Mosquito Population Dynamics Modeling

The generic model of mosquito population dynamics developed by Cailly et al. [17 (link)] represents all of the steps of the mosquito life cycle (Figure 2). It considers ten different stages: three aquatic stages (E, eggs; L, larvae; P, pupae), one emerging adult stage (A_em), three nulliparous stages (A_1h, A_1g, A_1o), and three parous stages (A_2h, A_2g, A_2o). In the adult stage, females only are represented. Parous females are females that have oviposited at least once, whereas nulliparous females have never laid eggs. Adults are subdivided regarding their behaviour during the gonotrophic cycle (h, host-seeking; g, transition from engorged to gravid; o, oviposition site seeking). Once parous, females repeat their gonotrophic cycle until death. The events driving the transitions between stages are: egg mortality or hatching, larva mortality, pupation (moult of larvae to pupae), pupa mortality, adult emergence, mortality, engorgement, egg maturing, and oviposition. The model takes into account density-dependent mortality of the larval stage [28 ], and pupa density-dependent success of adult emergence. Density-dependent mortality was assumed at the larval stage as it is has been often observed [28 ,29 (link)]. Pupa density-dependent success of adult emergence was assumed as emergence success was found negatively correlated to pupa density [30 ].
The model is based on a system of ordinary differential equations (ODE). For Aedes populations in temperate climate, the eggs stop hatching at the beginning of the unfavorable period, during which diapause occurs. All other stages will continue their development or transition to the next stage. Thus, the ODE system is:

Model parameters are in Greek letters. They are constant. For stage X, γ_X is the transition rate to the next stage, μ_X the mortality rate, and β_X the egg laying rate. σ is the sex-ratio at the emergence. μ_r is an additional adult mortality rate related to the seeking behavior, applied only on adult stages involving risky movements (host or oviposition site seeking).
Model functions are in Latin letters. They depend on parameters and weather-driven functions (i.e., functions of temperature, humidity or precipitation varying over time). For stage X, f_X is the transition function to the next stage, m_X the mortality function, and k_X the environment’s carrying capacity which limits the population growth due to density-dependent processes.