Create an ‘SISe’ model to be used by the simulation framework.
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
)SISe
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.
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.
a data.frame with the scheduled events, see
SimInf_model.
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.
Indirect transmission rate of the environmental infectious pressure
The recovery rate from infected to susceptible
Shed rate from infected individuals
The decay of the environmental infectious pressure in interval 1.
The decay of the environmental infectious pressure in interval 2.
The decay of the environmental infectious pressure in interval 3.
The decay of the environmental infectious pressure in interval 4.
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).
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).
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).
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).
The background environmental infectious pressure
The time dependent beta is divided into four intervals of the year
where 0 <= day < 365Case 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)
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,
$$S \stackrel{\upsilon \varphi S}{\longrightarrow} I$$
$$I \stackrel{\gamma I}{\longrightarrow} S$$
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 \(\gamma\), measured per individual and per unit of time. Finally, the environmental infectious pressure in each node is evolved by,
$$\frac{d\varphi(t)}{dt} = \frac{\alpha I(t)}{N(t)} - \beta(t) \varphi(t) + \epsilon$$
where \(\alpha\) is the average shedding rate of the pathogen to
the environment per infected individual and \(N = S + I\) 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:
The number of sucsceptible in each node
The number of infected in each node