David Winsemius

2017-Jun-21 20:30 UTC

### [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 > 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

Marine Regis

2017-Jun-22 03:06 UTC

### [R] 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 <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-helpR-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}}