Restif2007 - Vaccination invasion

Restif2007 - Vaccination invasion

This model is described in the article:

Vaccination and the dynamics
of immune evasion.

Restif O, Grenfell BT.
J R Soc Interface 2007 Feb; 4(12):
143-153
Abstract:

Vaccines exert strong selective pressures on pathogens,
favouring the spread of antigenic variants. We propose a simple
mathematical model to investigate the dynamics of a novel
pathogenic strain that emerges in a population where a previous
strain is maintained at low endemic level by a vaccine. We
compare three methods to assess the ability of the novel strain
to invade and persist: algebraic rate of invasion;
deterministic dynamics; and stochastic dynamics. These three
techniques provide complementary predictions on the fate of the
system. In particular, we emphasize the importance of
stochastic simulations, which account for the possibility of
extinctions of either strain. More specifically, our model
suggests that the probability of persistence of an invasive
strain (i) can be minimized for intermediate levels of vaccine
cross-protection (i.e. immune protection against the novel
strain) and (ii) is lower if cross-immunity acts through a
reduced infectious period rather than through reduced
susceptibility.

This
version of the model can be used for both the stochastic and the
deterministic simulations described in the article. For
deterministic interpretations with infinite population sizes, set
the population size 
N = 1. The model does reproduces the deterministic
time course. The initial values are set to the steady state
values for a latent infection with strain 1 with an invading
infection of strain 2 (I2=1e-06), 100 percent vaccination with a
susceptibility reduction τ=0.7 at birth (p=1), and all other
parameters as in figure 3 of the publication. 
To
be compatible with older software tools, the english letter names
instead of the greek symbols were used for parameter names:

parameter
symbol
name

transmission rate
β
beta

recovery rate
γ
gamma

birth/death rate
μ
mu

rate of loss of natural immunity
σ
sigma

rate of loss of vaccine immunity
σ
v
sigmaV

reduction of susceptibility by primary infection
θ
theta

reduction of infection period by primary infection
ν
nu

reduction of susceptibility by vaccination
τ
tau

reduction of infection period by vaccination
η
eta

Originally
created by libAntimony v1.4 (using libSBML 3.4.1)

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BIOMD0000000294.
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