Claire Dufourd

Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control

The aim of this paper is to develop a mathematical model to simulate mosquito dispersal and its control taking into account environmental parameters, like wind, temperature, or landscape elements. We particularly focus on the Aedes albopictus mosquito which is now recognized as a major vector of human arboviruses, like chikungunya, dengue, or yellow fever. One way to prevent those epidemics is to control the vector population. Biological control tools, like the Sterile Insect Technique (SIT), are of great interest as an alternative to chemical control tools which are very detrimental to the environment. The success of SIT is based not only on a good knowledge of the biology of the insect, but also on an accurate modeling of the insects distribution. We consider a compartmental approach and derive temporal and spatio-temporal models, using Advection-Diffusion-Reaction equations to model mosquito dispersal. Periodic releases of sterilized males are modeled with an impulse differential equation. Finally, using the splitting operator approach, and well-suited numerical methods for each operator, we provide numerical simulations for mosquito spreading, and test different vector control scenarios. We show that environmental parameters, like vegetation, can have a strong influence on mosquito distribution and in the efficiency of vector control tools, like SIT.

Spatio‐temporal Modeling of Mosquito Distribution

We consider a quasilinear parabolic system to model mosquito displacement. In order to use efficiently vector control tools, like insecticides, and mechanical control, it is necessary to provide density estimates of mosquito populations, taking into account the environment and entomological knowledges. After a brief introduction to mosquito dispersal modeling, we present some theoretical results. Then, considering a compartmental approach, we get a quasilinear system of PDEs. Using the time splitting approach and appropriate numerical methods for each operator, we construct a reliable numerical scheme. Considering vector control scenarii, we show that the environment can have a strong influence on mosquito distribution and in the efficiency of vector control tools.

Simulations and parameter estimation of a trap-insect model using a finite element approach

Estimating pest population size is of utmost importance in biological control. However field experiments can be difficult and expensive to conduct, with no guarantee that useable results will be produced. In this context, the development of mathematical models and numerical tools is crucial to improve the field experiments by suggesting relevant data which can be used to estimate parameters related to the pest’s biology and to the traps (e.g. duration of the experiments, distance of the releases, etc.). Here we develop a trap-insect model (TIM), based on coupled partial differential equations. The model is studied theoretically and a finite element algorithm is developed and implemented. A protocol for parameter estimation is also proposed and tested, with various data. Among other results, we show that entomological knowledge is absolutely necessary for efficient estimation of parameters, in particular population size.

Mathematical model for pest-insect control using mating disruption and trapping

Controlling pest insects is a challenge of main importance to preserve crop production. In the context of Integrated Pest Management (IPM) programs, we develop a generic model to study the impact of mating disruption control using an artificial female pheromone to confuse males and adversely affect their mating opportunities. Consequently the reproduction rate is diminished leading to a decline in the population size. For more efficient control, trapping is used to capture the males attracted by the artificial pheromone. The model, derived from biological and ecological assumptions, is governed by a piecewise smooth system of ODEs. A theoretical analysis of the model without control is first carried out to establish the properties of the endemic equilibrium. Then, control is added and the theoretical analysis of the model enables to identify threshold values of pheromone which are practically interesting for field applications. In particular, we show that there is a threshold above which the global asymptotic stability of the trivial equilibrium is ensured, i.e. the population goes to extinction. Finally, we illustrate the theoretical results via numerical experiments.

Sensitivity Analysis of Trap-Models for Insects

In order to control a wild insect population with SIT (Sterile Insect Technique), it is necessary to estimate this population. This can be done with experimental data (using traps), combined with appropriate dispersal models, like those studied in [1, 2]. However the observed trap data depend on some (unknown) population parameters, like the diffusivity, and some (unknown) trap parameters, like the attractive force. Therefore the value of the population density is to be identified jointly with the value of other parameters related to the insects and the traps. The possibility of robust identification of multiple parameters using interferences between the traps was demonstrated in [1]. In this talk we present a global sensitivity analysis of the model developed and studied in ...