Warning

Important: This is the documentation of code no longer in active development. This is the link to the current docs: covid19-inference

Models

covid19_inference.SIR_with_change_points(new_cases_obs, change_points_list, date_begin_simulation, num_days_sim, diff_data_sim, N, priors_dict=None, weekends_modulated=False, weekend_modulation_type='step')[source]
Parameters:
  • new_cases_obs (list or array) – Timeseries (day over day) of newly reported cases (not the total number)
  • change_points_list (list of dicts) –

    List of dictionaries, each corresponding to one change point.

    Each dict can have the following key-value pairs. If a pair is not provided, the respective default is used.

    • pr_mean_date_begin_transient : datetime.datetime, NO default
    • pr_median_lambda : number, same as default priors, below
    • pr_sigma_lambda : number, same as default priors, below
    • pr_sigma_date_begin_transient : number, 3
    • pr_median_transient_len : number, 3
    • pr_sigma_transient_len : number, 0.3
  • date_begin_simulation (datetime.datetime) – The begin of the simulation data
  • num_days_sim (integer) – Number of days to forecast into the future
  • diff_data_sim (integer) – Number of days that the simulation-begin predates the first data point in new_cases_obs. This is necessary so the model can fit the reporting delay. Set this parameter to a value larger than what you expect to find for the reporting delay.
  • N (number) – The population size. For Germany, we used 83e6
  • priors_dict (dict) –

    Dictionary of the prior assumptions

    Possible key-value pairs (and default values) are:
    • pr_beta_I_begin : number, default = 100
    • pr_median_lambda_0 : number, default = 0.4
    • pr_sigma_lambda_0 : number, default = 0.5
    • pr_median_mu : number, default = 1/8
    • pr_sigma_mu : number, default = 0.2
    • pr_median_delay : number, default = 8
    • pr_sigma_delay : number, default = 0.2
    • pr_beta_sigma_obs : number, default = 10
    • week_end_days : tuple, default = (6,7)
    • pr_mean_weekend_factor : number, default = 0.7
    • pr_sigma_weekend_factor :number, default = 0.17
  • weekends_modulated (bool) – Whether to add the prior that cases are less reported on week ends. Multiplies the new cases numbers on weekends by a number between 0 and 1, given by a prior beta distribution. The beta distribution is parametrised by pr_mean_weekend_factor and pr_sigma_weekend_factor
  • weekend_modulation_type ('step' or 'abs_sine':) – whether the weekends are modulated by a step function, which only multiplies the days given by week_end_days by the week_end_factor, or whether the whole week is modulated by an abs(sin(x)) function, with an offset with flat prior.
Returns:

pymc3.Model – Returns an instance of pymc3 model with the change points
covid19_inference.SEIR_with_extensions(new_cases_obs, change_points_list, date_begin_simulation, num_days_sim, diff_data_sim, N, priors_dict=None, with_random_walk=True, weekends_modulated=False, weekend_modulation_type='step')[source]
This model includes 3 extensions to the SIR_model_with_change_points:
  1. The SIR model now includes a incubation period during which infected people are not infectious, in the spirit of an SEIR model. In contrast to the SEIR model, the length of incubation period is not exponentially distributed but has a lognormal distribution.
  2. People that are infectious are observed with a delay that is now lognormal distributed. In the SIR_model_with_change_points we assume a fixed delay between infection and observation.
  3. lambda_t has an additive term given by a Gaussian random walk. Thereby, we want to fit any deviation in lambda_t that is not captured by the change points. If the change points are wisely chosen, and the rest of the model captures the dynamics well, one would expect that the amplitude of the random walk is small. In this case, the posterior distribution of sigma_random_walk will be small.
Parameters:
  • new_cases_obs (list or array) – Timeseries (day over day) of newly reported cases (not the total number)
  • change_points_list (list of dicts) –

    List of dictionaries, each corresponding to one change point

    Each dict can have the following key-value pairs. If a pair is not provided, the respective default is used.

    • pr_mean_date_begin_transient: datetime.datetime, NO default
    • pr_median_lambda: float, default: 0.4
    • pr_sigma_lambda: float, default: 0.5
    • pr_sigma_begin_transient: float, default: 3
    • pr_median_transient_len: float, default: 3
    • pr_sigma_transient_len: float, default: 0.3
  • date_begin_simulation (datetime.datetime.) – The begin of the simulation data
  • num_days_sim (integer) – Number of days to forecast into the future
  • diff_data_sim (integer) – Number of days that the simulation-begin predates the first data point in new_cases_obs. This is necessary so the model can fit the reporting delay. Set this parameter to a value larger than what you expect to find for the reporting delay.
  • N (number) – The population size. For Germany, we used 83e6
  • priors_dict (dict) –

    Dictionary of the prior assumptions

    Possible key-value pairs (and default values) are:
    • pr_beta_I_begin : number, default: 100
    • pr_beta_E_begin_scale : number, default: 10
    • pr_median_lambda_0 : number, default: 2
    • pr_sigma_lambda_0 : number, default: 0.7
    • pr_median_mu : number, default: 1/3
    • pr_sigma_mu : number, default: 0.3
    • pr_median_delay : number, default: 5
    • pr_sigma_delay : number, default: 0.2
    • scale_delay : number, default: 0.3
    • pr_beta_sigma_obs : number, default: 10
    • pr_sigma_random_walk : number, default: 0.05
    • pr_mean_median_incubation : number, default: 5
      https://www.ncbi.nlm.nih.gov/pubmed/32150748 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7014672/ about -1 day compared to the sources day because persons likely become infectious before.
    • pr_sigma_median_incubation : number, default: 1
      The error from the sources above is smaller, but as the -1 day is a very rough estimate, we take here a larger error.
    • sigma_incubation : number, default: 0.418
      https://www.ncbi.nlm.nih.gov/pubmed/32150748
  • with_random_walk (boolean) – whether to add a Gaussian walk to lambda_t. computationolly expensive
Returns:

pymc3.Model – Returns an instance of pymc3 model with the change points