Create an SISe model

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

Usage

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
)

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.

If integer: Represents the specific time points (e.g., days, hours) at which to record the state.
If Date: Coerced to a numeric vector representing the day of the year (1–366) relative to the first date in the vector. The original Date objects are preserved as names for the numeric vector, facilitating time-series plotting.

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

Indirect transmission rate of the environmental infectious pressure

gamma

A numeric vector with the recovery rate from infected to susceptible. Each node can have a different gamma value. The vector must have length 1 or nrow(u0). If the vector has length 1 but the model contains more nodes, the value is repeated for all nodes.

alpha

Shedding rate of the pathogen to the environment per infected individual.

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

Value

SISe

Details

The SISe model contains two compartments: Susceptible ($S$) and Infected ($I$). Additionally, it includes a continuous environmental compartment ($\varphi$) to model the shedding of a pathogen to the environment.

The model is defined by two state transitions:

$$S \stackrel{\upsilon \varphi S}{\longrightarrow} I$$ $$I \stackrel{\gamma I}{\longrightarrow} S$$

where the transition rate from susceptible to infected is proportional to the environmental contamination $\varphi$ and the transmission rate $\upsilon$. The recovery rate $\gamma$ moves individuals from infected back to susceptible.

The environmental infectious pressure $\varphi(t)$ in each node evolves according to:

$$\frac{d\varphi(t)}{dt} = \frac{\alpha I(t)}{N(t)} - \beta(t) \varphi(t) + \epsilon$$

where:

$\alpha$ is the shedding rate per infected individual.
$N(t) = S + I$ is the total population size in the node.
$\beta(t)$ is the seasonal decay/removal rate, which varies throughout the year.
$\epsilon$ is the background infectious pressure.

The environmental pressure is evolved using the Euler forward method and saved at time points in tspan.

Seasonal Decay ($\beta(t)$): The decay rate $\beta(t)$ is piecewise constant, defined by four intervals determined by the parameters end_t1, end_t2, end_t3, and end_t4 (days of the year, where 0 <= day < 365). The year is divided into four intervals based on the sorted order of these endpoints. The interval that wraps around the year boundary (from the last endpoint to day 365, then from day 0 to the first endpoint) receives the same rate as the interval preceding the first endpoint. Three orderings are supported:

Case 1: end_t1 < end_t2 < end_t3 < end_t4

Interval 1: [0, end_t1) with rate beta_t1
Interval 2: [end_t1, end_t2) with rate beta_t2
Interval 3: [end_t2, end_t3) with rate beta_t3
Interval 4: [end_t3, end_t4) with rate beta_t4
Interval 1 (wrap-around): [end_t4, 365) with rate beta_t1

Case 2: end_t3 < end_t4 < end_t1 < end_t2

Interval 3: [0, end_t3) with rate beta_t3
Interval 4: [end_t3, end_t4) with rate beta_t4
Interval 1: [end_t4, end_t1) with rate beta_t1
Interval 2: [end_t1, end_t2) with rate beta_t2
Interval 3 (wrap-around): [end_t2, 365) with rate beta_t3

Case 3: end_t4 < end_t1 < end_t2 < end_t3

Interval 4: [0, end_t4) with rate beta_t4
Interval 1: [end_t4, end_t1) with rate beta_t1
Interval 2: [end_t1, end_t2) with rate beta_t2
Interval 3: [end_t2, end_t3) with rate beta_t3
Interval 4 (wrap-around): [end_t3, 365) with rate beta_t4

These different orderings allow the model to handle seasonal patterns where, for example, a winter peak crosses the year boundary.

The argument u0 must be a data.frame with one row for each node with the following columns:

S: The number of susceptible in each node
I: The number of infected in each node

Usage

Arguments

Value

Details

See also