Skip to main content

Table 2 State variables, expressions and (fixed) parameters of the SIMPOP model

From: Modelling the impact of larviciding on the population dynamics and biting rates of Simulium damnosum (s.l.): implications for vector control as a complementary strategy for onchocerciasis elimination in Africa

Notation Definition and units Expression Mean Reference
E(t, T W ) Mean no. of simuliid eggs at time t and water temperature T W Eqn. (1) [23]
\( {\displaystyle \begin{array}{l}{L}_1\left(t,{T}_W\right);{L}_i\left(t,{T}_W\right)\\ {}2\le i\le 7\end{array}} \) Mean no. of 1st instar larvae and of 2nd to of 7th instar larvae at t and T W Eqn. (2) This study
P(t, T W ) Mean no. of pupae at t and T W Eqn. (3) [23]
N(t, T W , T) Mean no. of nullipars at time t, water temperature T W and air temperature T Eqn. (4) [23]
Ψ(t, T W , T) Mean no. of parous flies at t, T W and T Eqn. (5) [23]
V(t, T W , T) Mean no. of vectors at t, T W and T N(t, T W , T) + Ψ(t, T W , T) [23]
Δ E (T W ) Duration of egg stage at water temperature T W (days) 11.493  exp(−0.0701T W ) [23]
Δ L (T W ) Duration of larval stage at T W (days) 87.527  exp(−0.0785T W ) [23]
Δ P (T W ) Duration of pupal stage at T W (days) 20.098  exp(−0.0699T W ) [23]
\( {\mu}_E^0 \) Background per capita rate of eggs (day–1) 0.05 [23]
\( {\mu}_L^1 \) Mortality rate of larvae due to larviciding (day-1) \( \left[-\ln \left(1-{\varepsilon}_L\right)-{\mu}_L^0\right] \) This study
β N Per nulliparous fly rate of oviposition (day–1) \( \frac{\varepsilon_N\left\{\exp \left[-{\mu}_V(T)g(T)\right]\right\}}{g(T)} \) [23]
β P Per parous fly rate of oviposition (day-1) \( \frac{\varepsilon_P{\mu}_V(T)}{\left\{\exp \left[{\mu}_V(T)g(T)\right]-1\right\}} \) [23]
ε N Per capita mean no. of eggs per nulliparous fly S. damnosum (s.s.)/S.sirbanum
S. squamosum
[23, 62, 63]
ε P Per capita mean no. of eggs per parous fly S. damnosum (s.s.)/S. sirbanum
S. squamosum
[23, 62, 63]
DBR Daily biting rate (day-1) Eqn. (6)