[R-sig-dyn-mod] to model the cross-diffusion term

[胡艺]

Dear all,

I would like to consider the cross-diffusion term in a SEIR metapopulation
model to account for the behavior of the susceptible to avoid high density
of the infected in disease transmission. my codes are as follows:

library(deSolve)
library(ReacTran)

## The model equations
SEIR2D <- function (t, y, parms)  {
  S  <- matrix(y[1:N^2], N, N)
  E  <- matrix(y[(N^2 + 1):(2*N^2)], N, N)
  I  <- matrix(y[(2*N^2 + 1):(3*N^2)], N, N)
  R  <- matrix(y[(3*(N^2) + 1):(4*N^2)], N, N)

  infect <- beta * I * S
  recovr <- nu * I

  dS <- -infect + tran.2D(S, dx = dx, dy = dy, D.x = D1, D.y = D1)$dC
                + *tran.2D(I, dx = dx, dy = dy, D.x = D2, D.y = D2)$dC*
#cross-diffusion term
  dI <- infect - recovr  + tran.2D(I, dx = dx, dy = dy, D.x = D3, D.y =
D3)$dC
  dR <- recovr
  list(c(dS, dI, dR))
}
But as said in the manual of* tran.2D {ReacTran}  *that "There is no
provision (yet) to deal with cross-diffusion. Set D.x and D.y different
only if cross-diffusion effects are unimportant.", therefore, my question
is that if *tran.2D(I, dx = dx, dy = dy, D.x = D2, D.y = D2)$dC* can denote
the cross-diffusion term. If not, would you please help me in coding the
cross-diffusion. Any reply would be appreciated.

Yi Hu

-- 
Yi Hu, MD, PhD, Lecturer
Dept.of Epidemiology and Biostatistics, School of Public Health, Fudan
University
Office:Room 443, Building 8
Address:No. 130 Dong'an  Road,Shanghai,China
Postcode:200032

	[[alternative HTML version deleted]]