Larvae mortality

The mortality rate of larvae is an important factor for transmission, and is strongly temperature dependent [#!kirby:09!#]. The VECTRI model sets a base daily survival rate for larvae ${P_{L,surv}}_0=0.825$ taken from [#!ermert:11a!#], slightly lower than the values given by [#!hoshen:04!#,#!bomblies:08!#]. Development of larvae is negatively affected by larvae over-population due to competition for resources [#!armstrong:61!#]. This is incorporated in VECTRI by reducing survival rate proportionally by a factor related to resource constraints:

$$P_{L,surv}= \left(1-\frac{M_{L}}{w M_{L,max}}\right) K_{flush} {P_{L,surv}}_0.$$ (3)

In the first term on the right, $M_{L}$ is the total larvae biomass per unit surface area of a water body, and $w$ is the fraction coverage of a grid cell by potential breeding sites (not open water) and is given by the surface hydrology component described below. If $w=0$ the survival rate $P_{L,surv}$ is also zero. The maximum carrying capacity, $M_{L,max}$, is set to 300 mg m$^{-2}$ and larvae mass is assumed to increase linearly with a stage 4 larvae having a mean mass of 0.45 mg, both following [#!depinay:04!#,#!bomblies:08!#] closely. All larvae die above a water temperature of $T_{L,max}$.

Flushing of larvae by heavy rainfall has been suggested to be an important cause of larva mortality [#!martens:95b!#,#!thomson:05!#]. Using an artificial pond apparatus [#!paaijmans:07a!#], a 17.5% daily mortality rate of first stage larvae reducing to 4.8% for forth stage larvae was estimated, although the authors state that these figures could represent an underestimate due to the symmetry of the pond apparatus and the lack of sampling of more extreme rainfall amounts during the experiment campaign. On the other hand, vegetation in natural pools and the apparent ability for Anopheles gambiae larvae to take avoidance measures to avoid flushing could imply a lower flushing rate [#!muirhead:58!#]. In order take the simplest possible relationship in VECTRI, flushing rate is represented as exponential function of rate rate, and is related linearly to the larvae fractional growth state $L_f$:

$$K_{flush}=L_f+(1-L_f)\left( (1-K_{flush,\infty}) e^{\frac{-R_d}{\tau_{flush}}}+K_{flush,\infty} \right),$$ (4)

where $R_d$ is the rainfall rate in mm day$^{-1}$, $\tau_{flush}$ describes how quickly the effect increases as a function of $R_d$, and $K_{flush,\infty}$ is the maximum value of $K_{flush}$ for newly hatched first stage larvae at extremely high rain-rates. In contrast the flushing effect is zero ( $K_{flush}=1$) at all rain rates for stage 4 larvae just prior to adult emergence ($L_f=1$, corresponding to the larvae bin $i=N_{L}$). The relationship is illustrated in Fig.2. Since flushing is a function of daily rate rate at relatively high spatial resolution $\tau_{flush}$ is set to 50 mm day$^{-1}$. In order to give mortality rates of first stage and forth stage comparable to [#!paaijmans:07a!#] for typical daily rain rates in the tropics, a value of 0.4 is adopted for $K_{flush,\infty}$.

Table: Larvae scheme parameters

parameter	definition	default	units
nlarv_scheme	larvae water temperature scheme (1,2,3)	1
	1=ermert:2011a,2=jepsen47,3=bayoh lindsey 2003
nsurvival_scheme	mosquito survival temperature scheme (1,2,3)	2
	1=MartinsI,2=MartinsII,3=Bayoh(not yet!)