SISe3_sp: Create an 'SISe3_sp' model
In stewid/SimInf: A Framework for Data-Driven Stochastic Disease Spread Simulations
SISe3_sp R Documentation
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
(see ‘Details’). The parameter u0 can also be an
object that can be coerced to a data.frame, for
example, 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)
stewid/SimInf documentation built on April 21, 2024, 8:46 a.m.
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| SISe3_sp | R Documentation |
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 |
tspan |
A vector (length >= 1) of increasing time points
where the state of each node is to be returned. Can be either
an |
events |
a |
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)
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