epi_analysis

Module containing functions that performs epidemiology based analysis via algebraic manipulation, such as the basic reproduction number

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

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()

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()

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].