MYZ Component Derivatives for the SI Mosquito Module

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): $$Z=e^{-\mathrm{\Omega }\tau }\cdot Y$$

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

• $K$ is the mosquito dispersal matrix

The four parameters describing mortality and migration are used to construct a demographic matrix: $$\mathrm{\Omega }=\text{diag}\left(g\right)-(\text{diag}(1-\mu )-K)\cdot \text{diag}\left(\sigma \right)$$

The emergence rate of adult mosquitoes, $\mathrm{\Lambda }$, is computed by F_emerge, and the derivatives are given by the equations: $$\begin{array}{rr}dM/dt=& \mathrm{\Lambda }-\mathrm{\Omega }\cdot M\\ dY/dt=& fq\kappa (M-Y)-\mathrm{\Omega }\cdot Y\end{array}.$$