CovidSIRDMixture¶
- class aftercovid.models.CovidSIRDMixture[source]¶
The model extends model @see cl CovidSIRD and assumes there are two variants of the same virus. The term beta1 * beta2 * S * I1 / N * I2 / N means that for all people being in contact with both virus, the second one wins as it is more contagious.
<<<
from aftercovid.models import CovidSIRDMixture model = CovidSIRDMixture() print(model.to_rst())
>>>
CovidSIRDMixture
Quantities
S: personnes non contaminées
I1: nombre de personnes malades ou contaminantes pour le premier variant
I2: nombre de personnes malades ou contaminantes pour le second variant
R: personnes guéries (recovered)
D: personnes décédées
Constants
N: population
Parameters
beta1: taux de transmission dans la population
beta2: second taux de transmission dans la population
mu: 1/. : durée moyenne jusque la guérison
nu: 1/. : durée moyenne jusqu’au décès
Equations
\[\begin{split}\begin{array}{l} \frac{dD}{dt} = \nu \left(I_{1} + I_{2}\right) \\ \frac{dI1}{dt} = - \frac{I_{1} I_{2} S \beta_{1} \beta_{2}}{N^{2}} - I_{1} \mu - I_{1} \nu + \frac{I_{1} S \beta_{1}}{N} \\ \frac{dI2}{dt} = - I_{2} \mu - I_{2} \nu + \frac{I_{2} S \beta_{2}}{N} \\ \frac{dR}{dt} = \mu \left(I_{1} + I_{2}\right) \\ \frac{dS}{dt} = \frac{I_{1} I_{2} S \beta_{1} \beta_{2}}{N^{2}} - \frac{I_{1} S \beta_{1}}{N} - \frac{I_{2} S \beta_{2}}{N} \end{array}\end{split}\]Visual representation:
See Base implementation for SIR models to get the methods common to SIRx models.
