covasim.utils module

Numerical utilities for running Covasim.

These include the viral load, transmissibility, and infection calculations at the heart of the integration loop.

sample(dist=None, par1=None, par2=None, size=None, **kwargs)

Draw a sample from the distribution specified by the input. The available distributions are:

• ‘uniform’ : uniform distribution from low=par1 to high=par2; mean is equal to (par1+par2)/2
• ‘normal’ : normal distribution with mean=par1 and std=par2
• ‘lognormal’ : lognormal distribution with mean=par1 and std=par2 (parameters are for the lognormal distribution, not the underlying normal distribution)
• ‘normal_pos’ : right-sided normal distribution (i.e. only positive values), with mean=par1 and std=par2 of the underlying normal distribution
• ‘normal_int’ : normal distribution with mean=par1 and std=par2, returns only integer values
• ‘lognormal_int’ : lognormal distribution with mean=par1 and std=par2, returns only integer values
• ‘poisson’ : Poisson distribution with rate=par1 (par2 is not used); mean and variance are equal to par1
• ‘neg_binomial’ : negative binomial distribution with mean=par1 and k=par2; converges to Poisson with k=∞

Parameters:

• dist (str) – the distribution to sample from
• par1 (float) – the “main” distribution parameter (e.g. mean)
• par2 (float) – the “secondary” distribution parameter (e.g. std)
• size (int) – the number of samples (default=1)
• kwargs (dict) – passed to individual sampling functions

Returns:

A length N array of samples

Examples:

cv.sample() # returns Unif(0,1)
cv.sample(dist='normal', par1=3, par2=0.5) # returns Normal(μ=3, σ=0.5)
cv.sample(dist='lognormal_int', par1=5, par2=3) # returns a lognormally distributed set of values with mean 5 and std 3

Notes

Lognormal distributions are parameterized with reference to the underlying normal distribution (see: https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.random.lognormal.html), but this function assumes the user wants to specify the mean and std of the lognormal distribution.

Negative binomial distributions are parameterized with reference to the mean and dispersion parameter k (see: https://en.wikipedia.org/wiki/Negative_binomial_distribution). The r parameter of the underlying distribution is then calculated from the desired mean and k. For a small mean (~1), a dispersion parameter of ∞ corresponds to the variance and standard deviation being equal to the mean (i.e., Poisson). For a large mean (e.g. >100), a dispersion parameter of 1 corresponds to the standard deviation being equal to the mean.

get_pdf(dist=None, par1=None, par2=None)

Return a probability density function for the specified distribution. This is used for example by test_num to retrieve the distribution of times from symptom-to-swab for testing. For example, for Washington State, these values are dist=’lognormal’, par1=10, par2=170.

set_seed(seed=None)

Reset the random seed – complicated because of Numba, which requires special syntax to reset the seed. This function also resets Python’s built-in random number generated.

Parameters:seed (int) – the random seed

n_binomial(prob, n)

Perform multiple binomial (Bernolli) trials

Parameters:

• prob (float) – probability of each trial succeeding
• n (int) – number of trials (size of array)

Returns:

Boolean array of which trials succeeded

Example:

outcomes = cv.n_binomial(0.5, 100) # Perform 100 coin-flips

binomial_filter(prob, arr)

Binomial “filter” – the same as n_binomial, except return the elements of arr that succeeded.

Parameters:

• prob (float) – probability of each trial succeeding
• arr (array) – the array to be filtered

Returns:

Subset of array for which trials succeeded

Example:

inds = cv.binomial_filter(0.5, np.arange(20)**2) # Return which values out of the (arbitrary) array passed the coin flip

binomial_arr(prob_arr)

Binomial (Bernoulli) trials each with different probabilities.

Parameters:prob_arr (array) – array of probabilities Returns:Boolean array of which trials on the input array succeeded

Example:

outcomes = cv.binomial_arr([0.1, 0.1, 0.2, 0.2, 0.8, 0.8]) # Perform 6 trials with different probabilities

n_multinomial(probs, n)

An array of multinomial trials.

Parameters:

• probs (array) – probability of each outcome, which usually should sum to 1
• n (int) – number of trials

Returns:

Array of integer outcomes

Example:

outcomes = cv.multinomial(np.ones(6)/6.0, 50)+1 # Return 50 die-rolls

poisson

A Poisson trial.

Parameters:rate (float) – the rate of the Poisson process

Example:

outcome = cv.poisson(100) # Single Poisson trial with mean 100

n_poisson

An array of Poisson trials.

Parameters:

• rate (float) – the rate of the Poisson process (mean)
• n (int) – number of trials

Example:

outcomes = cv.n_poisson(100, 20) # 20 Poisson trials with mean 100

n_neg_binomial(rate, dispersion, n, step=1)

An array of negative binomial trials. See cv.sample() for more explanation.

Parameters:

• rate (float) – the rate of the process (mean, same as Poisson)
• dispersion (float) – dispersion parameter; lower is more dispersion, i.e. 0 = infinite, ∞ = Poisson
• n (int) – number of trials
• step (float) – the step size to use if non-integer outputs are desired

Example:

outcomes = cv.n_neg_binomial(100, 1, 50) # 50 negative binomial trials with mean 100 and dispersion roughly equal to mean (large-mean limit)
outcomes = cv.n_neg_binomial(1, 100, 20) # 20 negative binomial trials with mean 1 and dispersion still roughly equal to mean (approximately Poisson)

choose

Choose a subset of items (e.g., people) without replacement.

Parameters:

• max_n (int) – the total number of items
• n (int) – the number of items to choose

Example:

choices = cv.choose(5, 2) # choose 2 out of 5 people with equal probability (without repeats)

choose_r

Choose a subset of items (e.g., people), with replacement.

Parameters:

• max_n (int) – the total number of items
• n (int) – the number of items to choose

Example:

choices = cv.choose_r(5, 10) # choose 10 out of 5 people with equal probability (with repeats)

choose_w(probs, n, unique=True)

Choose n items (e.g. people), each with a probability from the distribution probs.

Parameters:

• probs (array) – list of probabilities, should sum to 1
• n (int) – number of samples to choose
• unique (bool) – whether or not to ensure unique indices

Example:

choices = cv.choose_w([0.2, 0.5, 0.1, 0.1, 0.1], 2) # choose 2 out of 5 people with nonequal probability.

true(arr)

Returns the indices of the values of the array that are true: just an alias for arr.nonzero()[0].

Parameters:arr (array) – any array

Example:

inds = cv.true(np.array([1,0,0,1,1,0,1])) # Returns array([0, 3, 4, 6])

false(arr)

Returns the indices of the values of the array that are false.

Parameters:arr (array) – any array

Example:

inds = cv.false(np.array([1,0,0,1,1,0,1]))

defined(arr)

Returns the indices of the values of the array that are not-nan.

Parameters:arr (array) – any array

Example:

inds = cv.defined(np.array([1,np.nan,0,np.nan,1,0,1]))

undefined(arr)

Returns the indices of the values of the array that are not-nan.

Parameters:arr (array) – any array

Example:

inds = cv.defined(np.array([1,np.nan,0,np.nan,1,0,1]))

itrue(arr, inds)

Returns the indices that are true in the array – name is short for indices[true]

Parameters:

• arr (array) – a Boolean array, used as a filter
• inds (array) – any other array (usually, an array of indices) of the same size

Example:

inds = cv.itrue(np.array([True,False,True,True]), inds=np.array([5,22,47,93]))

ifalse(arr, inds)

Returns the indices that are true in the array – name is short for indices[false]

Parameters:

• arr (array) – a Boolean array, used as a filter
• inds (array) – any other array (usually, an array of indices) of the same size

Example:

inds = cv.ifalse(np.array([True,False,True,True]), inds=np.array([5,22,47,93]))

idefined(arr, inds)

Returns the indices that are defined in the array – name is short for indices[defined]

Parameters:

• arr (array) – any array, used as a filter
• inds (array) – any other array (usually, an array of indices) of the same size

Example:

inds = cv.idefined(np.array([3,np.nan,np.nan,4]), inds=np.array([5,22,47,93]))

iundefined(arr, inds)

Returns the indices that are undefined in the array – name is short for indices[undefined]

Parameters:

• arr (array) – any array, used as a filter
• inds (array) – any other array (usually, an array of indices) of the same size

Example:

inds = cv.iundefined(np.array([3,np.nan,np.nan,4]), inds=np.array([5,22,47,93]))

itruei(arr, inds)

Returns the indices that are true in the array – name is short for indices[true[indices]]

Parameters:

• arr (array) – a Boolean array, used as a filter
• inds (array) – an array of indices for the original array

Example:

inds = cv.itruei(np.array([True,False,True,True,False,False,True,False]), inds=np.array([0,1,3,5]))

ifalsei(arr, inds)

Returns the indices that are false in the array – name is short for indices[false[indices]]

Parameters:

• arr (array) – a Boolean array, used as a filter
• inds (array) – an array of indices for the original array

Example:

inds = cv.ifalsei(np.array([True,False,True,True,False,False,True,False]), inds=np.array([0,1,3,5]))

idefinedi(arr, inds)

Returns the indices that are defined in the array – name is short for indices[defined[indices]]

Parameters:

• arr (array) – any array, used as a filter
• inds (array) – an array of indices for the original array

Example:

inds = cv.idefinedi(np.array([4,np.nan,0,np.nan,np.nan,4,7,4,np.nan]), inds=np.array([0,1,3,5]))

iundefinedi(arr, inds)

Returns the indices that are undefined in the array – name is short for indices[defined[indices]]

Parameters:

• arr (array) – any array, used as a filter
• inds (array) – an array of indices for the original array

Example:

inds = cv.iundefinedi(np.array([4,np.nan,0,np.nan,np.nan,4,7,4,np.nan]), inds=np.array([0,1,3,5]))