The egg distribution matrix, \(\cal U\), allocates a portion of eggs laid by adult mosquitoes in each patch to each one of the aquatic habitats in the patch.
Value
a nHabitats \(\times\) nPatches matrix describing egg distribution, \(\cal U\)
Details
The algorithm is motivated by the notion of mosquito searching for aquatic habitat and a quantity we call habitat availability, \(Q\). Each habitat is assigned a search weight, \(\omega\). In the simplest case, habitat availability is the sum of \(\omega\) by patch, which uses the habitat membership matrix, \(\cal N\). If the habitats in the model got all the eggs, then $$Q = \cal N \cdot \omega.$$ The fraction of eggs in the \(j^{th}\) patch laid in the \(i^{th}\) habitat is \(\omega_i / Q_j.\) To make the model extensible, habitat availability sums all the places where mosquitoes might lay eggs, including ovitraps and unsuitable habitats. If every element in \(Q\) were positive, the egg distribution matrix would be: $${\cal U} = \mbox{diag}\left(\omega \right) \cdot {\cal N}^T \cdot \mbox{diag} \left(\frac{1}{Q}\right).$$ To avoid dividing by zero, the zero elements in \(Q\) are set to an arbitrary positive value.
See also
The membership matrix \(\cal N\) is computed by create_habitat_matrix
Total habitat availability, \(\cal Q\), is computed by compute_Q
The availability of ovitraps and bad habitats is setup in setup_EGG_LAYING