Restif2007 - Vaccination invasion

This model is described in the article:

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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total target population size

birth/death rate

transmission rate

basic reproductive ratio (beta/(gamma+mu))

recovery rate

fraction of individuals vaccinated at birth

rate of immunity loss

rate of immunity loss of vacinated individuals

fraction of individuals infected with strain 1

fraction of individuals infected with strain 2

fraction of susceptible individuals

fraction of vaccinated uninfected individuals

fraction of individuals immune against strain 1 exclusively after infection

fraction of individuals immune against strain 2 exclusively after infection

fraction of individuals immune to both strains