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Urn, Baby, Urn: A Simpler Approach to Studying Epidemic Models and the Efficacy of Disease-Prevention Policies

In this paper, we explore the use of urn models to describe and analyze the long-term effects of various disease-controlling policies on the spread of an infection through a population. These policies include vaccination with all/nothing vaccines or leaky vaccines, ring vaccination with the all/nothing vaccine, and contact tracing. The populations are described via the Susceptible-Infected-Susceptible (SIS) model with demography, the SIS model without demography and the Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Susceptible (SIR) models. We show that these urn models, often simpler than their respective deterministic and stochastic counterparts, yield, in most cases, the same average qualitative dynamics. We also examine the definitions and implications of equilibria and stability in these systems.

Article Number:
BU-1521-M

Year:
1999

Authors:
Michael Stuart Montgomery Lanham, Centre College
Desiree Mesa, California State Polytechnic University, Pomona
Jesús Francisco Rodríguez, Cornell University
Dianna Soliz Torres, Westminster College

urn_baby_urn_a_simpler_approach_to_studying_epidemic_models_and_the_efficacy_of_disease_prevention_policies.pdf