - 12 days. Properties - symptomatic and isolated.

Note that the characteristics of each stage are very different from the perspective of disease transmission. For example, individuals in the first stage can still be cured by vaccination. Alternately, note that those in the third stage are the ones responsible for infecting the susceptible population, since they are infectious, but not yet diagnosed and isolated.

2. Disease transmission results from homogeneous mixing among susceptible and asymptomatic-infectious (Stage 3) individuals. This corresponds to a worst-case scenario in a large city like New York. In such a city, the public transportation might serve as an almost perfect mixing pot, ensuring that each infectious person is almost equally likely to infect every other person.

3. A Trace Vaccination strategy works by isolating and interviewing newly detected symptomatic cases (individuals who leave Stage 3 of the disease to enter Stage 4). These individuals become known as "index cases." By interviewing them, authorities generate a list of people who have potentially come in contact with the disease (the phrase "Ring Vaccination" refers to this "ring" of people). In practice, only a certain fraction of the vulnerable contacts are successfully found through this method.

The people that are identified by index cases are placed on a queue to be vaccinated. However, the queue is serviced by a finite number of vaccinators with limited capabilities so individuals must sometimes wait for vaccination. Furthermore, the vaccine fails a certain fraction of the time, so some individuals return to the freely mixing population as susceptible or already infected with smallpox.

4. A Mass Vaccination Strategy is much simpler. When an outbreak is detected, the entire city population is immediately moved onto the vaccination queue. No interviews are necessary, and people are vaccinated in a random order.

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