The SI model for mosquito infection
dynamics has the defined variable classes:
\(M\) is the density of mosquitoes in each patch;
\(Y\) is the density of infected mosquitoes in each patch.
The density of infectious mosquitoes in each patch is given by a term (returned by F_fqZ.SI): $$Z = e^{-\Omega \tau} \cdot Y$$
The model blood feeding parameters are:
\(f\) is the overall blood feeding rate
\(q\) is the human fraction for blood feeding
The parameters describing egg laying (see F_eggs.SI) are:
\(\nu\) is the egg laying rate
\(\xi\) is the number of eggs per batch
The model demographic parameters are:
\(g\) is the mortality rate
\(\sigma\) is the emigration rate
\(\mu\) is the emigration loss rate
\(\cal K\) is the mosquito dispersal matrix
The four parameters describing mortality and migration are used to construct a demographic matrix: $$\Omega = \mbox{diag}\left(g\right) - \left(\mbox{diag}\left(1-\mu\right) - \cal K \right) \cdot \mbox{diag}\left(\sigma\right)$$
The emergence rate of adult mosquitoes, \(\Lambda\), is computed by F_emerge, and the derivatives are given by the equations: $$ \begin{array}{rr} dM/dt = & \Lambda - \Omega \cdot M \\ dY/dt = & f q \kappa (M-Y) - \Omega \cdot Y \end{array}. $$
Usage
# S3 method for class 'SI'
dMYZdt(t, y, pars, s)