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## WHAT IS IT?

In epidemiology, spatial and temporal variables are used to compute vaccination efficacy and effectiveness. The chosen resolution and scale of a spatial or spatio-temporal analysis will affect the results. When calculating vaccination efficacy, for example, a simple environment that offers various ideal outcomes is often modeled using coarse scale data aggregated on an annual basis. In contrast to the inadequacy of this aggregated method, this research uses agent based modeling of fine-scale neighborhood data centered around the interactions of infants in daycare and their families to demonstrate an accurate reflection of vaccination capabilities. Despite being able to prevent major symptoms, recent studies suggest that acellular Pertussis does not prevent the colonization and transmission of Bordetella Pertussis bacteria. After vaccination, a treated individual becomes a potential asymptomatic carrier of the Pertussis bacteria, rather than an immune individual. Agent based modeling enables the measurable depiction of asymptomatic carriers that are otherwise unaccounted for when calculating vaccination efficacy and effectiveness. Using empirical data from a Florida Pertussis outbreak case study, the results of this model demonstrate that asymptomatic carriers bias the calculated vaccination efficacy and reveal a need for reconsidering current methods that are widely used for calculating vaccination efficacy and effectiveness.

## HOW IT WORKS

The model is running by default on a 100x100 patch square. Each patch is measured at 5 pixels.

The **bacteria?** variable is a simplified represenation of the genus, Bordtella, this variable can be used in any agent. The model only represents the species, Bordtella pertussis, which is the most likely species within the genus Bordtella to produce severe reactions within children. One species that was not represented, Bordtella parapertussis, can produce a milder reaction in humans. Bordtella bronchiseptica, Bordtella avium, Bordtella trematum, and Bordtella holmesii rarely found in human infections¹ and are also not factored in this model. Turtles infected with symptomatic Bordtella pertussis progress through four phases until recovery.

The four phases of pertussis represented in this model are incubation, catarrhal, paroxysmal, and convalescent. Incubation occurs for seven days, catarrhal occurs for fourteen days, paroxysmal occurs for forty-two days, and convalescent occurs for ten days. After progressing through all of the stages a turtle is considered recovered and it is recovered, marked by the color green.

The **asymptomatic-carriers?** variable can be turned on or off via the interface (see section "HOW TO USE IT"). If this variable is turned on then individuals who are vaccinated are still able to carry the vaccine without showing any major symptoms associated with pertussis. They progress through the stages of the disease and can pass the pertussis bacteria to immunized as well as non-vaccinated turtles during this time period.

Turtles who are infected progress through the phases of Pertussis disease as defined by the CDC. An incubation period is followed by the Catarrhal, Paroxysmal and Convalesence stage. A turtle who progresses through these stages is considered recovered.²

Research regarding a preschool with a Pertussis outbreak in Florida was used as a basis for turtle varriables such as **model-vaccine-efficacy**, **model-relative-risk**, **model-attack-rate-vaccinated**, and **model-attack-rate-unvaccinated**.

- model-vaccine-efficacy = (1 - Relative Risk) * 100
- model-relative-risk = Attack Rate (Fully-Vaccinated) / Attack Rate (Not Up to Date)

Fully vaccinated children are those who are in compliance with the _Recommended Immunization Schedule for Children and Adolescents Aged 18 Years or Younger, UNITED STATES_, which is approved by the Advisory Committee on Immunization Practices (ACIP), American Academy of Pediatrics (AAP), American Academy of Family Physicians (AAFP) and American College of Obstetricians and Gynecologists (ACOG) and published by the Center for Disease Control (CDC).³ Unvaccinated are all of those who are considered not up to date with this vaccination schedule. In this model, those who are not up to date with the vaccination schedule are the same as those who are not vaccinated at all.

- model-attack-rate-vaccinated = Vaccinated Infected / Population
- model-attack-rate-unvaccinated = Unvaccinated Infected / Population

## HOW TO USE IT

The **Setup!** button clears the **turtles* and resets the **ticks**. It also prints the CSV header in the command prompt, as long as it is the first time setup has happened or the **clear-all** button has been used.

The **clear** button on the Command Prompt should abe clicked prior to running the program to clear the data from the Command Prompt. This will make it easier to copy everything from the command prompt into a CSV file.

The **Go!** button will proceed forward a single tick.

The **Go! (Forever)** button will proceed forward an infinite number of ticks and iterations or until depressed by a second click.

The **initial-infants** slider allows you to choose the number of initial infants.

The **pct-initial-infants-vaccinated** slider allows you to choose the number of initial infants that will be vaccinated. Users, need to ensure that their % of vaccination equates to whole number divisions of the initial-infant population to ensure accuracy of the model.

The **vaccine-efficacy** slider allows you to choose the effectiveness of the vaccination. When bacteria carrying turtles come into contact with vaccinated turtles who are not carrying bacteria, then this is the % chance that they will acquire the bacteria for each tick that they enter or stay in the 2 patch radius of the carrying turtle.

These are Pre-Selected-Settings:

- "High Vaccination, Low Efficacy" (90% vaccination, 10% efficacy)
- "High Vaccination, Mid Efficacy" (90% vaccination, 50% efficacy)
- "High Vaccination, High Efficacy" (90% vaccination, 90% efficacy)
- "Mid Vaccination, Low Efficacy" (50% vaccination, 10% efficacy)
- "Mid Vaccination, Mid Efficacy" (50% vaccination, 50% efficacy)
- "Mid Vaccination, High Efficacy" (50% vaccination, 90% efficacy)
- "Low Vaccination, Low Efficacy" (10% vaccination, 10% efficacy)
- "Low Vaccination, Mid Efficacy" (10% vaccination, 50% efficacy)
- "Low Vaccination, High Efficacy" (10% vaccination, 90% efficacy)

There are a lot of sliders, switches and buttons to explore. Dig through the code, pull out things you like, or modify and use them to create your own models. I would appreciate a citation to my research article if you do use functionality from this model. The article also contains additional information about this model:

https://doi.org/10.5194/isprs-annals-IV-4-W2-37-2017

## CREDITS AND REFERENCES

**1.** VON KÖNIG, C. W., RIFFELMANN, M., & COENYE, T. 2011. Volume I: section II: BACTERIOLOGY: GRAM-NEGATIVE BACTERIA: Chapter 43: Bordetella and Related Genera. Manual Of Clinical Microbiology, 739.
**2.** CDC. Epidemiology & Prevention of Vaccine-Preventable Diseases 13th Edition. 2017. Ch 16. Pg 261-278. Accessed via https://www.cdc.gov/vaccines/pubs/pinkbook/index.html. (last accessed 12 March 2017)
**3.** CDC. Recommended Immunization Schedule for Children and Adolescents Aged 18 Years or Younger (United States 2017). 2016. https://www.cdc.gov/vaccines/schedules/downloads/child/0-18yrs-child-combined-schedule.pdf (last accessed 11 March 2017).