Authors who contributed equally to the work.

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The mosquito

The Asian tiger mosquito

Due to the urgent need for intensive monitoring and risk-based surveillance of

In this paper, we present a weather-driven abundance model depicting the annual and inter-annual variations of

The study area includes the municipality of Nice and neighbouring municipalities from the French Riviera region where entomological longitudinal surveys on

Study area including the municipalities of Nice, La Gaude, Cagnes-sur-Mer, Villeneuve-Loubet, and Biot. Source: © IGN BD Adresse v2—EID Méditerranée, September 2011.

Mosquito sampling was performed in different locations of Nice conurbation, using ovitraps’ networks placed mostly in sites shaded by vegetation. The surveillance of eggs was chosen for detecting invasive mosquito species such as ^{©}, Aalsmeer, The Netherlands) filled with 2 L of tap water and the biolarvicide

Entomological collections for the surveillance of

Campaign | Trapping season | Ovitrap network | Result | ||||
---|---|---|---|---|---|---|---|

Location | Year | Beginning | End | Nb traps | Surface of the trapping area (ha) * | Sampling frequency | Annual max. of the mean number of collected eggs per ovitrap per capture session |

Nice 1 | 2008 | 25 Mar | 8 Dec | 30 | 328.7 | biweekly | 170 |

Nice 1 | 2009 | 16 Apr | 9 Dec | 50 | 517.7 | biweekly | 233 |

Nice 1 | 2010 | 15 Apr | 2 Dec | 50 | 517.7 | biweekly | 462 |

Nice 1 | 2011 | 21 Apr | 14 Dec | 50 | 517.7 | biweekly | 311 |

Cagnes-sur-Mer | 2010 | 21 Jun | 15 Nov | 15 | 30.5 | weekly | 177 |

Cagnes-sur-Mer | 2011 | 28 Mar | 28 Nov | 18 | 41.6 | weekly | 169 |

La Gaude | 2010 | 16 Jul | 8 Oct | 22 | 17.9 | biweekly | 566 |

Biot | 2010 | 16 Jul | 8 Oct | 25 | 40.3 | biweekly | 830 |

Villeneuve-Loubet | 2011 | 6 May | 30 Nov | 15 | 3.8 | biweekly | 1,108 |

Nice 2 | 2011 | 11 May | 18 Nov | 15 | 2.7 | biweekly | 654 |

Daily rainfall and temperature data from 2008 to 2011 recorded in Nice Airport were obtained from the national meteorological service “Météo France”. Indeed, we assumed that the population dynamics of

As for all mosquito species, the life cycle of

The generic model of mosquito population dynamics developed by Cailly _{em}_{1h}_{1g}_{1o}_{2h}_{2g}_{2o}

The model is based on a system of ordinary differential equations (ODE). For

Model diagram of

Model parameters are in Greek letters. They are constant. For stage X, _{X}_{X}_{X}_{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 (_{X}_{X}_{X}

We defined specific parameter values, forcing functions, transition functions between stages of the life cycle, and mortality functions to adapt the model to

Because of the large phenotypic variability of the Asian tiger mosquito [

Parameter values of the model of mosquito population dynamics adapted to

Parameter | Definition | Value | Reference |
---|---|---|---|

β_{1} |
Number of eggs laid by ovipositing nulliparous females (per female) | 95 | [ |

β_{2} |
Number of eggs laid by ovipositing parous females (per female) | 75 | [ |

κ_{L} |
Standard environment carrying capacity for larvae (larvae ha^{−1}) |
250,000 | To our best knowledge |

κ_{P} |
Standard environment carrying capacity for pupae (pupae ha^{−1}) |
250,000 | To our best knowledge |

σ | Sex-ratio at the emergence | 0.5 | [ |

μ_{E} |
Egg mortality rate (day^{−1}) |
0.05 | (Lacour, unpublished) |

μ_{L} |
Minimum larva mortality rate (day^{−1}) |
0.08 | (Lacour, unpublished) |

μ_{P} |
Minimum pupa mortality rate (day^{−1}) |
0.03 | (Lacour, unpublished) |

μ_{em} |
Mortality rate during adult emergence (day^{−1}) |
0.1 | (Lacour, unpublished) |

μ_{A} |
Minimum adult mortality rate (day^{−1}) |
0.02 | [ |

μ_{r} |
Adult mortality rate related to seeking behavior (day^{−1}) |
0.08 | To our best knowledge |

T_{E} |
Minimal temperature needed for egg development (°C) | 10.4 | [ |

TDD_{E} |
Total number of degree-day necessary for egg development (°C) | 110 | (Lacour, unpublished) |

γ_{Aem} |
Development rate of emerging adults (day^{−1}) |
0.4 | To our best knowledge |

γ_{Ah} |
Transition rate from host-seeking to engorged adults (day^{−1}) |
0.2 | To our best knowledge |

γ_{Ao} |
Transition rate from oviposition site-seeking to host-seeking adults (day^{−1}) |
0.2 | To our best knowledge |

T_{Ag} |
Minimal temperature needed for egg maturation (°C) | 10 | [ |

TDD_{Ag} |
Total number of degree-days necessary for egg maturation (°C) | 77 | [ |

t_{start} |
Start of the favorable season | 10 Mar | [ |

t_{end} |
End of the favorable season | 30 Sept | [ |

The end of the favorable period is defined as the moment when 90% of eggs laid enter into diapause. Diapause is genetically programmed in _{L}_{P}

The two forcing function variables are temperature (T) and precipitation (P), both varying over time. Daily mean temperature and precipitation were used. Precipitation is known to trigger egg hatching of _{E}

Values of T_{X} and TDD_{X} are given in

The development of other aquatic stages (larvae and pupae) is positively correlated to temperature within an optimum range [

Functions of the model of mosquito population dynamics adapted to

Function | Definition | Expression |
---|---|---|

_{E} |
Transition function from egg to larva | Equation (2) |

_{L} |
Transition function from larva to pupa | f_{L}(t) = −0.0007. T²(t) + 0.0392. T(t) − 0.3911 |

_{P} |
Transition function from pupa to emerging adult | f_{P}(t) = 0.0008. T²(t) − 0.0051. T(t) + 0.0319 |

_{Ag} |
Transition function from engorged adult to oviposition site—seeking adult | Equation (2) |

_{L} |
Larva mortality (day^{−1}) |
m_{L}(t) = exp(−T(t)/2) + μ_{L} |

_{P} |
Pupa mortality rate (day^{−1}) |
m_{P}(t) = exp(−T(t)/2) + μ_{P} |

_{A} |
Adult mortality rate (day^{−1}) |
m_{A}(t) = max(μA; 0.04417 + 0.00217. T(t)) |

_{L} |
Environment carrying capacity of larvae (ha^{−1}) |
Equation (3) |

_{P} |
Environment carrying capacity of pupae (ha^{−1}) |
Equation (3) |

Temperature also impacts the mortality rates of larvae, pupae and adults. Expressions were derived from Shaman

Finally, we considered that the precipitations impact the environment’s carrying capacity (_{X}_{X} (t)= κ_{X}_{norm}(t)+1),

Values of _{X}_{norm}

The model predicts the abundance of mosquitoes per stage (_{em}_{1h}_{1g}_{1o}_{2h}_{2g}_{2o}_{h}_{1h}_{2h}_{l}

The differential equations were discretized using the explicit Euler method that we implemented in Scilab 5.1 [^{6} eggs (stage E),

Because the collected eggs in ovitraps are removed after sampling, we compared the observed average number of eggs per trap (relative to the maximum value of the observed average number of eggs per trap) in each site (Nice-1 and -2, Cagnes-sur-Mer, La Gaude, Biot, and Villeneuve-Loubet) with the simulated abundances of eggs newly laid (_{l}

We carried out a global sensitivity analysis, varying simultaneously all of the model’s parameters described in

The dynamics of

Based on observed temperatures and precipitations from 2008 to 2011, the model showed

_{1h}_{1g}_{1o}_{2h}_{2g}_{2o}

Simulated mosquito abundances were highly consistent with field data collected in Nice-1, 2008–2011 (

Model validation. (_{l}

The variations in the peak in adult abundance, in the attack rate and in the parity rate were mainly explained by six of the 20 parameters: the mortality rate at emergence (_{em}_{P}_{end}_{Ah}_{Ao}

Contribution of model parameters to model output variance. Only parameters contributing to more than 1% of output variance were retained here. No interaction was retained.

Therefore, the better these parameters are known, the more precise the model will be in predicting these outputs. Further knowledge thus is needed concerning especially the mortality rate at emergence and the carrying capacity in pupae, which are quite uncertain parameters. A lower mortality at emergence, a higher carrying capacity in pupae, a longer favorable period, and a higher sex-ratio increased the peak abundance in adults and the attack rate (

Variations of model outputs (in lines) with parameters contributing to more than 10% of their variance (in columns): 3 levels were tested per factor (nominal value ±10%). For each considered parameter and model output, a box-and-whisker diagram graphically depicts the maximum, minimum, median, lower and upper quartiles values of the model output obtained from the simulations with three different levels of the parameter tested.

As far as we know, our model is the first mechanistic model of the dynamics of populations of

These results clearly show that the underlying assumptions on the main drivers of Asian tiger mosquito dynamics in this region (

It should be noted that our model was easily adapted from a generic, mechanistic climate-driven model of mosquito populations developed by Cailly

Using a mechanistic approach, we can study the impact of temperatures and rainfall on the dynamics of

On the other hand, previous observational studies stress the lack of clear relationship between precipitations and

The sensitivity analysis identified six key parameters for the population dynamics model of

The sensitivity analysis demonstrates the importance for an invasive mosquito population in a temperate climate of the duration of the favorable period. To survive mosquito phenology must be adapted to their local environment, including a timely, appropriate initiation of the diapause process.

The environment’s carrying capacity in larvae and pupae could be better estimated from field studies. These values depend on the number of available breeding sites in the field and on larval and pupal densities, which can reach up to 10 individuals per cm² in laboratory [

The model’s parameters identified as the most influential could be the potential control points of the biological system. Hence, vector-control strategies achieving the modification of these parameters can be expected to influence notably the biting rate and therefore the associated risk of pathogen transmission to humans and animals.

Chemical or biological treatments of larval instars, as well as the physical destruction of breeding containers will increase the mortality rate at emergence and decrease the environment’s carrying capacity in pupae. Obviously, adult mosquito control treatments will increase the mortality rate of adults. The use of repellents may raise the length of the host-seeking phase and, consequently, the related lethality.

Modifying the end date of the favorable period of activity for mosquito is

To the best of our knowledge, there is no method to change the sex-ratio at the emergence. Yet, the impact of sterile insect technique (SIT), consisting in releasing sterile males which will compete with wild males for mating with females, could be modeled as a first approximation by diminishing the sex-ratio at the emergence. Indeed, females which have mated with a sterile male will have no offspring, and could be removed from the modeled adult population.

The primary application of our model is its use to elaborate and test effective control strategies against the Asian tiger mosquito. Indeed, there is currently no clearly-defined and efficient vector control strategy. All existing tools present problems for routine large scale applications [

Another perspective of the use of our model concerns the assimilation of the predicted abundance of host-seeking mosquitoes into a predictive model of host-vector contacts taking into account the human population density and exposure [

The population dynamics of

This study was conducted within the framework of the European Life+ project (“Integrated Mosquito Control Management”, LIFE08/ENV/F/000488). The authors thank Didier Fontenille (Institut de Recherche pour le Développement—IRD), Benjamin Roche (IRD), Lucas Léger (IRD), Yvon Perrin (Centre national d’Expertise sur les Vecteurs—CNEV), and Jean-Michel Roques (AMENYS), for fruitful discussions on the modelling of

The authors declare no conflict of interest.