Restif2007 - Vaccination invasion
View the 2015-02 Model of the Month entry for this modelThis model is described in the article:
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)
This model is hosted on BioModels Database and identified by: BIOMD0000000294.
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- Vaccination and the dynamics of immune evasion.
- Restif O, Grenfell BT
- Journal of the Royal Society, Interface , 2/ 2007 , Volume 4 , pages: 143-153 , PubMed ID: 17210532
- Department of Veterinary Medicine, University of Cambridge, Cambridge Infectious Diseases Consortium, Madingley Road, Cambridge CB3 0ES, UK. or226@cam.ac.uk
- 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.
Metadata information
Gene Ontology entry of bacterium into host cell
Human Disease Ontology pertussis
Name | Description | Size | Actions |
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Model files |
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BIOMD0000000294_url.xml | SBML L2V4 representation of Restif2007 - Vaccination invasion | 49.77 KB | Preview | Download |
Additional files |
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BIOMD0000000294.m | Auto-generated Octave file | 8.55 KB | Preview | Download |
BIOMD0000000294.xpp | Auto-generated XPP file | 6.11 KB | Preview | Download |
BIOMD0000000294.svg | Auto-generated Reaction graph (SVG) | 46.08 KB | Preview | Download |
BIOMD0000000294-biopax2.owl | Auto-generated BioPAX (Level 2) | 27.14 KB | Preview | Download |
BIOMD0000000294-biopax3.owl | Auto-generated BioPAX (Level 3) | 43.27 KB | Preview | Download |
BIOMD0000000294.sci | Auto-generated Scilab file | 162.00 bytes | Preview | Download |
BIOMD0000000294.png | Auto-generated Reaction graph (PNG) | 203.24 KB | Preview | Download |
BIOMD0000000294_urn.xml | Auto-generated SBML file with URNs | 49.51 KB | Preview | Download |
BIOMD0000000294.pdf | Auto-generated PDF file | 239.85 KB | Preview | Download |
BIOMD0000000294.vcml | Auto-generated VCML file | 65.61 KB | Preview | Download |
- Model originally submitted by : Lukas Endler
- Submitted: 21-Dec-2010 04:00:08
- Last Modified: 18-May-2017 12:16:20
Revisions
: Variable used inside SBML models
Species | Initial Concentration/Amount |
---|---|
R Homo sapiens |
0.0 item |
S Homo sapiens |
0.0588235 item |
I1 Homo sapiens ; Bordetella pertussis |
0.00176967 item |
I2 Homo sapiens ; Bordetella pertussis |
1.0E-6 item |
Reactions | Rate | Parameters |
---|---|---|
gamma/(1-eta)*Iv2 gamma/(1-eta)*Iv2 |
gamma = NaN per_year; eta = 0.5 dimensionless | |
mu*(1-p)*N mu*(1-p)*N |
p = 1.0 dimensionless; mu = NaN per_year | |
mu*S mu*S |
mu = NaN per_year | |
beta*S*(I1+J1)/N beta*S*(I1+J1)/N |
beta = NaN per_year | |
beta*S*(I2+J2+Iv2)/N beta*S*(I2+J2+Iv2)/N |
beta = NaN per_year | |
sigma*R1 sigma*R1 |
sigma = NaN per_year | |
sigma*R2 sigma*R2 |
sigma = NaN per_year | |
sigma*R sigma*R |
sigma = NaN per_year | |
sigmaV*V sigmaV*V |
sigmaV = NaN per_year | |
mu*I1 mu*I1 |
mu = NaN per_year | |
gamma*I1 gamma*I1 |
gamma = NaN per_year | |
mu*I2 mu*I2 |
mu = NaN per_year | |
gamma*I2 gamma*I2 |
gamma = NaN per_year |
(added: 10 Jan 2011, 23:17:27, updated: 10 Jan 2011, 23:17:27)
For each value of tau, the model was started with the steady state values for a latent infection with strain 1. As described in the article, invasion of strain 2 was simulated by using an initial value of 1e-06/N for strain 2.
The parameters plotted are:
V : V_frac
strain 1 : strain1_frac
strain 2 : strain2_frac