DGobj.simul.mechanistic: Simulation of a DG object under a mechanistic model
In StrainRanking: Ranking of Pathogen Strains

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Simulation of a DG object under a mechanistic model generating a multi-strain epidemic with multiple introductions over a square grid.

1 2	DGobj.simul.mechanistic(sqrtn, size1, size2, theta, beta, M, delta, plots = FALSE)

`sqrtn`	[Positive integer] Side size of the square grid over which the epidemic is simulated. The inter-node distance in the grid is one in the horizontal and vertical directions. The total number of grid nodes is sqrtn^2.
`size1`	[Positive integer] Maximum number of grid nodes where pathogen isolates are collected (sampling sites).
`size2`	[Positive integer] Maximum number of pathogen isolates sampled in each sampling site.
`theta`	[Vector of positive numerics] Fitness coefficients of the strains. The length of this vector determines the number of strains in the epidemic.
`beta`	[Vector of postive numerics of size 2] Immigration parameters. The first component is the expected number of immigration nodes for every strain. The second component is the expected number of pathogen units in each immigration node.
`M`	[Positive integer] Number of time steps of the epidemic.
`delta`	[Positive numeric] Dispersal parameter.
`plots`	[Logical] If TRUE, plots are produced. The plots show the curse of the epidemic for each strain and the proportion of each strain in space at the final time step.

The effective number of sampling sites is the maximum of size1 and the number of sites occupied at the last time of the simulation.

In each sampling site, the effective number of sampled isolates is the maximum of size2 and the number of pathogen isolates in the site.

The immigration time T^{immigr}_s at which the sub-epidemic due to strain s is initiated is randomly drawn between 1 and M with probabilities P(T^{immigr}_s=t)=(M-t)^2/∑_{k=1}^M (M-k)^2.

The number of immigration nodes is drawn from the binomial distribution with size sqrtn^2 and with expectation given by the first component of beta. The immigration nodes are uniformly drawn in the grid.

At time T^{immigr}_s, the numbers of pathogen units of strain s at the immigration nodes are independently drawn under the Poisson distribution with mean equal to the second component of beta.

An object from the DG class.

Demographic measurements, say Y_i(M-1) and Y_i(M), made at the grid nodes and at times M-1 and M, are transformed into the values Z_i=\log≤ft(\frac{1+Y_i(M-1)}{1+Y_i(M)}\right) characterizing the temporal growth of the epidemic in space at the end of the epidemic. The growth variable Z_i is given in the thrid column of the demographic slot of the returned DG object.

Soubeyrand, S., Tollenaere, C., Haon-Lasportes, E. and Laine, A.-L.

Soubeyrand S., Tollenaere C., Haon-Lasportes E. & Laine A.-L. (2014). Regression-based ranking of pathogen strains with respect to their contributions to natural epidemics. PLOS ONE 9(1): e86591.

DGobj-class, DGobj.rawdata, DGobj.simul.regression

## Simulation of a data set
DGmech=DGobj.simul.mechanistic(sqrtn=10, size1=30, size2=10, theta=c(1.5,2,3), 
	beta=c(5,5), M=7, delta=0.2)
summary(DGmech)

## Simulation of a data set and plots of the sub-epidemics for the strains and their
## proportions in space at the final time step
DGmech=DGobj.simul.mechanistic(sqrtn=10, size1=30, size2=10, theta=c(1.5,2,3), 
	beta=c(5,5), M=7, delta=0.2, plots=TRUE)
summary(DGmech)