R help - Jul 2017 - How to apply a system of ordinary differential equations to a cell grid?

Hello,

I am developing an agent-based model to simulate the spread of infectious
diseases in heterogeneous landscapes composed of habitat polygons (or clumps of
connected cells). To simplify the model, I consider a habitat grid (or raster)
containing the polygon ID of each cell. In addition, I have epidemiological
parameters associated with each polygon ID. At each time step, the parameter
values change in the polygon. Thus, the data frame ?landscape? (see below) is
updated at each time step. Here is an example at t = 0:

landscape <- data.frame(polygon_ID = seq(1, 10, by = 1),
                        beta = sample(c(100, 200, 400, 600), 10, replace =
TRUE),
                        gamma = sample(c(25, 26, 27, 28), 10, replace = TRUE))

To study the disease dynamics, I also am developing a compartmental model based
on a system of ordinary differential equations (ODEs). Here is an example to
represent the system of ODEs:

solve_sir_model <- function (times, parameters) {

  sir_model <- function (times, states, parameters) {

    with(as.list(c(states, parameters)), {

      dSdt <- -beta*S*I
      dIdt <- beta*S*I-gamma*I
      dRdt <- gamma*I
      dNdt <- dSdt + dIdt + dRdt

      return(list(c(dSdt, dIdt, dRdt, dNdt)))

    })
  }

  states <- c(S = 99, I = 1, R = 0, N = 100)
  return(ode(y = states, times = times, func = sir_model, parms = parameters))
}

require(deSolve)
output <- as.data.frame(solve_sir_model(times = seq(0, 5, by = 1), parameters
= c(beta = 400, gamma = 28)))

Here is my question: at each time step, is it possible to apply the system of
ODEs to each habitat polygon (thus each row) in the data frame ?landscape?? I am
using lsoda as an ODE solver. Do I need to use another solver to apply the ODEs
at each time step?

Thank you very much for your advice.
Have a nice day
Marine


	[[alternative HTML version deleted]]

> On Jun 21, 2017, at 12:48 PM, Marine Regis <marine.regis at
hotmail.fr> wrote:
> 
> Hello,
> 
> I am developing an agent-based model to simulate the spread of infectious
diseases in heterogeneous landscapes composed of habitat polygons (or clumps of
connected cells). To simplify the model, I consider a habitat grid (or raster)
containing the polygon ID of each cell. In addition, I have epidemiological
parameters associated with each polygon ID. At each time step, the parameter
values change in the polygon. Thus, the data frame ?landscape? (see below) is
updated at each time step. Here is an example at t = 0:
> 
> landscape <- data.frame(polygon_ID = seq(1, 10, by = 1),
>                        beta = sample(c(100, 200, 400, 600), 10, replace =
TRUE),
>                        gamma = sample(c(25, 26, 27, 28), 10, replace =
TRUE))
> 
> To study the disease dynamics, I also am developing a compartmental model
based on a system of ordinary differential equations (ODEs). Here is an example
to represent the system of ODEs:
> 
> solve_sir_model <- function (times, parameters) {
> 
>  sir_model <- function (times, states, parameters) {
> 
>    with(as.list(c(states, parameters)), {
> 
>      dSdt <- -beta*S*I
>      dIdt <- beta*S*I-gamma*I
>      dRdt <- gamma*I
>      dNdt <- dSdt + dIdt + dRdt
> 
>      return(list(c(dSdt, dIdt, dRdt, dNdt)))
> 
>    })
>  }
> 
>  states <- c(S = 99, I = 1, R = 0, N = 100)
>  return(ode(y = states, times = times, func = sir_model, parms =
parameters))
> }
> 
> require(deSolve)
> output <- as.data.frame(solve_sir_model(times = seq(0, 5, by = 1),
parameters = c(beta = 400, gamma = 28)))
> 
> Here is my question: at each time step, is it possible to apply the system
of ODEs to each habitat polygon (thus each row) in the data frame ?landscape?? I
am using lsoda as an ODE solver. Do I need to use another solver to apply the
ODEs at each time step?
> 
> Thank you very much for your advice.
> Have a nice day
> Marine
> 
There's also ode.2D in the same package {deSolve} and it's help page has
a 2-d diffusion example that might be cognate.
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
David Winsemius
Alameda, CA, USA

Thank you very much for your answer. I'm not sure if I can use the function
ode.2 because it's a solver for 2-D partial differential equation problems.
My equations don't contain diffusion parameters.


Thank you for your help

Marine


________________________________
De : David Winsemius <dwinsemius at comcast.net>
Envoy? : mercredi 21 juin 2017 22:30
? : Marine Regis
Cc : r-help at r-project.org
Objet : Re: [R] How to apply a system of ordinary differential equations to a
cell grid?

> On Jun 21, 2017, at 12:48 PM, Marine Regis <marine.regis at
hotmail.fr> wrote:
>
> Hello,
>
> I am developing an agent-based model to simulate the spread of infectious
diseases in heterogeneous landscapes composed of habitat polygons (or clumps of
connected cells). To simplify the model, I consider a habitat grid (or raster)
containing the polygon ID of each cell. In addition, I have epidemiological
parameters associated with each polygon ID. At each time step, the parameter
values change in the polygon. Thus, the data frame ?landscape? (see below) is
updated at each time step. Here is an example at t = 0:
>
> landscape <- data.frame(polygon_ID = seq(1, 10, by = 1),
>                        beta = sample(c(100, 200, 400, 600), 10, replace =
TRUE),
>                        gamma = sample(c(25, 26, 27, 28), 10, replace =
TRUE))
>
> To study the disease dynamics, I also am developing a compartmental model
based on a system of ordinary differential equations (ODEs). Here is an example
to represent the system of ODEs:
>
> solve_sir_model <- function (times, parameters) {
>
>  sir_model <- function (times, states, parameters) {
>
>    with(as.list(c(states, parameters)), {
>
>      dSdt <- -beta*S*I
>      dIdt <- beta*S*I-gamma*I
>      dRdt <- gamma*I
>      dNdt <- dSdt + dIdt + dRdt
>
>      return(list(c(dSdt, dIdt, dRdt, dNdt)))
>
>    })
>  }
>
>  states <- c(S = 99, I = 1, R = 0, N = 100)
>  return(ode(y = states, times = times, func = sir_model, parms =
parameters))
> }
>
> require(deSolve)
> output <- as.data.frame(solve_sir_model(times = seq(0, 5, by = 1),
parameters = c(beta = 400, gamma = 28)))
>
> Here is my question: at each time step, is it possible to apply the system
of ODEs to each habitat polygon (thus each row) in the data frame ?landscape?? I
am using lsoda as an ODE solver. Do I need to use another solver to apply the
ODEs at each time step?
>
> Thank you very much for your advice.
> Have a nice day
> Marine
>
There's also ode.2D in the same package {deSolve} and it's help page has
a 2-d diffusion example that might be cognate.
>
>        [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
R-help Info Page - Homepage - SfS ? Seminar for
Statistics<https://stat.ethz.ch/mailman/listinfo/r-help>
stat.ethz.ch
The main R mailing list, for announcements about the development of R and the
availability of new code, questions and answers about problems and solutions
using R ...


> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
David Winsemius
Alameda, CA, USA


	[[alternative HTML version deleted]]

I'm looking for a histogram variant in which data points are plotted as
labelled rectangles 'piled up' to form a histogram. I've posted an
example at https://www.dropbox.com/s/ozi8bhdn5kqaufm/labelled_histogram.png?dl=0

It seems to have a long pedigree, as I see it (as in this example) in documents
going back beyond the '80s. But I've not seen it in recent textbooks. So
it may be one of those older graphical displays that's just fallen out of
use.

General questions:
i) Does this thing have a name?
ii) Can anyone point me to a literature source for it? 

... and the R question:
ii) Is it already hiding somewhere in an R package?*

S Ellison

*If it's not, I'll be adding it to one, hence the hunt for due
credit/sources



*******************************************************************
This email and any attachments are confidential. Any use...{{dropped:8}}

It seems that the method `iteration` in the function `ode` can be useful in my
case:
> Method "iteration" is special in that here the function func
should
> return the new value of the state variables rather than the rate of
> change. This can be used for individual based models, for difference
> equations, or in those cases where the integration is performed within
> func).
I have tested the method but I don't understand why it doesn't work with
one time step:

    solve_sir_model <- function (times, parameters) {

      sir_model <- function (times, states, parameters) {

        with(as.list(c(states, parameters)), {

          dSdt <- -beta*S*I
          dIdt <- beta*S*I-gamma*I
          dRdt <- gamma*I
          dNdt <- dSdt + dIdt + dRdt

          return(list(c(dSdt, dIdt, dRdt, dNdt)))

        })
      }

      states <- c(S = 99, I = 1, R = 0, N = 100)
      return(ode(y = states, times = times, func = sir_model, parms =
parameters, method = "iteration"))
    }

    require(deSolve)
    output <- as.data.frame(solve_sir_model(times = 0, parameters = c(beta =
400, gamma = 28)))

 Error in iteration(y, times, func, parms, ...) :
   times should be equally spaced In addition: Warning messages:
1: In min(x) : no non-missing arguments to min; returning Inf
2: In max(x) : no non-missing arguments to max; returning -Inf

Thank you very much for your help.
Marine



________________________________
De : David Winsemius <dwinsemius at comcast.net>
Envoy? : mercredi 21 juin 2017 22:30
? : Marine Regis
Cc : r-help at r-project.org
Objet : Re: [R] How to apply a system of ordinary differential equations to a
cell grid?

> On Jun 21, 2017, at 12:48 PM, Marine Regis <marine.regis at
hotmail.fr> wrote:
>
> Hello,
>
> I am developing an agent-based model to simulate the spread of infectious
diseases in heterogeneous landscapes composed of habitat polygons (or clumps of
connected cells). To simplify the model, I consider a habitat grid (or raster)
containing the polygon ID of each cell. In addition, I have epidemiological
parameters associated with each polygon ID. At each time step, the parameter
values change in the polygon. Thus, the data frame ?landscape? (see below) is
updated at each time step. Here is an example at t = 0:
>
> landscape <- data.frame(polygon_ID = seq(1, 10, by = 1),
>                        beta = sample(c(100, 200, 400, 600), 10, replace =
TRUE),
>                        gamma = sample(c(25, 26, 27, 28), 10, replace =
TRUE))
>
> To study the disease dynamics, I also am developing a compartmental model
based on a system of ordinary differential equations (ODEs). Here is an example
to represent the system of ODEs:
>
> solve_sir_model <- function (times, parameters) {
>
>  sir_model <- function (times, states, parameters) {
>
>    with(as.list(c(states, parameters)), {
>
>      dSdt <- -beta*S*I
>      dIdt <- beta*S*I-gamma*I
>      dRdt <- gamma*I
>      dNdt <- dSdt + dIdt + dRdt
>
>      return(list(c(dSdt, dIdt, dRdt, dNdt)))
>
>    })
>  }
>
>  states <- c(S = 99, I = 1, R = 0, N = 100)
>  return(ode(y = states, times = times, func = sir_model, parms =
parameters))
> }
>
> require(deSolve)
> output <- as.data.frame(solve_sir_model(times = seq(0, 5, by = 1),
parameters = c(beta = 400, gamma = 28)))
>
> Here is my question: at each time step, is it possible to apply the system
of ODEs to each habitat polygon (thus each row) in the data frame ?landscape?? I
am using lsoda as an ODE solver. Do I need to use another solver to apply the
ODEs at each time step?
>
> Thank you very much for your advice.
> Have a nice day
> Marine
>
There's also ode.2D in the same package {deSolve} and it's help page has
a 2-d diffusion example that might be cognate.
>
>        [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
R-help -- Main R Mailing List: Primary help - Homepage -
SfS<https://stat.ethz.ch/mailman/listinfo/r-help>
stat.ethz.ch
The main R mailing list, for announcements about the development of R and the
availability of new code, questions and answers about problems and solutions
using R ...


> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
David Winsemius
Alameda, CA, USA


	[[alternative HTML version deleted]]