[R] epidemiology ode likelihood, hierarchical model

[Melen]

Hi all,

I study epidemiology of soilborne disease.
I have this ode model

dS/dt = - (rp(t) X + rs(t) I) * S

with X=1 ; rp(t) = ap exp( - bp*t) ;

 rs(t) = as exp (-0.5 ( ln (t/ds) / bs)² )

The data I have are not directly the infected individuals (which is a
hidden state) but the Diseases ones (individuals who show aerial
symptoms). I have studied with experiments the relationship between
the infected I and the diseases D and I find a delay increasing
linearly with a logNormal error.

I would like to estimate the parameters of this model but as you can
see using an ode solver package and the least square method to fit the
model is not a good idea!
Do you think it is possible to use a bayesian state space model with I
as a Hidden state with this ode epidemiological model ?

If not, it is at least possible to fit this ode model using a
likelihood method instead of using least square ?

Wich R package appears to be the most adapted ?

Thank you!

Melen