Forecasting¶
Forecasting with the inferred parameters, error bars and, if there are latent variables, inferred initial conditions.
SIR¶
-
class
pyross.forecast.SIR¶ Susceptible, Infected, Removed (SIR) Ia: asymptomatic Is: symptomatic
…
Parameters: - parameters (dict) –
- Contains the following keys:
- alpha: float
- Estimate mean value of fraction of infected who are asymptomatic.
- beta: float
- Estimate mean value of rate of spread of infection.
- gIa: float
- Estimate mean value of rate of removal from asymptomatic individuals.
- gIs: float
- Estimate mean value of rate of removal from symptomatic individuals.
- fsa: float
- fraction by which symptomatic individuals do not self-isolate.
- cov: np.array( )
- covariance matrix for all the estimated parameters.
- M (int) – Number of compartments of individual for each class. I.e len(contactMatrix)
- Ni (np.array(3*M, )) – Initial number in each compartment and class
-
simulate()¶
-
simulate() Parameters: - S0 (np.array(M,)) – Initial number of susceptables.
- Ia0 (np.array(M,)) – Initial number of asymptomatic infectives.
- Is0 (np.array(M,)) – Initial number of symptomatic infectives.
- contactMatrix (python function(t), optional) – The social contact matrix C_{ij} denotes the average number of contacts made per day by an individual in class i with an individual in class j The default is None.
- Tf (float, optional) – Final time of integrator. The default is 100.
- Nf (Int, optional) – Number of time points to evaluate.The default is 101,
- Ns (int, optional) – Number of samples of parameters to take. The default is 1000.
- nc (int, optional) –
- epsilon (np.float64, optional) – Acceptable error in leap. The default is 0.03.
- tau_update_frequency (int, optional) –
- verbose (bool, optional) – Verbosity of output. The default is False.
- Ti (float, optional) – Start time of integrator. The default is 0.
- method (str, optional) – Pyross integrator to use. The default is “deterministic”.
- events (list of python functions, optional) – List of events that the current state can satisfy to change behaviour of the contact matrix. Event occurs when the value of the function changes sign. Event.direction determines which direction triggers the event, takign values {+1,-1}. The default is [].
- contactMatricies (list of python functions) – New contact matrix after the corresponding event occurs The default is [].
- events_repeat (bool, optional) – Wheither events is periodic in time. The default is false.
- events_subsequent (bool, optional) – TODO
Returns: out_dict –
- Dictionary containing the following keys:
- X: list
List of resultant trajectories
- t: list
List of times at which X is evaluated.
- X_mean : list
Mean trajectory of X
- X_std : list
Standard devation of trajectories of X at each time point.
<init params> : Initial parameters passed at object instantiation. sample_parameters : list of parameters sampled to make trajectories.
Return type: dict
- parameters (dict) –
SIR_latent¶
-
class
pyross.forecast.SIR_latent¶ Susceptible, Infected, Removed (SIR) Ia: asymptomatic Is: symptomatic
Latent inference class to be used when observed data is incomplete. …
Parameters: - parameters (dict) –
- Contains the following keys:
- alpha: float
- Estimate mean value of fraction of infected who are asymptomatic.
- beta: float
- Estimate mean value of rate of spread of infection.
- gIa: float
- Estimate mean value of rate of removal from asymptomatic individuals.
- gIs: float
- Estimate mean value of rate of removal from symptomatic individuals.
- fsa: float
- fraction by which symptomatic individuals do not self-isolate.
- cov: np.array( )
- Covariance matrix for all the estimated parameters.
- S0: np.array(M,)
- Estimate initial number of susceptables.
- Ia0: np.array(M,)
- Estimate initial number of asymptomatic infectives.
- Is0: np.array(M,)
- Estimate initial number of symptomatic infectives.
- cov_init : np.array((3*M, 3*M)) :
- Covariance matrix for the initial state.
- M (int) – Number of compartments of individual for each class. I.e len(contactMatrix)
- Ni (np.array(3*M, )) – Initial number in each compartment and class
-
simulate()¶
-
simulate() Parameters: - contactMatrix (python function(t), optional) – The social contact matrix C_{ij} denotes the average number of contacts made per day by an individual in class i with an individual in class j The default is None.
- Tf (float) – Final time of integrator.
- Nf (Int) – Number of time points to evaluate.
- Ns (int) – Number of samples of parameters to take.
- nc (int, optional) –
- epsilon (np.float64, optional) – Acceptable error in leap. The default is 0.03.
- tau_update_frequency (int, optional) – TODO
- verbose (bool, optional) – Verbosity of output. The default is False.
- Ti (float, optional) – Start time of integrator. The default is 0.
- method (str, optional) – Pyross integrator to use. The default is “deterministic”.
- events (list of python functions, optional) – List of events that the current state can satisfy to change behaviour of the contact matrix. Event occurs when the value of the function changes sign. Event.direction determines which direction triggers the event, takign values {+1,-1}. The default is [].
- contactMatricies (list of python functions) – New contact matrix after the corresponding event occurs The default is [].
- events_repeat (bool, optional) – Wheither events is periodic in time. The default is false.
- events_subsequent (bool, optional) – TODO
Returns: out_dict –
- Dictionary containing the following keys:
- X: list
List of resultant trajectories
- t: list
List of times at which X is evaluated.
- X_mean : list
Mean trajectory of X
- X_std : list
Standard devation of trajectories of X at each time point.
<init params> : Initial parameters passed at object instantiation. sample_parameters : list of parameters sampled to make trajectories. sample_inits : List of initial state vectors tried.
Return type: dict
- parameters (dict) –
SEIR¶
-
class
pyross.forecast.SEIR¶ Susceptible, Exposed, Infected, Removed (SEIR) Ia: asymptomatic Is: symptomatic :param parameters:
- Contains the following keys:
- alpha: float
- Estimate mean value of fraction of infected who are asymptomatic.
- beta: float
- Estimate mean value of rate of spread of infection.
- gIa: float
- Estimate mean value of rate of removal from asymptomatic individuals.
- gIs: float
- Estimate mean value of rate of removal from symptomatic individuals.
- fsa: float
- fraction by which symptomatic individuals do not self-isolate.
- gE: float
- Estimated mean value of rate of removal from exposed individuals.
- cov: np.array( )
- covariance matrix for all the estimated parameters.
Parameters: - M (int) – Number of compartments of individual for each class. I.e len(contactMatrix)
- Ni (np.array(4*M, )) – Initial number in each compartment and class
-
simulate()¶
-
simulate() Parameters: - S0 (np.array(M,)) – Initial number of susceptables.
- E0 (np.array(M,)) – Initial number of exposed.
- Ia0 (np.array(M,)) – Initial number of asymptomatic infectives.
- Is0 (np.array(M,)) – Initial number of symptomatic infectives.
- contactMatrix (python function(t), optional) – The social contact matrix C_{ij} denotes the average number of contacts made per day by an individual in class i with an individual in class j The default is None.
- Tf (float, optional) – Final time of integrator. The default is 100.
- Nf (Int, optional) – Number of time points to evaluate.The default is 101,
- Ns (int, optional) – Number of samples of parameters to take. The default is 1000.
- nc (int, optional) –
- epsilon (np.float64, optional) – Acceptable error in leap. The default is 0.03.
- tau_update_frequency (int, optional) –
- verbose (bool, optional) – Verbosity of output. The default is False.
- Ti (float, optional) – Start time of integrator. The default is 0.
- method (str, optional) – Pyross integrator to use. The default is “deterministic”.
- events (list of python functions, optional) – List of events that the current state can satisfy to change behaviour of the contact matrix. Event occurs when the value of the function changes sign. Event.direction determines which direction triggers the event, takign values {+1,-1}. The default is [].
- contactMatricies (list of python functions) – New contact matrix after the corresponding event occurs The default is [].
- events_repeat (bool, optional) – Wheither events is periodic in time. The default is false.
- events_subsequent (bool, optional) – TODO
Returns: out_dict –
- Dictionary containing the following keys:
- X: list
List of resultant trajectories
- t: list
List of times at which X is evaluated.
- X_mean : list
Mean trajectory of X
- X_std : list
Standard devation of trajectories of X at each time point.
<init params> : Initial parameters passed at object instantiation. sample_parameters : list of parameters sampled to make trajectories.
Return type: dict
SEIR_latent¶
-
class
pyross.forecast.SEIR_latent¶ Susceptible, Exposed, Infected, Removed (SEIR) Ia: asymptomatic Is: symptomatic
Latent inference class to be used when observed data is incomplete.
Parameters: - parameters (dict) –
- Contains the following keys:
- alpha: float
- Estimate mean value of fraction of infected who are asymptomatic.
- beta: float
- Estimate mean value of rate of spread of infection.
- gIa: float
- Estimate mean value of rate of removal from asymptomatic individuals.
- gIs: float
- Estimate mean value of rate of removal from symptomatic individuals.
- fsa: float
- fraction by which symptomatic individuals do not self-isolate.
- gE: float
- Estimated mean value of rate of removal from exposed individuals.
- cov: np.array( )
- covariance matrix for all the estimated parameters.
- S0: np.array(M,)
- Estimate initial number of susceptables.
- E0: np.array(M,)
- Estimate initial number of exposed.
- Ia0: np.array(M,)
- Estimate initial number of asymptomatic infectives.
- Is0: np.array(M,)
- Estimate initial number of symptomatic infectives.
- cov_init : np.array((3*M, 3*M)) :
- Covariance matrix for the initial state.
- M (int) – Number of compartments of individual for each class. I.e len(contactMatrix)
- Ni (np.array(4*M, )) – Initial number in each compartment and class
-
simulate()¶
-
simulate() Parameters: - contactMatrix (python function(t), optional) – The social contact matrix C_{ij} denotes the average number of contacts made per day by an individual in class i with an individual in class j The default is None.
- Tf (float, optional) – Final time of integrator. The default is 100.
- Nf (Int, optional) – Number of time points to evaluate.The default is 101,
- Ns (int, optional) – Number of samples of parameters to take. The default is 1000.
- nc (int, optional) –
- epsilon (np.float64, optional) – Acceptable error in leap. The default is 0.03.
- tau_update_frequency (int, optional) –
- verbose (bool, optional) – Verbosity of output. The default is False.
- Ti (float, optional) – Start time of integrator. The default is 0.
- method (str, optional) – Pyross integrator to use. The default is “deterministic”.
- events (list of python functions, optional) – List of events that the current state can satisfy to change behaviour of the contact matrix. Event occurs when the value of the function changes sign. Event.direction determines which direction triggers the event, takign values {+1,-1}. The default is [].
- contactMatricies (list of python functions) – New contact matrix after the corresponding event occurs The default is [].
- events_repeat (bool, optional) – Wheither events is periodic in time. The default is false.
- events_subsequent (bool, optional) – TODO
Returns: out_dict –
- Dictionary containing the following keys:
- X: list
List of resultant trajectories
- t: list
List of times at which X is evaluated.
- X_mean : list
Mean trajectory of X
- X_std : list
Standard devation of trajectories of X at each time point.
<init params> : Initial parameters passed at object instantiation. sample_parameters : list of parameters sampled to make trajectories. sample_inits : List of initial state vectors tried.
Return type: dict
- parameters (dict) –
SEAIRQ¶
-
class
pyross.forecast.SEAIRQ¶ Susceptible, Exposed, Infected, Removed (SEIR) Ia: asymptomatic Is: symptomatic A: Asymptomatic and infectious :param parameters:
- Contains the following keys:
- alpha: float
- Estimate mean value of fraction of infected who are asymptomatic.
- beta: float
- Estimate mean value of rate of spread of infection.
- gIa: float
- Estimate mean value of rate of removal from asymptomatic individuals.
- gIs: float
- Estimate mean value of rate of removal from symptomatic individuals.
- fsa: float
- fraction by which symptomatic individuals do not self-isolate.
- gE: float
- Estimated mean value of rate of removal from exposed individuals.
- gA: float
- Estimated mean value of rate of removal from activated individuals.
- cov: np.array( )
- covariance matrix for all the estimated parameters.
- tE : float
- testing rate and contact tracing of exposeds
- tA : float
- testing rate and contact tracing of activateds
- tIa: float
- testing rate and contact tracing of asymptomatics
- tIs: float
- testing rate and contact tracing of symptomatics
Parameters: - M (int) – Number of compartments of individual for each class. I.e len(contactMatrix)
- Ni (np.array(4*M, )) – Initial number in each compartment and class
-
simulate()¶
-
simulate() Parameters: - S0 (np.array) – Initial number of susceptables.
- E0 (np.array) – Initial number of exposeds.
- A0 (np.array) – Initial number of activateds.
- Ia0 (np.array) – Initial number of asymptomatic infectives.
- Is0 (np.array) – Initial number of symptomatic infectives.
- Q0 (np.array) – Initial number of quarantineds.
- contactMatrix (python function(t), optional) – The social contact matrix C_{ij} denotes the average number of contacts made per day by an individual in class i with an individual in class j The default is None.
- Tf (float, optional) – Final time of integrator. The default is 100.
- Nf (Int, optional) – Number of time points to evaluate.The default is 101,
- Ns (int, optional) – Number of samples of parameters to take. The default is 1000.
- nc (int, optional) –
- epsilon (np.float64, optional) – Acceptable error in leap. The default is 0.03.
- tau_update_frequency (int, optional) –
- verbose (bool, optional) – Verbosity of output. The default is False.
- Ti (float, optional) – Start time of integrator. The default is 0.
- method (str, optional) – Pyross integrator to use. The default is “deterministic”.
- events (list of python functions, optional) – List of events that the current state can satisfy to change behaviour of the contact matrix. Event occurs when the value of the function changes sign. Event.direction determines which direction triggers the event, takign values {+1,-1}. The default is [].
- contactMatricies (list of python functions) – New contact matrix after the corresponding event occurs The default is [].
- events_repeat (bool, optional) – Wheither events is periodic in time. The default is false.
- events_subsequent (bool, optional) – TODO
Returns: out_dict –
- Dictionary containing the following keys:
- X: list
List of resultant trajectories
- t: list
List of times at which X is evaluated.
- X_mean : list
Mean trajectory of X
- X_std : list
Standard devation of trajectories of X at each time point.
<init params> : Initial parameters passed at object instantiation. sample_parameters : list of parameters sampled to make trajectories.
Return type: dict
SEAIRQ_latent¶
-
class
pyross.forecast.SEAIRQ_latent¶ Susceptible, Exposed, Infected, Removed (SEIR) Ia: asymptomatic Is: symptomatic A: Asymptomatic and infectious
Latent inference class to be used when observed data is incomplete. :param parameters:
- Contains the following keys:
- alpha: float
- Estimate mean value of fraction of infected who are asymptomatic.
- beta: float
- Estimate mean value of rate of spread of infection.
- gIa: float
- Estimate mean value of rate of removal from asymptomatic individuals.
- gIs: float
- Estimate mean value of rate of removal from symptomatic individuals.
- fsa: float
- fraction by which symptomatic individuals do not self-isolate.
- gE: float
- Estimated mean value of rate of removal from exposed individuals.
- gA: float
- Estimated mean value of rate of removal from activated individuals.
- cov: np.array( )
- covariance matrix for all the estimated parameters.
- tE : float
- testing rate and contact tracing of exposeds
- tA : float
- testing rate and contact tracing of activateds
- tIa: float
- testing rate and contact tracing of asymptomatics
- tIs: float
- testing rate and contact tracing of symptomatics
- S0: np.array(M,)
- Estimate initial number of susceptables.
- E0: np.array(M,)
- Estimate initial number of exposed.
- A0: np.array(M,)
- Estimate initial number of activated.
- Ia0: np.array(M,)
- Estimate initial number of asymptomatic infectives.
- Is0: np.array(M,)
- Estimate initial number of symptomatic infectives.
- Q0: np.array(M,)
- Estimate initial number of quarantined.
- cov_init : np.array((3*M, 3*M)) :
- Covariance matrix for the initial state.
Parameters: - M (int) – Number of compartments of individual for each class. I.e len(contactMatrix)
- Ni (np.array(4*M, )) – Initial number in each compartment and class
-
simulate()¶
-
simulate() Parameters: - contactMatrix (python function(t), optional) – The social contact matrix C_{ij} denotes the average number of contacts made per day by an individual in class i with an individual in class j The default is None.
- Tf (float, optional) – Final time of integrator. The default is 100.
- Nf (Int, optional) – Number of time points to evaluate.The default is 101,
- Ns (int, optional) – Number of samples of parameters to take. The default is 1000.
- nc (int, optional) –
- epsilon (np.float64, optional) – Acceptable error in leap. The default is 0.03.
- tau_update_frequency (int, optional) –
- verbose (bool, optional) – Verbosity of output. The default is False.
- Ti (float, optional) – Start time of integrator. The default is 0.
- method (str, optional) – Pyross integrator to use. The default is “deterministic”.
- events (list of python functions, optional) – List of events that the current state can satisfy to change behaviour of the contact matrix. Event occurs when the value of the function changes sign. Event.direction determines which direction triggers the event, takign values {+1,-1}. The default is [].
- contactMatricies (list of python functions) – New contact matrix after the corresponding event occurs The default is [].
- events_repeat (bool, optional) – Wheither events is periodic in time. The default is false.
- events_subsequent (bool, optional) – TODO
Returns: out_dict –
- Dictionary containing the following keys:
- X: list
List of resultant trajectories
- t: list
List of times at which X is evaluated.
- X_mean : list
Mean trajectory of X
- X_std : list
Standard devation of trajectories of X at each time point.
<init params> : Initial parameters passed at object instantiation. sample_parameters : list of parameters sampled to make trajectories. sample_inits : List of initial state vectors tried.
Return type: dict