Chikungunya: an unusual vector-borne disease. Overview and new research trends

Since the huge epidemic of Chikungunya in 2006 in Réunion Island and in India, and since the small outbreak in 2007 in Italy, a few Chikungunya cases were reported in september 2010 in the south-east of France, indicating that even northern and developed countries can be affected. Since the epidemic in Réunion Island, our knowledge on the Chikungunya virus and its principal vector in Réunion Island, Aedes albopictus, have increased (see [6] for instance). Chikungunya is an unusual vector-borne disease. For instance, it has been proved that the virus has a strong impact on the life-span of the infected mosquitoes [6]. After some works on the modeling of the epidemic and on the efficiency of chemical vector control tools, like adulticides and larvicides, [1, 2], a new project, the SIT-project, has began in 2009. It aims to investigate the possible use of the "Pulsed" Sterile Insect Technique (PSIT) as an alternative to insecticides, principally because mosquito can develop a resistance to insecticides and because SIT only impacts the mosquito population [3]. In particular, in [3], we show that frequent and small releases of sterile males can be efficient to control an epidemic, if it is used early after the beginning of the epidemic or as a preventive control tool. Up to now, all published models are temporal models, i.e. they don't take into account the spatial component. Based on the previous works [1, 2], we have filled this gap by considering a Patch model that takes into account population migration between some cities in Réunion Island [1]. We compute a general Basic Reproduction Number, R0;G, related to this patch model, and show that even if locally R0 is less than 1, R0;G can be greater than 1. This indicates that population displacements can globally induce an outbreak. For practical purposes, we show that vector control in some places where locally R0 is large, can be efficient to control "globally" the epidemic. Finally, following the P-SIT study, we add the spatial component in the modelling of the mosquito population, which leads to a system of non linear partial differential equations [5]. The aim is to "optimize" vector control by reducing the breeding sites or/and by using the P-SIT control. We illustrate the presentation with numerical simulations. (Texte intégral

Vector control for the chikungunya disease: chemical control versus biological control: a mathematical point of view.

The aim of this talk is to present recent investigations on the Chikungunya Disease that hitted Réunion Island, a French territory in Indian Ocean, in 2005 and 2006. Chikungunya is a vectorborne Disease, usually localized in Asia and East-Africa. In 2005, it was the first time that a developed country was affected by this virus. In July 2007, a small outbreak raised in Italy, indicating that the South of Europe is potentialy threatened. In recent works, we have proposed and studied a mathematical model to explain the outbreak of 2005 and possible links with the explosive epidemic of 2006. We also have focused our study in the comparison on different mosquito control tools (adulticide, larvicide, and mechanical control), in order to know if it would have been possible to contain or to stop the epidemic of 2006. Recently, a new project has began to check the feasability of the Sterile Insect Technique (SIT) as a tool for vector-control in Réunion Island. After a short review on the Chikungunya virus, its principal Vector, Aedes albopictus, and recent biological results, we will present the mathematical models developed to assess the efficacy of the vector-control tools used in Réunion Island. We will introduce the SIT project, provide some recent results, and compare them to the previous ones. Finally, we will end the presentation with some prospective works. (Texte intégral

An overview on (mathematical) plant growth modelling and applications

Plants are very complex systems. If agronomic plants, like rice, maize or corn, are essential to provide food or other kind of goods, trees are also essential to preserve the carbon balance, or even to absorb carbon surplus. Despite the great importance of plants, only a small number of modellers, and applied mathematicians are involved in the modelling, the development of mathematical tools, the simulation of plant growth, and, in general, in problems related to Agronomy or Forestry. In fact, the amount of knowledges necessary to understand how a plant is growing is huge and only a multidisciplinary approach can be used to overcome the encountered di_culties. Phenomena are so complex, that even botanist, agronomists and foresters still debate how to handle them e_ciently in plant growth models, and, more important, what are the essential ingredients to take into account to obtain a realistic modeling. Indeed, if we know very precisely what is going on in photosynthesis, transpiration processes,..., we didn't yet succeed in the development of macroscopic laws, like in Physics or in Mechanics. Plant growth modelling is not only challenging from the scienti_c point of view, but is also crucial for real applications, like, for instance, improving crop yields, developing biological tools against Pest attacks, studying the impact of climate change, time evolution of rain forests,.... Thus not only plant growth modeling is challenging but its interactions with the environment too. Up to now people have used di_erent modeling for plant growth, like empirical models, geometric models, process-based models or functional and structural plant models [7].... AMAP laboratory (BotAny and coMputationAl Plant architecture) is a place where Botany, Ecophysiology, Plant Architecture, Applied Mathematics, and Computer Science are deeply connected [1]. AMAP has become World leader in Botany, in Plant Architecture [3], and, based on biological knowledges, has developed several Simulation tools, like AMAPsim: (see [2] for an overview) 1 The aim of this lecture is to show the diversity of the problems encountered in the area of plant growth modeling, through an overview on di_erent ongoing studies in AMAP. After a brief recall on some "basic" knowledges' in Botany and in Ecophysiology, I will present di_erent problems related to plant growth, root growth [4, 5], biomechanics [6], ecology, ... using discrete or continuous models. The wide diversity of problems encountered leads to very interresting mathematical problems, that deserve theoretical and numerical investigations. CIRAD is an International Centre of Agronomic Research for Developing Countries. It is based in Montpellier (France). About 800 researchers, around the world, are working in life sciences, social sciences and engineering sciences, applied to agriculture, food and rural territories. (Texte intégral

Intraguild predation and conservation of endangered seabirds. modelling, theory and nonstandard approximations

Seabirds breeding on islands are vulnerable to introduced predators, such as rats and cats, and the removal of such predators is generally viewed as a priority for seabird conservation and restoration. However, multiple invasive mammal species interacting may generate unexpected outcomes following the removal (eradication) of one species. Generally these indirect interactions are not well understood or demonstrated. We propose and study a prey (seabird)-mesopredator (rat)-superpredator (cat) model, taking into account the juvenile stages in the prey population, in order to direct conservation management for seabird conservation [4,5]. We give a more biologically realistic di_erential system than those studied before [2,3], in particular for long-lived seabird species. We present a theoretical study and show existence and uniqueness of a positive solution as well as a qualitative study of the equilibria that may appear [5]. Because standard numerical methods, usually implemented in scienti_c softwares, like Scilab or Matlab, can fail to give the right biological approximations [1,5], we propose a reliable algorithm that preserves most of the qualitative properties of the continuous system, using the theory of nonstandard _nite di_erence methods. We illustrate our approach with Barau's Petrel, an endemic seabird from Réunion Island. (Résumé d'auteur

Biological vector control with the sterile insect technique for the chilungunya disease

Chikungunya is a vector-borne Disease, usually localized in Asia and East-Africa, with Aedes albopictus mosquito as the principal vector for the Chikungunya virus. In 2005 and 2006, Réunion Island faced two epidemics of Chikungunya: the 2006's epidemic was particularly dramatic. This was the _rst time that a developed country, like Réunion Island, was a_ected by this virus. In July 2007, a small outbreak occurred in Italy, indicating that the South of Europe is potentialy threatened. In recent works [1,2], we proposed and studied a mathematical model to explain the outbreak of 2005 and possible links with the explosive epidemic of 2006. These studies speci_cally focus on the comparison of di_erent mosquito control tools (adulticide, larvicide, and mechanical control) in order to know if it would have been possible to contain or to completely avert the 2006 epidemic. We showed that the combination of the three control tools (with a suitable period of release and a su_cient duration of the treatment) would have been useful to control the explosive epidemic of 2006 [2]. As far as we know, Aedes albopictus in Réunion Island is yet sensitive to Deltamethrin, the only authorized adulticide, but can become resistant, like in Martinique, a West Indies French Island. Moreover, Réunion Island is a hot spot of endemicity and, thus, the use of chemical control tools can be limited. It is also necessary to study and to check the feasibility of other vector control tools such as the Sterile Insect Technique (SIT). To this e_ect, a project called TIS (Technique d'Insecte Stérile), funded by the French Ministry of Health, the European Union and the Regional Council is ongoing in Réunion Island. The aim of this talk is to give a short introduction to the TIS project and to present some recent mathematical results related to the SIT-LSIR model considered for the Chikungunya disease. Moreover, because mechanical control (destruction of breeding sites) is a very cheap and sustainable alternative, we combine mechanical control and SIT control. We present several numerical simulations to assess the e_cacy of the SIT vector-control in comparison with the Chemical vector control, studied in [2]. We show that SIT (impulse) control could be useful to control the wild mosquito population and thus lower the risk of an epidemic. (Résumé d'auteur

Finite element approach to trap-insect model

The trap-insect model considered in this presentation comprises a system of two advection-diffusion-reaction equations. We develop finite element approximation of the solution of the model in order to produce accurate numerical simulations using a non-uniform triangulation. The algorithm is used for computing estimates of the parameters of the insect population. Particular attention is paid to estimating the population size, including the case of spatially heterogeneous population distributions. Using traps is the common practice to gain knowledge on the presence of a particular insect population and its density. This work aims to contribute to optimizing field protocols for accurate parameters estimation. (Texte intégral

Sterile insect technology for control of Anopheles mosquito: a mathematical feasibility study

Anopheles mosquito is a vector responsible for the transmission of diseases like Malaria which a_ect many people. Hence its control is a major prevention strategy. Sterile Insect Technology (SIT) is a nonpolluting method of insect control that relies on the release of sterile males. Mating of the released sterile males with wild females leads to non hatching eggs. Thus, if sterile males are released in su_cient numbers or over a su_cient period of time, it can leads to the local reduction or elimination of the wild population. We study the e_ectiveness of the application of SIT for control of Anopheles mosquito via mathematical modeling. Our main result is that there exists a threshold release rate ^_ depending only on the basic o_spring number R and the wild mosquito equilibrium for males such that a release rate higher than ^_ results in elimination of the mosquito population irrespective of its initial size. A release rate _ which is lower than ^_ eliminates the mosquito populations only if it is su_ciently small. If the population is at the wild equilibrium it is reduced by a percentage depending on _ and R only. (Résumé d'auteur

Modelling interactions between plants and bioagressors. Mathematical perspectives

In many countries around the world, and in particular in Southern countries, the food demand is increasing while arable lands are reducing or being more and more impacted by bioagressors (pests and pathogens), due, partly, to climate change. Many farmers cannot use pesticides due to their prohibitive price and because their usage is banned or more and more restricted. Thus, it is crucial to develop and study new biological control approaches. In fact, Crop protection is a challenging domain of research, even for mathematicians. Many experiments have been or are conducted around the world to test different innovative Bioagressors control tools or strategies. However, these experiments are often located in one place, they are expansive, difficult to conduct and to reproduce, and, according to some crops (perennial crops), may take several years.... Mathematical Modelling and Simulations can be of great help to study these (complex) systems in close connexion with the experiments. In this talk I will present different examples, based on ongoing works, where Mathematics can be helpfull and bring new insights about Plant-Bioagressors interactions. In particular modelling plant epidemiology or/and plant-insect interactions may lead to novel and challenging mathematical problems, from the theoretical and numerical point of view... with, in addition, pratical applications. (Texte intégral