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Malthusian (Exponential) Growth Model

Source: R/diffEq_models.R
model_malthus.Rd

Solves the Malthusian growth equation: $$\frac{dN}{dt} = r \, N$$

Usage

model_malthus(init, params, times, ...)

Arguments

init

Named numeric vector, e.g. c(N = 100).

params

Named numeric vector, e.g. c(r = 0.3).

r

Intrinsic growth rate (per time unit).

times

Numeric vector of output times.

...

Additional arguments passed to ode_solver.

Value

A data.frame with columns time and N.

Details

The analytical solution is \(N(t) = N_0 \, e^{r t}\), which can be used to verify numerical accuracy.

Examples

res = model_malthus(
  init   = c(N = 100),
  params = c(r = 0.3),
  times  = seq(0, 10, by = 0.1)
)
# Compare with analytical solution
res$N_exact = 100 * exp(0.3 * res$time)
head(res)
#>   time        N  N_exact
#> 1  0.0 100.0000 100.0000
#> 2  0.1 103.0455 103.0455
#> 3  0.2 106.1838 106.1837
#> 4  0.3 109.4175 109.4174
#> 5  0.4 112.7498 112.7497
#> 6  0.5 116.1835 116.1834