# How to apply a system of ordinary differential equations to a cell grid?

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## 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]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: How to apply a system of ordinary differential equations to a cell grid?

 > On Jun 21, 2017, at 12:48 PM, Marine Regis <[hidden email]> 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]] > > ______________________________________________ > [hidden email] 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 ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: How to apply a system of ordinary differential equations to a cell grid?

 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 <[hidden email]> Envoyé : mercredi 21 juin 2017 22:30 À : Marine Regis Cc : [hidden email] 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 <[hidden email]> 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]] > > ______________________________________________ > [hidden email] mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-helpR-help Info Page - Homepage - SfS – Seminar for Statistics 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]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Hunting a histogram variant

 In reply to this post by David Winsemius 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=0It 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}} ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Hunting a histogram variant

 ?stem for something close and built in. Cheers, Bert Bert Gunter "The trouble with having an open mind is that people keep coming along and sticking things into it." -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip ) On Wed, Jun 21, 2017 at 9:01 PM, S Ellison <[hidden email]> wrote: > > 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 u...{{dropped:8}} ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Hunting a histogram variant

 In reply to this post by S Ellison-2 Two things to look at are ?monthplot which shows seasonal subseries plotted on an overall plot. The parallel to your example is small histograms plotted on an overall plot. That goes back (through the reference in the Blue Book (Becker, Chambers, and Wilks)) to Bill Cleveland and Irma Terpenning in JASA 77, 377, 52-62 (1982). Starting from scratch I would be inclined to build your design directly in grid, to place the subgraphs in the main graph, and then I would use lattice to design the subgraphs. See Paul Murrell's book Figure 7.18 (First Edition) showing plots of temperature for cities in Australia. Rich On Thu, Jun 22, 2017 at 12:01 AM, S Ellison <[hidden email]> wrote: > > 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 u...{{dropped:8}} ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Hunting a histogram variant

 In reply to this post by S Ellison-2 Hi, This looks very much like a waffle plot, which can be performed with color2D.matplot in the plotrix package. At the moment, the function fill.corner is used to produce the matrix, but this could be generalized to produce any shape of "waffle". The value display is already part of color2D.matplot. Jim On Thu, Jun 22, 2017 at 2:01 PM, S Ellison <[hidden email]> wrote: > > 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 u...{{dropped:8}} ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Hunting a histogram variant

 In reply to this post by S Ellison-2 and I almost forgot Derek Ogle's histStack again in the plotrix package. Jim On Thu, Jun 22, 2017 at 2:01 PM, S Ellison <[hidden email]> wrote: > > 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 u...{{dropped:8}} ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.