In ramp.xds, mosquito bionomics are
handled as a junction: each parameter describing adult mosquito ecology
or infection dynamics is handled as a port:
During basic setup, in
ramp.xds, the parameters are assigned constant values.Some parameters can be time-dependent to model forcing by weather or resource availability. Forcing is an advanced setup option. Advanced setup options are in
ramp.forcing-
Various modes of vector control are handled as another set of advanced setup options: advanced setup options for vector control are in
ramp.control.Vector control effects can be handled in one of two ways:vector control can affect the availability of resources, and the effects are computed through functional forms in response to available resources
vector control effect sizes can be computed.
Each module in ramp.xds or in the
satellite package ramp.library must be
capable of handling time-varying parameters, or it should report that
does not. For example, the module macdonald is not capable
of handling either forcing or vector control. We would say that it is a
strictly autonomous model: those capabilities are not in its skill
set. To handle forcing and vector control, we developed
GeM.
Mosquito Dispersal
In ramp.xds, mosquito dispersal is
understood conceptually as the result of a single flight bout.
Regardless of how well a mosquito can fly without the help of wind, wind
ends up being an important factor affecting mosquito dispersal, and it
is possible for a mosquito to travel reasonably long distances with the
help of the wind.
In adult mosquito modules, mosquito dispersal is described by a
square matrix with nPatches rows and columns. By
convention, all matrices have the form: \[
K = \left[ \begin{array}{ccccc}
-1 & k_{1,2} & k_{1,3} & \cdots & k_{1, n} \\
k_{2,1} & -1 & k_{2,3} & \cdots & k_{2, n} \\
k_{3,1} & k_{3,2} & -1 & \cdots & k_{3, n} \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
k_{n,1} & k_{n,2} & k_{n,3} & \cdots & -1 \\
\end{array} \right]
\] The values of the elements are thus constrained such that
there is no net dispersal loss from the system: \[\sum_j k_{i,j} = 1.\] The columns of sum
up to zero. A dispersal matrix, \(K,\)
thus describes the destinations of emigrating mosquitoes that survive
and stay in the system. Mosquito loss from a system due to emigration is
handled elsewhere.
Mosquito Demography
Mosquito survival and dispersal is described by a demographic matrix, denoted It is computed using several parameters:
- \(g\) — the daily mosquito mortality rate
- \(\sigma\) — the patch emigration rate
- \(\mu\) — the rate of emigration-related loss
- \(K\) — a dispersal matrix (see above)
These terms were designed to make it possible to develop and calibrate models for mosquito mortality that make it easy to specify how mosquitoes are lost from a system. The term \(\mu\) describes loss from a system that is associated with emigration: The emigration rate is \(\sigma,\) but only a fraction \(\sigma(1-\mu)\) land in an other patch. The remaining \(\sigma \mu\) are lost from the system. Mosquito mortality and migration are computed as a single object, \(\Omega,\) where
\[ \Omega = \mbox{diag} \left( g + \sigma \mu \right) - K \cdot \mbox{diag} \left( \sigma \left(1-\mu\right) \right) \] and in general:
\[ \frac{dM}{dt} = \Lambda - \Omega \cdot M\]
In delay differential equations with a constant EIP (\(\tau\)), survival and dispersal through the
EIP is given by: \[
\Upsilon = e^{-\Omega \tau}
\] which can be computed in R using expm.
Setup
See mosquito_dispersal.R
By default, \(\sigma=\mu=0\) and \(K\) is a matrix of all zeros.
mod <- xds_setup(nPatches=3)
get_K_matrix(mod)## [,1] [,2] [,3]
## [1,] 0 0 0
## [2,] 0 0 0
## [3,] 0 0 0
herethere
Another simple option is herethere that distributes
mosquitoes to every other patch with equal probability. The \(K\) matrix can be reconfigured after setup
using setup_K_matrix
mod <- setup_K_matrix("herethere", mod)
get_K_matrix(mod)## [,1] [,2] [,3]
## [1,] -1.0 0.5 0.5
## [2,] 0.5 -1.0 0.5
## [3,] 0.5 0.5 -1.0The same options can be passed as a named list Koptions
during basic setup:
mod <- xds_setup(nPatches=6, Koptions = "herethere")
get_K_matrix(mod)## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -1.0 0.2 0.2 0.2 0.2 0.2
## [2,] 0.2 -1.0 0.2 0.2 0.2 0.2
## [3,] 0.2 0.2 -1.0 0.2 0.2 0.2
## [4,] 0.2 0.2 0.2 -1.0 0.2 0.2
## [5,] 0.2 0.2 0.2 0.2 -1.0 0.2
## [6,] 0.2 0.2 0.2 0.2 0.2 -1.0
xy
If the patches have locations, given by a pair of vectors \(x\) and \(y,\) each one of length
nPatches and passed concatenated as xy, then a
dispersal matrix \(K\) is computed by
passing a kernel function that weights by distance. Setup calls
make_K_matrix
x = y = c(1:5)
xy = cbind(x=x,y=y)
F_d = function(d){exp(-d^1.8)}
K <- make_K_matrix_xy(xy, F_d)
round(K*1000)/1000## [,1] [,2] [,3] [,4] [,5]
## 1 -1.00 0.498 0.005 0.000 0.00
## 2 0.99 -1.000 0.495 0.005 0.00
## 3 0.01 0.498 -1.000 0.498 0.01
## 4 0.00 0.005 0.495 -1.000 0.99
## 5 0.00 0.000 0.005 0.498 -1.00
mod <- xds_setup(nPatches=5, Koptions = list(name = "xy", xy=xy, ker=F_d))
get_K_matrix(mod)## [,1] [,2] [,3] [,4] [,5]
## 1 -1.000000e+00 4.975756e-01 0.004820927 4.489989e-06 9.533409e-10
## 2 9.903493e-01 -1.000000e+00 0.495179073 4.844259e-03 8.936647e-06
## 3 9.641768e-03 4.975756e-01 -1.000000000 4.975756e-01 9.641768e-03
## 4 8.936647e-06 4.844259e-03 0.495179073 -1.000000e+00 9.903493e-01
## 5 9.533409e-10 4.489989e-06 0.004820927 4.975756e-01 -1.000000e+00
as_matrix
Finally, if the user wants to form some other kind of matrix, it can
be passed directly as Koptions:
mod <- xds_setup(nPatches=5, Koptions=K)
get_K_matrix(mod)## [,1] [,2] [,3] [,4] [,5]
## 1 -1.000000e+00 4.975756e-01 0.004820927 4.489989e-06 9.533409e-10
## 2 9.903493e-01 -1.000000e+00 0.495179073 4.844259e-03 8.936647e-06
## 3 9.641768e-03 4.975756e-01 -1.000000000 4.975756e-01 9.641768e-03
## 4 8.936647e-06 4.844259e-03 0.495179073 -1.000000e+00 9.903493e-01
## 5 9.533409e-10 4.489989e-06 0.004820927 4.975756e-01 -1.000000e+00
zero
An option is zero which sets the \(K\) matrix to all zeros.
mod <- setup_K_matrix("zero", mod)
get_K_matrix(mod)## [,1] [,2] [,3] [,4] [,5]
## [1,] 0 0 0 0 0
## [2,] 0 0 0 0 0
## [3,] 0 0 0 0 0
## [4,] 0 0 0 0 0
## [5,] 0 0 0 0 0