Implements the MY component using a BRQS (Blood-feeding / Resting / gravid Queue / Sugar-feeding) model of adult mosquito ecology and infection dynamics. Mosquitoes cycle through four behavioural states, and infection is tracked across all states with rate \(\tau\) governing progression from exposed (y) to infectious (z).

State Variables

Su, Bu, Ru, Qu

uninfected mosquitoes in the sugar-feeding, blood-feeding, resting, and gravid states

Sy, By, Ry, Qy

infected (exposed) mosquitoes in each behavioural state

Sz, Bz, Rz, Qz

infectious mosquitoes in each behavioural state

Parameters

f

blood feeding rate

q

human blood fraction

g

background mortality rate

rho

rate of leaving the sugar-feeding state to blood-feed

zeta

rate at which blood-feeding mosquitoes take a sugar meal

xi

rate of leaving the resting state

eta

rate of transition from resting to gravid

nu, theta

parameters governing the egg-laying / gravid state

delta

fraction of gravid mosquitoes returning to blood feeding

omega

fraction of emerging mosquitoes entering the sugar-feeding state

tau

rate of progression from exposed to infectious (\(1/\tau\) = EIP)

sigma_b, sigma_q, sigma_s

emigration rates in each state

Dynamics

$$ \begin{array}{rl} dB_u/dt &= (1-\omega)\Lambda + \rho S_u + (\nu+\theta)\delta Q_u + \xi R - (f+\zeta) B_u - \Omega_b \cdot B_u \\ dR_u/dt &= f(1-q\kappa) B_u - (\xi + \eta + g) R_u \\ dQ_u/dt &= \eta R_u - (\nu + \theta) Q_u - \Omega_q \cdot Q_u \\ dS_u/dt &= \omega\Lambda + \zeta B_u + (\nu+\theta)(1-\delta) Q_u - \rho S_u - \Omega_s \cdot S_u \\ \end{array} $$ with analogous equations for the infected (y) and infectious (z) classes, where the term \(\tau\) governs progression between infection stages.