Aquatic Habitat Membership Matrix
The aquatic habitat membership matrix \(\mathcal{N}\) is a \(p \times l\) matrix mapping aquatic
habitats to the patches which contain them. It should be attached
directly to the parameters list.
\[\begin{equation}
{\cal N} = \left[
\begin{array}{ccccc}
1 & 1 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 1\\
0 & 0 & 0 & 0 & 0\\
\end{array} \right]
\end{equation}\]
calN <- matrix(
data = c(1,1,1,0,0,
0,0,0,1,1,
0,0,0,0,0),
nrow = params$nPatches, ncol = params$nHabitats, byrow = TRUE
)
params$calN <- calN
Egg Dispersal Matrix
The egg dispersal matrix \(\mathcal{U}\) is a \(l \times p\) matrix describing how eggs
laid by adult mosquitoes in a patch are allocated among the aquatic
habitats in that patch. It is also attached directly to the parameters
list.
\[\begin{equation}
{\cal U} = \left[
\begin{array}{ccccc}
.7 & 0 & 0\\
.2 & 0 & 0\\
.1 & 0 & 0\\
0 & .8 & 0\\
0 & .2 & 0\\
\end{array} \right]
\end{equation}\]
xi <- matrix(c(.7, .2, .1, .8, .2), 5, 1)
params$calU <- t(calN %*% diag(as.vector(xi)))
Aquatic Mosquito Parameters
For this simulation, we use the basic competition model of larval
dynamics (see more here). It requires
specification of three parameters, \(\psi\) (maturation rates), \(\phi\) (density-independent mortality
rates), and \(\theta\)
(density-dependent mortality terms), and initial conditions. The
function exDE::make_parameters_L_basic does basic checking
of the input parameters and returns a list with the correct class for
method dispatch. The returned list is attached to the main parameter
list with name Lpar.
L0 <- rep(1, params$nHabitats)
psi <- rep(1/8, params$nHabitats)
phi <- rep(1/8, params$nHabitats)
theta <- c(1/10, 1/20, 1/40, 1/100, 1/10)
make_parameters_L_basic(pars = params, psi = psi, phi = phi, theta = theta, L0 = L0)
Adult Mosquito Parameters
We use the ODE version of the generalized Ross-Macdonald model (see
more here). Part of the specification of
parameters includes the construction of the mosquito dispersal matrix
\(\mathcal{K}\), and the mosquito
demography matrix \(\Omega\). Like for
the aquatic parameters, we use
exDE::make_parameters_MYZ_RM_ode to check parameter types
and return a list with the correct class for method dispatch. We attach
the returned list to the main parameter list with name
MYZpar.
g <- rep(1/12, params$nPatches)
sigma <- rep(1/12/2, params$nPatches)
calK <- t(matrix(
c(c(0, .6, .3),
c(.4, 0, .7),
c(.6, .4, 0)), 3, 3))
f <- rep(1/3, params$nPatches)
q <- rep(0.9, params$nPatches)
nu <- c(1/3,1/3,0)
eggsPerBatch <- 30
tau <- 12
M0 <- rep(100, params$nPatches)
G0 <- rep(10, params$nPatches)
Y0 <- rep(1, params$nPatches)
Z0 <- rep(0, params$nPatches)
Omega <- make_Omega(g, sigma, calK, params$nPatches)
Upsilon <- expm::expm(-Omega*tau)
make_parameters_MYZ_RM_ode(pars = params, g = g, sigma = sigma, calK = calK, tau = tau, f = f, q = q, nu = nu, eggsPerBatch = eggsPerBatch, M0 = M0, G0 = G0, Y0 = Y0, Z0 = Z0)
Mixing
Although not directly used in this example, we create the residency
membership matrix \(\mathcal{J}\), a
\(p \times n\) matrix indicating which
patch each human population strata resides in.
\[\begin{equation}
{\cal J} = \left[
\begin{array}{cccc}
0 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 \\
0 & 0 & 1 & 1 \\
\end{array} \right]
\end{equation}\]
calJ <- t(matrix(
c(c(0,0,0,0),
c(1,1,0,0),
c(0,0,1,1)), 4, 3
))
We then create the time at risk matrix \(\Psi\), a \(p
\times n\) matrix describing how each human strata spends their
time across patches.
\[\begin{equation}
\Psi = \left[
\begin{array}{cccc}
0.01 & .01 & .001 & .001 \\
0.95 & .92 & .04 & .02 \\
0.04 & .02 & .959 & .929 \\
\end{array}
\right]
\end{equation}\]
Psi <- t(matrix(
c(c(0.01,0.01,0.001,0.001),
c(.95,.92,.04,.02),
c(.04,.02,.959,.929)), 4, 3
))
We use the basic SIS (Susceptible-Infected-Susceptible) model for the
human component (see more here). We set it
up like the rest of the components, using
exDE::make_parameters_X_SIS to make the correct return
type, which is attached to the parameter list with name
Xpar.
H <- matrix(c(10,90, 100, 900), 4, 1)
X0 <- as.vector(0.2*H)
r <- rep(1/200, params$nStrata)
b <- rep(0.55, params$nStrata)
c <- c(0.1, .02, .1, .02)
make_parameters_X_SIS(pars = params, b = b, c = c, r = r, Psi = Psi, X0 = X0, H = as.vector(H))
