epi_analysis
Module containing functions that performs epidemiology based analysis via algebraic manipulation, such as the basic reproduction number
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pygom.model.epi_analysis.
DFE
(ode, disease_state) Returns the disease free equilibrium from an ode object
Parameters: - ode: :class:`.BaseOdeModel`
a class object from pygom
- diseaseState: array like
name of the disease states
Returns: - e: array like
disease free equilibrium
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pygom.model.epi_analysis.
R0
(ode, disease_state) Returns the basic reproduction number, in symbolic form when the parameter values are not available
Parameters: - ode: :class:`.BaseOdeModel`
a class object from pygom
- diseaseStateIndex: array like
name of the disease states
Returns: - e: array like
R0
See also
getDiseaseProgressionMatrices()
,getR0GivenMatrix()
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pygom.model.epi_analysis.
R0_from_matrix
(F, V, disease_state=None) Returns the symbolic form of the basic reproduction number. This will include the states symbols which is different from
getR0()
where the states is replaced by the values of the disease-free equilibrium.Parameters: - F: :class:`sympy.matrices.MatrixBase`
secondary infection rates
- V: :class:`sympy.matrices.MatrixBase`
disease progression rates
- disease_state: list like, optional
list of the disease state as
sympy.Symbol
. Defaults to None which assumes that \(F,V\) had been differentiated
Returns: - e:
sympy.matrices.MatrixBase
the eigenvalues of \(FV^{-1}\) for the disease states
See also
getDiseaseProgressionMatrices()
,getR0()
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pygom.model.epi_analysis.
disease_progression_matrices
(ode, disease_state, diff=True) Returns (F,V), the secondary infection rates and disease progression rate respectively.
Parameters: - ode: :class:`.BaseOdeModel`
an ode class in pygom
- diseaseStates: array like
the name of the disease states
- diff: bool, optional
if the first derivative of the matrices are return, defaults to true
Returns: - (F, V): tuple
The progression matrices. If diff=False, then we return the \(F_{i}\) and \(V_{i}\) matrices as per [Brauer2008].