| epidata {EpiILM} | R Documentation |
Simulates epidemic for the specified model type and parameters
Description
This function allows the user to simulate epidemics under different models and scenarios
Usage
epidata (type, n, tmin = NULL, tmax, sus.par, trans.par = NULL, beta = NULL, spark = NULL,
Sformula = NULL, Tformula = NULL, x = NULL, y = NULL,
inftime = NULL, infperiod = NULL, contact = NULL)
Arguments
type |
Type of compartment framework, with the choice of "SI" for Susceptible-Infectious diseases and "SIR" for Susceptible-Infectious-Removed. |
n |
Population size |
tmin |
The time point at which simulation begins, default value is one. |
tmax |
The last time point of simulation. |
sus.par |
Susceptibility parameter (>0). |
trans.par |
Transmissibility parameter (>0). |
beta |
Spatial parameter(s) (>0) or network parameter (s) (>0) if contact network is used. |
spark |
Sparks parameter (>=0), representing infections unexplained by other parts of the model (eg. infections coming in from outside the observed population), default value is zero. |
Sformula |
An object of class formula. See formula. Individual-level covariate information associated with susceptibility can be passed through this argument. An expression of the form |
Tformula |
An object of class formula. See formula. Individual-level covariate information associated with transmissibility can be passed through this argument. An expression of the form |
x |
X coordinates of individuals. |
y |
Y coordinates of individuals. |
inftime |
Times at which individuals are infected to initialize epidemic simulation. |
infperiod |
Length of infectious period for each individual. |
contact |
A contact network matrix or an array of contact network matrices. |
Details
We consider following two individual level models:
Spatial model:
P(i,t) =1- \exp\{-\Omega_S(i) \sum_{j \in I(t)}{\Omega_T(j)d_{ij}^{-\beta}- \varepsilon}\}
Network model:
P(i,t) =1- \exp\{-\Omega_S(i) \sum_{j \in I(t)}{\Omega_T(j)(\beta_1 C^{(1)}_{ij}} + \dots + \beta_n C^{(n)}_{ij} )- \varepsilon\}
where P(i,t) is the probability that susceptible individual i is infected at time point t, becoming infectious at time t+1;
\Omega_S(i) is a susceptibility function which accommodates potential risk factors associated with susceptible individual i contracting the disease; \Omega_T(j) is a transmissibility function which accommodates potential risk factors associated with infectious individual j; \varepsilon is a sparks term which represents infections originating from outside the population being observed or some other unobserved infection mechanism.
The susceptibility function can incorporate any individual-level covariates of interest and \Omega_S(i) is treated as a linear function of the covariates, i.e., \Omega_S(i) = \alpha_0 + \alpha_1 X_1(i) + \alpha_2 X_2 (i) + \dots +
\alpha_{n_s} X_{n_s} (i), where X_1(i), \dots, X_{n_s} (i) denote n_scovariates associated with susceptible individual $i$, along with susceptibility parameters \alpha_0,\dots,\alpha_{n_s} >0. If the model does not contain any susceptibility covariates then \Omega_S(i) = \alpha_0 is used. In a similar way, the transmissibility function can incorporate any individual-level covariates of interest associated with infectious individual. \Omega_T(j) is also treated as a linear function of the covariates, but without the intercept term, i.e., \Omega_T(j) = \phi_1 X_1(j) + \phi_2 X_2 (j) + \dots + \phi_{n_t} X_{n_t} (j), where X_1(j), \dots, X_{n_t} (j) denote the n_t covariates associated with infectious individual j, along with transmissibility parameters \phi_1,\dots,\phi_{n_t} >0. If the model does not contain any transmissibility covariates then \Omega_T(j) = 1 is used.
Value
An object of class epidata is returned containing the following:
- type
Type of compartment framework, with the choice of "SI" for Susceptible-Infectious diseases and "SIR" for Susceptible-Infectious-Removed
- XYcoordinates
The XY-coordinates of individuals.
- contact
Contact network matrix.
- inftime
The infection times of individuals.
- remtime
The removal times of individuals when
type= “SIR”.
References
Deardon, R., Brooks, S. P., Grenfell, B. T., Keeling, M. J., Tildesley, M. J., Savill, N. J., Shaw, D. J., and Woolhouse, M. E. (2010). Inference for individual level models of infectious diseases in large populations. Statistica Sinica, 20, 239-261.
Deardon, R., Fang, X., and Kwong, G.P.S. (2014). Statistical modelling of spatio-temporal infectious disease transmission in analyzing and modeling Spatial and temporal dynamics of infectious diseases, (Ed: D. Chen, B. Moulin, J. Wu), John Wiley & Sons. Chapter 11.
See Also
plot.epidata, epimcmc, epilike, pred.epi.
Examples
## Example 1: spatial SI model
# generate 100 individuals
x <- runif(100, 0, 10)
y <- runif(100, 0, 10)
covariate <- runif(100, 0, 2)
out1 <- epidata(type = "SI",n = 100, Sformula = ~covariate, tmax = 15,
sus.par = c(0.1, 0.3), beta = 5.0, x = x, y = y)
# Plots of epidemic progression (optional)
plot(out1, plottype = "spatial")
plot(out1, plottype = "curve", curvetype = "newinfect")
## Example 2: spatial SIR model
# generate infectious period(=3) for 100 individuals
lambda <- rep(3, 100)
out2 <- epidata(type = "SIR", n = 100, tmax = 15, sus.par = 0.3, beta = 5.0, infperiod = lambda,
x = x, y = y)
plot(out2, plottype = "spatial")
plot(out2, plottype = "curve", curvetype = "newinfect")
## Example 3: SI network model
contact1 <- matrix(rbinom(10000, 1, 0.1), nrow = 100, ncol = 100)
contact2 <- matrix(rbinom(10000, 1, 0.1), nrow = 100, ncol = 100)
diag(contact1[,] ) <- 0
diag(contact2[,] ) <- 0
contact <- array(c(contact1, contact2), dim = c(100, 100, 2))
out3 <- epidata(type = "SI", n = 100, tmax = 15, sus.par = 0.3, beta = c(3.0, 5.0),
contact = contact)
plot(out3, plottype = "curve", curvetype = "complete")
plot(out3, plottype = "curve", curvetype = "susceptible")
plot(out3, plottype = "curve", curvetype = "newinfect")
plot(out3, plottype = "curve", curvetype = "totalinfect")