Reference: Models

class pydemic.models.seirpp.NonMarkovianSEIRSimulationBase(total_population, age_distribution=1, *, r0=3.2, serial_dist=<GammaDistribution(shape=1.51, scale=2.64)>, mitigation=None, hetero_lambda=1.0, severity_profiles=None, seasonal_forcing_amp=0.2, peak_day=15)[source]

Main driver for non-Markovian simulations, used as a base class for SEIR++ variants.

The following arguments are required:

Parameters

total_population – The total size of the population.

The following keyword-only arguments are recognized:

Parameters

  • age_distribution – A numpy.ndarray specifying the relative fraction of the population in various age groups. Defaults to 1, i.e., no age grouping.

  • mitigation – A function of time specifying a multiplicative factor. Defaults to lambda t: 1.

  • r0 – The basic reproduction number.

  • serial_dist – The serial interval distribution, i.e., an instance of (a subclass of) DistributionBase).

  • hetero_lambda – The depletion coefficient that scales the effect changes in the susceptible population fraction have on infectivity. Defaults to 1.

  • seasonal_forcing_amp – The amplitude (i.e., maximum fractional change) in the force of infection due to seasonal effects.

  • peak_day – The day of the year at which seasonal forcing is greatest.

__call__(tspan, y0, dt=0.05)[source]
Parameters

  • tspan – A tuple specifying the initiala and final times (as pandas.Timestamp’s or as float’s specifying the number of days since Jan 1, 2020).

  • y0 – A dict with the initial values (as numpy.ndarray’s) for the 'infected' and 'susceptible' states.

  • dt – The timestep.

Returns

A SimulationResult with attributes t, the array of times of evaluation, and y, a dict of results where time proceeds along the first axis.

classmethod get_model_data(t, **kwargs)[source]

A wrapper to __init__() and __call__() for initializing and running a simulation from keyword arguments only (i.e., as used by LikelihoodEstimator.)

Parameters

t – A pandas.DatetimeIndex (or numpy.ndarray of times in days since 2020/1/1) of times at which to evaluate the solution.

The following keyword arguments are required:

Parameters

  • start_day – The day (relative to 2020/1/1) at which to begin the simulation—i.e., the day corresponding to the initial condition where initial_cases cases (evenly distributed over age_distribution) are introduced into the population.

  • total_population – The total size of the population.

  • initial_cases – The total numnber of initial cases.

  • age_distribution – A numpy.ndarray specifying the relative fraction of the population in various age groups.

In addition, a MitigationModel is created from passed keyword arguments via init_from_kwargs().

The following optional keyword arguments are also recognized:

Parameters

min_mitigation_spacing – The minimum number of days of separation between mitigation events. Defaults to 5.

All remaining keyword arguments are passed to __init__().

Raises

  • InvalidParametersError – if t specifies any days of evaluation which are not at least one day after start_day.

  • InvalidParametersError – if mitigation events are not ordered and separated by min_mitigation_spacing.

Returns

A pandas.DataFrame of simulation results.

class pydemic.models.SEIRPlusPlusSimulation(total_population, age_distribution=1, *, r0=3.2, serial_dist=<GammaDistribution(shape=1.51, scale=2.64)>, mitigation=None, hetero_lambda=1.0, severity_profiles=None, seasonal_forcing_amp=0.2, peak_day=15, ifr=None, incubation_dist=<GammaDistribution(shape=7.56, scale=0.727)>, p_symptomatic=1.0, p_positive=1.0, hospitalized_dist=<GammaDistribution(shape=2.64, scale=2.46)>, p_hospitalized=1.0, discharged_dist=<GammaDistribution(shape=2.25, scale=2.67)>, critical_dist=<GammaDistribution(shape=1, scale=2)>, p_critical=1.0, dead_dist=<GammaDistribution(shape=1, scale=7.5)>, p_dead=1.0, recovered_dist=<GammaDistribution(shape=1, scale=7.5)>, all_dead_dist=<GammaDistribution(shape=1, scale=2.5)>, all_dead_multiplier=1.0)[source]

SEIR++ model with unconnected infectivity loop. Readout topology is:

-> symptomatic
    -> hospitalized -> recovered
                    -> critical -> dead -> all_dead
                                -> hospitalized -> recovered

In addition to the arguments recognized by NonMarkovianSEIRSimulationBase, the following keyword-only arguments are recognized:

Parameters

  • age_distribution – A numpy.ndarray specifying the relative fraction of the population in various age groups.

  • ifr – The infection fatality ratio, i.e., the proportion of the infected population who eventually die. If not None, will rescale p_symptomatic to effect the passed value.

  • p_symptomatic – The distribution of the proportion of infected individuals who become symptomatic.

  • incubation_dist – The delay-time distribution for developing symptoms after being infected.

  • p_positive – The fraction of symptomatic individuals who are tested and test positive.

  • p_hospitalized – The distribution of the proportion of symptomatic individuals who enter the hospital.

  • hospitalized_dist – The delay-time distribution of entering the hospital after becoming symptomatic.

  • discharged_dist – The delay-time distribution of survivors being discharged after entering the hospital.

  • p_critical – The distribution of the proportion of hospitalized individuals who become critical.

  • critical_dist – The delay-time distribution of hospitalized individuals entering the ICU.

  • p_dead – The distribution of the proportion of ICU patients who die.

  • dead_dist – The delay-time distribution of ICU patients dying.

  • recovered_dist – The delay-time distribution of ICU patients recovering and returning to the general ward.

  • all_dead_multiplier – The ratio of total deaths to deaths occurring in the ICU.

  • all_dead_dist – The delay-time distribution between ICU deaths and all reported deaths.

Other utilities for modeling

class pydemic.distributions.DistributionBase[source]

Base class for distributions.

convolve_pdf(t, influx, prefactor=1, profile=None, method='fft', complement=False)[source]

Convolves an array influx with the PDF of the distribution.

Parameters

  • t – The times of evaluation.

  • influx – The array to be convolved, \(y\).

  • prefactor – A multiplicative prefactor, \(P\).

  • method – A str specifying whether to convolve by Fast Fourier Transform ('fft') or via direct covolution ('direct').

convolve_survival(t, influx, prefactor=1, method='fft')[source]

Convolves an array influx with the survival function of the distribution,

\[S(x) = 1 - \int \mathrm{d} x' \, f(x').\]
Parameters

  • t – The times of evaluation.

  • influx – The array to be convolved.

  • prefactor – A multiplicative prefactor.

  • method – A str specifying whether to convolve by Fast Fourier Transform ('fft') or via direct covolution ('direct').

class pydemic.GammaDistribution(mean=None, std=None, shape=None, scale=None)[source]

Implements functionality for the gamma distribution, with PDF

\[f(x) = \frac{1}{\Gamma(k) \theta^{k}} x^{k-1} e^{- x / \theta }\]

One can specify the distribution by its mean \(\mu\) and standard deviation \(\sigma\) or by the standard shape and scale parameters \(k\) and \(\theta\), which are related by

\[ \begin{align}\begin{aligned}k = \frac{\mu^2}{\sigma^2}\\\theta = \frac{\sigma^2}{\mu}.\end{aligned}\end{align} \]
Parameters

  • mean – The mean, \(\mu\).

  • std – The standard derviation, \(\sigma\).

  • shape – The shape, \(k\).

  • scale – The scale, \(\theta\).

Passed values for mean and std take precendece over those for shape and scale.

class pydemic.MitigationModel(t0, tf, t, factors, multiplier=None)[source]

An interface for creating (smooth, monotonic) piecewise linear functions. Subclasses scipy.interpolate.PchipInterpolator.

Constructs the interpolating function which takes the constant values factors[0] between t0 and t[0] and factors[-1] between t[-1] and tf.

Parameters

  • t0 – A float representing the first input value for interpolation.

  • tf – A float representing the last input value for interpolation.

  • t – A numpy.ndarray of interpolating nodes (between t0 and tf).

  • factors – A numpy.ndarray of function values to interpolate to at the nodes t.

classmethod init_from_kwargs(t0, tf, prefix='mitigation', **kwargs)[source]

A convenience constructor which collects values for t based on (sorted) keyword arguments beginning with mitigation_t with factors from those beginning with mitigation_factor.