SISe3_sp | R Documentation |
SISe3_sp
modelCreate an SISe3_sp
model to be used by the simulation
framework.
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 )
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 |
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 -- upsilon_1 phi S_1 --> I_1
I_1 -- gamma_1 I_1 --> S_1
S_2 -- upsilon_2 phi S_2 --> I_2
I_2 -- gamma_2 I_2 --> S_2
S_3 -- upsilon_3 phi S_3 --> I_3
I_3 -- gamma_3 I_3 --> S_3
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_1, γ_2, γ_3, measured per individual and per unit of time. Finally, the environmental infectious pressure in each node is evolved by,
dphi(t)/dt= alpha (I_1+I_2+I_3)/N+ D*sum_k(phi_k*N_k-phi_i*N_i)/(d_ik*N_i)-beta*phi_i
where α 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 β(t). 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:
The number of sucsceptible in age category 1
The number of infected in age category 1
The number of sucsceptible in age category 2
The number of infected in age category 2
The number of sucsceptible in age category 3
The number of infected in age category 3
SISe3_sp
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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