epipylib.model package

The model package is a collection of epidemic models.

SIR

The (S)usceptible (I)nfected (R)ecovered Model.

epipylib.model.sir.init_model(N, y0)

Initialize the SIR model.

Parameters:
  • y0 (int) – Infected rate at initial time step.
  • N (int) – Population
Returns:

Model at initial time step

Return type:

tuple(int, int, int)

epipylib.model.sir.simple(y, x, N, beta, gamma)

Defines the SIR simple model.

Parameters:
  • y (array) – Individuals at time step x
  • x (array) – Time step
  • N (int) – Population
  • beta (float) – The parameter controlling how often a susceptible-infected contact results in a new infection.
  • gamma (float) – The rate an infected recovers and moves into the resistant phase.
Returns:

S, I, R at time step n

Return type:

tuple(int/float, int/float, int/float)

epipylib.model.sir.vaccine(y, x, N, beta, gamma, nu)

Defines the SIR vaccine model.

Parameters:
  • y (array) – Individuals at time step x
  • x (array) – Time step
  • N (int) – Population
  • beta (float) – The parameter controlling how often a susceptible-infected contact results in a new infection.
  • gamma (float) – The rate an infected recovers and moves into the resistant phase.
  • nu (float) – The rate at which susceptible become vaccinated.
Returns:

S, I, R at time step n

Return type:

tuple(int/float, int/float, int/float)

epipylib.model.sir.wbad(y, x, N, beta, gamma, mu)

Defines the SIR with births and deaths model.

Parameters:
  • y (array) – Individuals at time step x
  • x (array) – Time step
  • N (int) – Population
  • beta (float) – The parameter controlling how often a susceptible-infected contact results in a new infection.
  • gamma (float) – The rate an infected recovers and moves into the resistant phase.
  • mu (float) – The parameter represents the average death rate
Returns:

S, I, R at time step n

Return type:

tuple(int/float, int/float, int/float)

SIRS

The (S)usceptible (I)nfected (R)ecovered (S)usceptible Model.

epipylib.model.sirs.init_model(N, y0)

Initialize the SIRS model.

Parameters:
  • y0 (int) – Infected rate at initial time step.
  • N (int) – Population
Returns:

Model at initial time step

Return type:

tuple(int, int, int)

epipylib.model.sirs.simple(y, x, N, beta, gamma, mu)

Defines the SIRS simple model.

Parameters:
  • y (array) – Individuals at time step x
  • x (array) – Time step
  • N (int) – Population
  • beta (float) – The parameter controlling how often a susceptible-infected contact results in a new infection.
  • gamma (float) – The rate an infected recovers and moves into the resistant phase.
  • mu (float) – The parameter represents the average death rate
Returns:

S, I, R at time step n

Return type:

tuple(int/float, int/float, int/float)

epipylib.model.sirs.wbad(y, x, N, beta, gamma, mu, f)

Defines the SIRS with births and deaths Model

Parameters:
  • y (array) – Individuals at time step x
  • x (array) – Time step
  • N (int) – Population
  • beta (float) – The parameter controlling how often a susceptible-infected contact results in a new infection.
  • gamma (float) – The rate an infected recovers and moves into the resistant phase.
  • mu (float) – The parameter represents the average death rate
  • f (float) – The parameter represents the average loss of immunity rate of recovered individuals
Returns:

S, I, R at time step n

Return type:

tuple(int/float, int/float, int/float)

SEIR

The (S)usceptible (E)xposed (I)nfected (R)ecovered Model.

epipylib.model.seir.init_model(N, y0)

Initialize the SEIR model.

Parameters:
  • y0 (int) – Infected rate at initial time step.
  • N (int) – Population
Returns:

Model at initial time step

Return type:

tuple(int, int, int)

epipylib.model.seir.simple(y, x, N, beta, gamma, sigma, mu)

Defines the SEIR simple model.

Parameters:
  • y (array) – Individuals at time step x
  • x (array) – Time step
  • N (int) – Population
  • beta (float) – The parameter controlling how often a susceptible-infected contact results in a new infection.
  • gamma (float) – The rate an infected recovers and moves into the resistant phase.
  • sigma (float) – The rate at which an exposed person becomes infective.
  • mu (float) – The parameter represents the average death rate
Returns:

S, E, I, R at time step n

Return type:

tuple(int/float, int/float, int/float)