The logistic growth model is given by dN/dt = rN(1-N/K)
where N
is the number (density) of indviduals at time
t
, K
is the carrying capacity of the
population, r
is the intrinsic growth rate of the
population. We assume r=b-d
where b
is the per
capita p.c. birth rate and d
is the p.c. death rate.
This model consists of two reaction channels,
N ---b---> N + N
N ---d'---> 0
where d'=d+(b-d)N/K
. The propensity functions are
a_1=bN
and a_2=d'N
.
Load package
Define parameters
Define initial state vector
Define state-change matrix
Define propensity functions
Run simulations with the Direct method
set.seed(1)
out <- ssa(
x0 = x0,
a = a,
nu = nu,
parms = parms,
tf = tf,
method = ssa.d(),
simName = simName,
verbose = FALSE,
consoleInterval = 1
)
ssa.plot(out, show.title = TRUE, show.legend = FALSE)
Run simulations with the Explict tau-leap method
set.seed(1)
out <- ssa(
x0 = x0,
a = a,
nu = nu,
parms = parms,
tf = tf,
method = ssa.etl(tau = .03),
simName = simName,
verbose = FALSE,
consoleInterval = 1
)
ssa.plot(out, show.title = TRUE, show.legend = FALSE)
Run simulations with the Binomial tau-leap method
set.seed(1)
out <- ssa(
x0 = x0,
a = a,
nu = nu,
parms = parms,
tf = tf,
method = ssa.btl(f = 5),
simName = simName,
verbose = FALSE,
consoleInterval = 1
)
ssa.plot(out, show.title = TRUE, show.legend = FALSE)
Run simulations with the Optimized tau-leap method