An Agent-Based Model of Recurring Epidemics in a Population with Quarantine Capabilities

1. Brendan GreenleyPeriod 3 An Agent-Based Model of Recurring Epidemics in a Population with Quarantine Capabilities

2. Why An Epidemic Model? • Epidemics have been responsible for great losses of life and have acted as a population control (Black Plague, Spanish Influenza) • Epidemics are still a cause of concern today and in the future (SARS, H1N1 Swine Flu) • Analyzing certain characteristics of an epidemic outbreak or response can help shape plans in case of a real outbreak. http://www.solarnavigator.net/animal_kingdom/animal_images/death_black_plague_street_scene.jpg

3. Why Agent-Based? • Originally tried System Dynamics • Agent-Based Modeling makes more sense • Individual behaviors differ and can greatly affect the course of an epidemic outbreak • A user can observe an individual agent over time • Children can inherit values from two parents • Continuous visual representation of population

4. Scope of project • Population/environment bounds dictated by computer resources • All about seeing how epidemics balance a hypothetical population where disease outbreaks are the only constraint. • Quarantine option allows for analysis on how a population’s response to a epidemic helps/hinders its overall carrying capacity • Aging, mating, and survival behaviors all seen in model

5. NetLogo • NetLogo 4.0.4 (Developed at Northwestern) • Programming environment/language allows for System Dynamics & Agent Based Modeling • Cross-platform support • Windows, *Nix, Mac • Depends on Java • Free!

6. Setup User Control Panel On-the-fly Plotting 2D World

7. User Control Panel (UCP)

8. UCP Details • mating-freq • The minimum amount of ticks an agent must wait between mating. • virus-mutation-rate • The number of ticks before the base-susceptibility of all agents is reassigned along a bell curve, a pocket of infections emerges. And quarantine efforts are reset from the quarantine area. • max-ticks-alive • The maximum amount of ticks an agent may live to. This is then plugged into an equation which determines the probability of an agent from dying from non-epidemic causes as a function of age. Important in limiting population spikes during spans of time free of epidemics • max-days-sick • An infected agent is hosts the epidemic for this amount of time. If an agent survives to this point, there is a 30% chance of him/her recovering and gaining immunity.

9. Unbounded 2D World

10. 2D World Breakdown:Immune Agents • Susceptibility value low enough that agent is safe from infection • Can only die from age, or by losing immunity due to a new virus mutation or by having susceptibility increase due to age. • Agents who survive an epidemic outbreak are immune until it mutates

11. 2D World Breakdown:Susceptible Agents • Susceptible agents are able to get sick, magnitude of susceptibility represented by shading (white to olive, somewhat susceptible to very susceptible) • Susceptibility values determined by age and a randomly distributed “base-susceptibility” value. (Use 9th polynomial representation of 1918 Influenza W-shaped susceptibility curve to adjust base-susceptibility with age.

12. Susceptibility Adjustment

13. 2D World Breakdown:Infected Agents • Moves more slowly than healthy agents • Can spread disease to neighbors • Leaves a red path behind • Forced to stay in quarantine zone if escorted there. • Gain immunity if they survive, though more likely to die.

14. 2D World Breakdown:Quarantine Officers • Number dictated by QuarantineMagnitude variable slider • Never mate or die from age • Take shortest path back to 3x3 quarantine zone once they have someone to escort. • Officer position and number are reset and recalculated every time the virus mutates.

15. Quarantine Zone

16. Procedures • General Agent: • Move in random direction, avoid escorted infected persons, quarantine zone • Check for potential mate • Check for exposure to epidemic • Check to see if natural death is going to occur • Age++ • Quarantine Agent: • Move in a random direction • Check for infected persons in a two patch radius, if any exist, force them to follow you • Take any infected persons escorting towards quarantine zone • If no infected agents being escorted, continue patrol spiddlement.wordpress.com

17. BehaviorSpace • Allows user to export data to spreadsheets and tables • Can incrementally increase specified variables as the model runs • Useful for post-run data analysis in Excel

18. Results • Severe, recurring epidemics can successfully limit a populations growth over the long term. • Quarantines can help raise the carrying capacity by 13%, and by even more with large magnitude quarantine responses.

20. Results (continued) • Increasing quarantine magnitude also increases the long-term mean population. • Type of relationship difficult to decipherer, appears to differ based on virus duration, world size, and initial-immunity variables.

23. In Conclusion • In a population where population restraints such as food, shelter, and personal safety are met, epidemics can act as a population constraint. • The implementation of a quarantine can increase the long-term carrying capacity of such a population, increasing the magnitude of the quarantine results in further increase in carrying capacity.

24. Timeline • First Quarter • Used System Dynamics Modeling • Second Quarter • Late Dec: Switched to Agent-Based Modeling, formed basic procedures and agent types • Jan: • Implemented susceptibility distribution • Implemented more realistic mating/children characteristics • Learned how to use BehaviorSpace

25. Timeline (Continued) • February • Implemented aging procedures • Have infected agents movement limited • March • Implemented quarantine zone • Added quarantine agents • Implemented quarantine officer patrolling • Implemented smarter susceptible agents (they avoid quarantine zones and officers on their way to the zone with infected persons in tow) • April/May • Made age a factor of susceptibility • Recalculated quarantine response every mutation • Data collection, making conclusions • Analyze runs with and without quarantine, and with differing magnitudes of quarantines responses and conclude effects on carrying capacity.

26. Project Evolution • System Dynamics -> Agent Based • Short-term -> Long-term • Predetermined equations -> complex system affected by hundreds of individual decisions

27. Future Extensions • Create version where world is bounded. • Give users a factor representing selfishness/selflessness, where infected agents take it upon themselves to seek quarantine or instead seek to avoid quarantine officers. • Give quarantine agents specified paths to sweep • Introduce multiple quarantine areas.

28. Thank You.