mio::iseir::Model Class Reference

#include <model.h>

Collaboration diagram for mio::iseir::Model:

Public Member Functions
TimeSeries< ScalarType > const &	calculate_EIR ()
	Calculate the distribution of the population in E, I and, R based on the calculated values for S. More...
	Model (TimeSeries< ScalarType > &&init, ScalarType dt_init, int N_init, const Pa &Parameterset_init=Pa())
	Create an IDE SEIR model. More...
TimeSeries< ScalarType > const &	simulate (int t_max)
	Simulate the evolution of infection numbers with the given IDE SEIR model. More...

Public Attributes
Pa	parameters {}

Private Types
using	Pa = ParametersBase
using	Vec = Eigen::VectorX< ScalarType >

Private Member Functions
ScalarType	central_difference_quotient (TimeSeries< ScalarType > const &ts_ide, InfectionState compartment, Eigen::Index idx) const
	Numerical differentiation of one compartment using a central difference quotient. More...
ScalarType	generalized_beta_distribution (ScalarType tau, ScalarType p=3.0, ScalarType q=10.0) const
	Density of the generalized beta distribution used for the function f_{beta} of the IDE SEIR model. More...
ScalarType	num_integration_inner_integral (Eigen::Index idx) const
	Numerical integration of the inner integral of the integro-differential equation for the group S using a trapezoidal sum. More...

Private Attributes
ScalarType	m_dt {0}
Eigen::Index	m_k {0}
Eigen::Index	m_l {0}
int	m_N {0}
TimeSeries< ScalarType >	m_result
TimeSeries< ScalarType >	m_result_SEIR

Member Typedef Documentation

Pa

using mio::iseir::Model::Pa = ParametersBase

private

Vec

using mio::iseir::Model::Vec = Eigen::VectorX<ScalarType>

private

Constructor & Destructor Documentation

Model()

mio::iseir::Model::Model ( TimeSeries< ScalarType > &&  init, ScalarType  dt_init, int  N_init, const Pa &  Parameterset_init = Pa()  )

inline

Create an IDE SEIR model.

Parameters

[in,out]	init	TimeSeries with the initial values of the number of susceptibles at associated initial times. The time steps in this vector should be equidistant and equal to the time step used for the simulation. A certain history of time steps and values for susceptibles is needed. A warning is displayed if the condition is violated. Co be more precise, the first time point needs to be smaller than -(k-1)*TimeStep with k=ceil((InfectiousTime + LatencyTime)/TimeStep). The last time point in this vector should be a time 0.
[in]	dt_init	The size of the time step used for numerical simulation.
[in]	N_init	The population of the considered region.

Member Function Documentation

calculate_EIR()

TimeSeries<ScalarType> const& mio::iseir::Model::calculate_EIR ( )

inline

Calculate the distribution of the population in E, I and, R based on the calculated values for S.

The values are calculated using the average latency and infection time, not using model equations. The simulated values of S are used for this purpose, so the simulate() function should be called beforehand.

Returns

The result of the calculation stored in an TimeSeries. The TimeSeries contains the simulation time and an associated Vector with values for S, E, I, and R.

central_difference_quotient()

ScalarType mio::iseir::Model::central_difference_quotient ( TimeSeries< ScalarType > const &  ts_ide, InfectionState  compartment, Eigen::Index  idx  ) const

inlineprivate

Numerical differentiation of one compartment using a central difference quotient.

Parameters

[in]	ts_ide	TimeSeries with the time steps already calculated. Used as function values in numerical differentiation.
[in]	idx	Time index at which the numerical differentiation should be performed.
[in]	compartment	Compartment for which the numerical differentiation is to be performed.

Returns

Numerically approximated derivative of the function belonging to the compartment at the point t[idx].

generalized_beta_distribution()

ScalarType mio::iseir::Model::generalized_beta_distribution ( ScalarType  tau, ScalarType  p = 3.0, ScalarType  q = 10.0  ) const

inlineprivate

Density of the generalized beta distribution used for the function f_{beta} of the IDE SEIR model.

Parameters

[in]	tau	evaluation point of the generalized Beta distribution.
[in]	p	parameter p of the generalized Beta distribution.
[in]	q	parameter q of the generalized Beta distribution.

Returns

Evaluation of the generalized beta distribution at the given evaluation point.

num_integration_inner_integral()

ScalarType mio::iseir::Model::num_integration_inner_integral ( Eigen::Index  idx ) const

inlineprivate

Numerical integration of the inner integral of the integro-differential equation for the group S using a trapezoidal sum.

Parameters

[in]

idx

Index of the point of time used in the inner integral.

Returns

Result of the numerical integration.

simulate()

TimeSeries<ScalarType> const& mio::iseir::Model::simulate ( int  t_max )

inline

Simulate the evolution of infection numbers with the given IDE SEIR model.

The simulation is performed by solving the underlying model equation numerically. Here, an integro-differential equation is to be solved. The model parameters and the initial data are used.

Parameters

[in]

t_max

Last simulation day. If the last point of time of the initial TimeSeries was 0, the simulation will be executed for t_max days.

Returns

The result of the simulation, stored in a TimeSeries with simulation time and associated number of susceptibles.

Member Data Documentation

m_dt

ScalarType mio::iseir::Model::m_dt {0}

private

m_k

Eigen::Index mio::iseir::Model::m_k {0}

private

m_l

Eigen::Index mio::iseir::Model::m_l {0}

private

m_N

int mio::iseir::Model::m_N {0}

private

m_result

TimeSeries<ScalarType> mio::iseir::Model::m_result

private

m_result_SEIR

TimeSeries<ScalarType> mio::iseir::Model::m_result_SEIR

private

parameters

Pa mio::iseir::Model::parameters {}