SISe: Create a SISe model

In SimInf: A Framework for Data-Driven Stochastic Disease Spread Simulations

Create a SISe model

Description

Create an ‘SISe’ model to be used by the simulation framework.

Usage

SISe(
  u0,
  tspan,
  events = NULL,
  phi = NULL,
  upsilon = NULL,
  gamma = NULL,
  alpha = NULL,
  beta_t1 = NULL,
  beta_t2 = NULL,
  beta_t3 = NULL,
  beta_t4 = NULL,
  end_t1 = NULL,
  end_t2 = NULL,
  end_t3 = NULL,
  end_t4 = NULL,
  epsilon = NULL
)

Arguments

u0	A data.frame with the initial state in each node (see ‘Details’).
tspan	A vector (length >= 1) of increasing time points where the state of each node is to be returned. Can be either an integer or a Date vector. A Date vector is coerced to a numeric vector as days, where tspan[1] becomes the day of the year of the first year of tspan. The dates are added as names to the numeric vector.
events	a data.frame with the scheduled events, see SimInf_model.
phi	A numeric vector with the initial environmental infectious pressure in each node. Will be repeated to the length of nrow(u0). Default is NULL which gives 0 in each node.
upsilon	Indirect transmission rate of the environmental infectious pressure
gamma	The recovery rate from infected to susceptible
alpha	Shed rate from infected individuals
beta_t1	The decay of the environmental infectious pressure in interval 1.
beta_t2	The decay of the environmental infectious pressure in interval 2.
beta_t3	The decay of the environmental infectious pressure in interval 3.
beta_t4	The decay of the environmental infectious pressure in interval 4.
end_t1	vector with the non-inclusive day of the year that ends interval 1 in each node. Will be repeated to the length of nrow(u0).
end_t2	vector with the non-inclusive day of the year that ends interval 2 in each node. Will be repeated to the length of nrow(u0).
end_t3	vector with the non-inclusive day of the year that ends interval 3 in each node. Will be repeated to the length of nrow(u0).
end_t4	vector with the non-inclusive day of the year that ends interval 4 in each node. Will be repeated to the length of nrow(u0).
epsilon	The background environmental infectious pressure

Details

The ‘SISe’ model contains two compartments; number of susceptible (S) and number of infectious (I). Additionally, it contains an environmental compartment to model shedding of a pathogen to the environment. Consequently, the model has two state transitions,

S -- upsilon phi S --> I

I -- gamma I --> S

where the transition rate per unit of time from susceptible to infected is proportional to the concentration of the environmental contamination phi in each node. Moreover, the transition rate from infected to susceptible is the recovery rate γ, measured per individual and per unit of time. Finally, the environmental infectious pressure in each node is evolved by,

dphi(t) / dt = alpha I(t) / N(t) - beta(t) phi(t) + epsilon

where α is the average shedding rate of the pathogen to the environment per infected individual and N = S + I the size of the node. The seasonal decay and removal of the pathogen is captured by β(t). It is also possible to include a small background infectious pressure ε to allow for other indirect sources of environmental contamination. The environmental infectious pressure phi(t) in each node is evolved each time unit by the Euler forward method. The value of phi(t) is saved at the time-points specified in tspan.

The argument u0 must be a data.frame with one row for each node with the following columns:

S

The number of sucsceptible in each node

I

The number of infected in each node

Value

SISe

Beta

The time dependent beta is divided into four intervals of the year

where 0 <= day < 365

Case 1: END_1 < END_2 < END_3 < END_4
INTERVAL_1 INTERVAL_2     INTERVAL_3     INTERVAL_4     INTERVAL_1
[0, END_1) [END_1, END_2) [END_2, END_3) [END_3, END_4) [END_4, 365)

Case 2: END_3 < END_4 < END_1 < END_2
INTERVAL_3 INTERVAL_4     INTERVAL_1     INTERVAL_2     INTERVAL_3
[0, END_3) [END_3, END_4) [END_4, END_1) [END_1, END_2) [END_2, 365)

Case 3: END_4 < END_1 < END_2 < END_3
INTERVAL_4 INTERVAL_1     INTERVAL_2     INTERVAL_3     INTERVAL_4
[0, END_4) [END_4, END_1) [END_1, END_2) [END_2, END_3) [END_3, 365)

SimInf documentation built on Jan. 23, 2023, 5:43 p.m.