The SI module for the MY component

Implements the MY component using a simple SI (Susceptible-Infected) model of adult mosquito infection dynamics.

State Variables

M

density of adult mosquitoes

Y

density of infected adult mosquitoes

Parameters

f

blood feeding rate

q

human blood fraction

eip

extrinsic incubation period (\(\tau\))

g

mosquito mortality rate

sigma

emigration rate

mu

emigration loss rate

K

mosquito dispersal matrix

Demography

The demographic matrix, \(\Omega\) is computed as $$\Omega = \mbox{diag}\left(g + \sigma \mu \right) - K \cdot \mbox{diag}\left(\sigma \left(1-\mu\right)\right)$$

Inputs

Emergence – Lambda or \(\Lambda\), is computed by the ML-Interface using outputs of the L Component

Net Infectiousness – kappa or \(\kappa\), is computed by the XY-Interface using outputs of the XH Component

Dynamics

$$ \begin{array}{rl} dM/dt &= \Lambda - \Omega \cdot M \\ dY/dt &= fq\kappa(M-Y) - \Omega \cdot Y \\ \end{array}$$

Net Infective Biting

This model incorporates mortality and dispersal through the EIP, but it ignores the delay. The density of infectious mosquitoes is thus: $$Z = e^{-\Omega \tau} \cdot Y$$ so net infective biting, the fqZ term, is given by: $$fqZ = fq \left(e^{-\Omega \tau} \cdot Y\right)$$