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dnat
2017 Jun 21
4
How to apply a system of ordinary differential equations to a cell grid?
...ere 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...
2008 Nov 21
1
lsoda warning "too much accuracy requested"
...)
SI <- 80
model <- function(t, x, parms) {
H <- x[1]
BA <- x[2]
N <- x[3]
with(as.list(parms), {
dHdt <- (b/c)*(((a**c)*((H)**(1-c))-H))
dBAdt <- -(BA*b)*(c0+(c1*SI)-log(BA))/(log(1-((H/a)**c)))
dNdt <- N*alpha*(((log(1-((H/a)**c)))/b)**beta) - (gamma*BA)
list(c(dHdt, dBAdt, dNdt))
})
}
times <- seq(0, 40, 1)
parms <- c(a=(SI*1.258621)-1.32759, b=0.1, c=0.4, c0=4.6012, c1=0.013597,
alpha=0.0005, beta=0.5, gamma=0.01)
start <- c(H=0.1, B...
2017 Jul 17
0
How to apply a system of ordinary differential equations to a cell grid?
...rk 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)
out...
2005 Oct 27
1
Fitting of Non-Linear Diff Equations and Parameter Estimation
...R 2.2.0 with Windows XP
i am trying to fit nonlinear differential equation to data sets which looks
like this:
Week N C
0 1 1
1 5 6
2 6.2 12.2
3 59 71.2
4 39 110.2
5 38 148.2
6 44 192.2
7 20.4 212.6
8 19.4 232
9 34.2 266.2
10 35.4 301.6
and i need to fit these data to the following diff equation:
dNdt=a*N-b*N*C, dCdt=N^2,
Where a=birth rate, b=death rate and N= Current count, C= Cumulative Count.
i need to fit the differential equation, solve and obtain parameters a,b.
can someone help with this,
Thanks
Raj
[[alternative HTML version deleted]]
2017 Jun 21
0
How to apply a system of ordinary differential equations to a cell grid?
...:
>
> 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 <-...