Effects of the infectious period distribution on predicted transitions in childhood disease dynamics

by Olga Krylova, and David J. D. Earn

InterfaceVolume 10(84):20130098

July 6, 2013

©2013 by The Royal Society

Probability density functions for several Erlang distributions with the same mean (13 days, marked with a vertical grey line) but different shape parameter n (see equation (1.1)).

Olga Krylova, and David J. D. Earn J. R. Soc. Interface 2013;10:20130098

©2013 by The Royal Society

Asymptotic and perturbation analysis of the sinusoidally forced SI1R model (equations (1.2), n = 1) parameterized for measles (γ−1 = 13 days, ν = 0.02 yr−1, α = 0.08).

Olga Krylova, and David J. D. Earn J. R. Soc. Interface 2013;10:20130098

©2013 by The Royal Society

Measles in New York City, 1928–1972.

Olga Krylova, and David J. D. Earn J. R. Soc. Interface 2013;10:20130098

©2013 by The Royal Society

SInR measles bifurcation diagrams as a function of for several values of the shape parameter of the infectious period distribution (n = 1, 3, 10, ∞), with other parameters fixed (mean infectious

period 1/γ = 13 days, birth rate ν = 0.02 per year, seasonal ...

Olga Krylova, and David J. D. Earn J. R. Soc. Interface 2013;10:20130098

©2013 by The Royal Society

Transient dynamics of the measles SInR model for n = 1, 3 and 10 as a function of .

Olga Krylova, and David J. D. Earn J. R. Soc. Interface 2013;10:20130098

©2013 by The Royal Society

Dynamical structure of the SInR model with a mean infectious period 1/γ = 13 days.

Olga Krylova, and David J. D. Earn J. R. Soc. Interface 2013;10:20130098

©2013 by The Royal Society

SEmInR bifurcation diagrams as a function of for several values of the shape parameters of the latent and infectious period distributions.

Olga Krylova, and David J. D. Earn J. R. Soc. Interface 2013;10:20130098

©2013 by The Royal Society

Transient dynamics of the measles SEmInR model for (m,n) = (1,1), (8,5) and (20,20) as a function of .

Olga Krylova, and David J. D. Earn J. R. Soc. Interface 2013;10:20130098

©2013 by The Royal Society

Two-parameter bifurcation diagrams and transient-period contour plots for the measles SEmInR model (mean latent period 1/σ = 8 days, mean infectious period 1/γ = 5 days).

Olga Krylova, and David J. D. Earn J. R. Soc. Interface 2013;10:20130098

©2013 by The Royal Society

Two-parameter bifurcation diagram and transient-period contour plot for the measles SInR model with the mean generation time chosen to be the same as in the SEmInR model for each value of

the shape parameter of the infectious period distribution, n.

Olga Krylova, and David J. D. Earn J. R. Soc. Interface 2013;10:20130098

©2013 by The Royal Society

Two-parameter bifurcation diagram and transient-period contour plot for the measles SInR model with fixed mean generation time, Tgen = 13 days.

Olga Krylova, and David J. D. Earn J. R. Soc. Interface 2013;10:20130098

©2013 by The Royal Society