Implements a Macdonald-style delay differential equation model of adult mosquito ecology and infection dynamics, consistent with the model published by George Macdonald in 1952. This formulation is actually closer to one published by Aron & May (1982).
State Variables
Mdensity of adult mosquitoes
Ydensity of infected adult mosquitoes
Zdensity of infectious adult mosquitoes
Parameters
fblood feeding rate
qhuman blood fraction
gmortality rate
sigmapatch emigration
muemigration-related loss
Kthe dispersal matrix
tauextrinsic incubation period (\(\tau\))
The demographic matrix \(\Omega\) is formulated as $$ \Omega = \mbox{diag} \left( g + \sigma \mu \right) + K \cdot \mbox{diag} \left( \sigma \left(1-\mu\right) \right) $$ Survival and dispersal through the EIP is $$ \Upsilon = e^{-\Omega \tau} $$
Dynamics
The dynamical system is described by a coupled set of delay differential equations. In these equations, a sub-scripted variable or term denotes its lagged value: \(M_\tau = M(t-\tau)\).
$$ \begin{array}{rl} dM/dt &= \Lambda - \Omega \cdot M \\\\ dY/dt &= fq\kappa(M-Y) - \Omega \cdot Y \\\\ dZ/dt &= \Upsilon \cdot (fq\kappa)_\tau(M_\tau-Y_\tau) - \Omega \cdot Z \\\\ \end{array} $$