SISe3: Create a 'SISe3' model

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

Create a SISe3 model

Description

Create a SISe3 model to be used by the simulation framework.

Usage

SISe3(
  u0,
  tspan,
  events = NULL,
  phi = NULL,
  upsilon_1 = NULL,
  upsilon_2 = NULL,
  upsilon_3 = NULL,
  gamma_1 = NULL,
  gamma_2 = NULL,
  gamma_3 = 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, i.e., the number of individuals in each compartment in each node when the simulation starts (see ‘Details’). The parameter u0 can also be an object that can be coerced to a data.frame, e.g., a named numeric vector will be coerced to a one row data.frame.
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_1	Indirect transmission rate of the environmental infectious pressure in age category 1
upsilon_2	Indirect transmission rate of the environmental infectious pressure in age category 2
upsilon_3	Indirect transmission rate of the environmental infectious pressure in age category 3
gamma_1	The recovery rate from infected to susceptible for age category 1
gamma_2	The recovery rate from infected to susceptible for age category 2
gamma_3	The recovery rate from infected to susceptible for age category 3
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 SISe3 model contains two compartments in three age categories; number of susceptible (S_1, S_2, S_3) and number of infectious (I_1, I_2, I_3). Additionally, it contains an environmental compartment to model shedding of a pathogen to the environment. Consequently, the model has six state transitions,

S_1 \stackrel{\upsilon_1 \varphi S_1}{\longrightarrow} I_1

I_1 \stackrel{\gamma_1 I_1}{\longrightarrow} S_1

S_2 \stackrel{\upsilon_2 \varphi S_2}{\longrightarrow} I_2

I_2 \stackrel{\gamma_2 I_2}{\longrightarrow} S_2

S_3 \stackrel{\upsilon_3 \varphi S_3}{\longrightarrow} I_3

I_3 \stackrel{\gamma_3 I_3}{\longrightarrow} S_3

where the transition rate per unit of time from susceptible to infected is proportional to the concentration of the environmental contamination \varphi in each node. Moreover, the transition rate from infected to susceptible is the recovery rate \gamma_1, \gamma_2, \gamma_3, measured per individual and per unit of time. Finally, the environmental infectious pressure in each node is evolved by,

\frac{d\varphi(t)}{dt} = \frac{\alpha \left(I_1(t) + I_2(t) + I_3(t)\right)}{N(t)} - \beta(t) \varphi(t) + \epsilon

where \alpha is the average shedding rate of the pathogen to the environment per infected individual and N = S_1 + S_2 + S_3 + I_1 + I_2 + I_3 the size of the node. The seasonal decay and removal of the pathogen is captured by \beta(t). It is also possible to include a small background infectious pressure \epsilon to allow for other indirect sources of environmental contamination. The environmental infectious pressure \varphi(t) in each node is evolved each time unit by the Euler forward method. The value of \varphi(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_1

The number of sucsceptible in age category 1

I_1

The number of infected in age category 1

S_2

The number of sucsceptible in age category 2

I_2

The number of infected in age category 2

S_3

The number of sucsceptible in age category 3

I_3

The number of infected in age category 3

Value

SISe3

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 June 22, 2024, 9:27 a.m.