SISe3_sp {SimInf}

Create an SISe3_sp model

Description

Create an SISe3_sp model to be used by the simulation framework.

Usage

SISe3_sp(
  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,
  distance = NULL,
  coupling = 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).

distance

The distance matrix between neighboring nodes

coupling

The coupling between neighboring nodes

Details

The SISe3_sp 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. Moreover, it also includes a spatial coupling of the environmental contamination among proximal nodes to capture between-node spread unrelated to moving infected individuals. 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_i(t)}{dt} = \frac{\alpha \left(I_{i,1}(t) + I_{i,2}(t) + I_{i,3}(t)\right)}{N_i(t)} + \sum_k{\frac{\varphi_k(t) N_k(t) - \varphi_i(t) N_i(t)}{N_i(t)} \cdot \frac{D}{d_{ik}}} - \beta(t) \varphi_i(t)

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. Next comes the spatial coupling among proximal nodes, where D is the rate of the local spread and d_{ik} the distance between holdings i and k. The seasonal decay and removal of the pathogen is captured by \beta(t). 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_sp

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)