On the duration of a Maki-Thompson epidemic

Area of Science:

• Mathematical modeling
• Epidemiology
• Social dynamics

Background:

• The Maki-Thompson model describes rumor propagation in a population.
• Previous work established that ~80% of a large population eventually learns a rumor.

Purpose of the Study:

• To derive the asymptotic mean duration of a rumor's spread in the Maki-Thompson model.
• To analyze the relationship between rumor duration and population size.

Main Methods:

• Mathematical derivation of the asymptotic mean time for rumor extinction.
• Analysis of the Maki-Thompson model under large population assumptions.

Main Results:

• The asymptotic mean duration a rumor persists is derived.
• Rumor duration grows slowly with population size (W).
• The formula for mean duration is approximately [2.68 ln(W) + 1.34]/μ time units, where μ is the average number of contacts per person per time unit.

Conclusions:

• The time it takes for a rumor to die out increases slowly with population size.
• The derived formula provides a quantitative estimate for rumor persistence duration in large populations.