Aquatic Habitats — xds_info_aquatic

Aquatic habitats are distributed among patches on a landscape.

membership: a vector: the patch index of each aquatic habitat
nHabitats: the number of habitats (length(membership))
searchQ: a vector: a search weight for each aquatic habitat

The Habitat Matrix

The habitat matrix is an nPatches $\times$ nHabitats matrix called $N$. It is constructed from the membership vector. In the matrix, $N_{i,j}$ is 1 if the $i^{th}$ patch contains the $j^{th}$ habitat. For example, a membership vector $(1,1,2)$ has a corresponding habitat matrix: $$ N = \left[ \begin{array}{ccc} 1&1&0\\ 0&0&1\\ \end{array} \right] $$ If $\alpha$ denotes the emergence rate of adult mosquitoes from each habitat, then the emergence rate at the patch, $\Lambda$ is: $$\Lambda = N \cdot \alpha$$

The Egg Distribution Matrix

Let $\omega$ denote the habitat search weights. Habitat availability ($Q$) is computed as: $$Q = N \cdot \omega.$$ Mosquitoes could also lay some eggs in available bad habitats ($B$) or in available ovitraps ($O$). The egg distribution matrix ($U$) is computed as $$U = \left( \mbox{diag} \left(\omega \right) \cdot N^T \right) \cdot \mbox{diag}\left( (Q+B+O)^{-1} \right).$$ In models where there are patches with no available habitat, $(Q+B+O)^{-1}$ is computed using the function diag_inverse, which fixes the divide-by-zero problem.