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Thresholds in transmission are responsible for critical changes in infectious disease epidemiology. The epidemic threshold indicates whether infection invades a totally susceptible population. The reinfection threshold indicates whether self-sustained transmission occurs in a population that has developed a degree of partial immunity to the pathogen (by previous infection or vaccination). In models that combine susceptible and partially immune individuals, the reinfection threshold is technically not a bifurcation of equilibria as correctly pointed out by Breban and Blower. However, we show that a branch of equilibria to a reinfection submodel bifurcates from the disease-free equilibrium as transmission crosses this threshold. Consequently, the full model indicates that levels of infection increase by two orders of magnitude and the effect of mass vaccination becomes negligible as transmission increases across the reinfection threshold.

Original publication

DOI

10.1016/j.jtbi.2005.03.001

Type

Journal article

Journal

J Theor Biol

Publication Date

07/09/2005

Volume

236

Pages

111 - 113

Keywords

Disease Outbreaks, Disease Susceptibility, Disease Transmission, Infectious, Humans, Immunity, Innate, Infection Control, Models, Biological, Models, Statistical, Recurrence