Tight Bounds for Asymptotic and Approximate Consensus

We study the performance of asymptotic and approximate consensus algorithms under harsh environmental conditions. The asymptotic consensus problem requires a set of agents to repeatedly set their outputs such that the outputs converge to a common value within the convex hull of initial values. This problem, and the related approximate consensus problem, are fundamental building blocks in distributed systems where exact consensus among agents is not required or possible, e.g., man-made distributed control systems, and have applications in the analysis of natural distributed systems, such as flocking and opinion dynamics. We prove tight lower bounds on the contraction rates of asymptotic consensus algorithms in dynamic networks, from which we deduce bounds on the time complexity of approximate consensus algorithms. In particular, the obtained bounds show optimality of asymptotic and approximate consensus algorithms presented in [Charron-Bost et al., ICALP'16] for certain dynamic networks, including the weakest dynamic network model in which asymptotic and approximate consensus are solvable. As a corollary we also obtain asymptotically tight bounds for asymptotic consensus in the classical asynchronous model with crashes. Central to our lower bound proofs is an extended notion of valency, the set of reachable limits of an asymptotic consensus algorithm starting from a given configuration. We further relate topological properties of valencies to the solvability of exact consensus, shedding some light on the relation of these three fundamental problems in dynamic networks

Ensuring successful introduction of Wolbachia in natural populations of Aedes aegypti by means of feedback control

The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of an efficient vaccine. The success of this operation requires locally careful planning to determine the adequate number of individuals carrying the Wolbachia parasite that need to be introduced into the natural population. The introduced mosquitoes are expected to eventually replace the Wolbachia-free population and guarantee permanent protection against the transmission of dengue to human. In this study, we propose and analyze a model describing the fundamental aspects of the competition between mosquitoes carrying Wolbachia and mosquitoes free of the parasite. We then use feedback control techniques to devise an introduction protocol which is proved to guarantee that the population converges to a stable equilibrium where the totality of mosquitoes carry Wolbachia.Comment: 24 pages, 5 figure

Epidemiological assessment of Wolbachia-based biocontrol for reduction of dengue morbidity

International audienceWolbachia-based biological control has recently emerged as an ecologically friendly and potentially cost-effective method for prevention and control of dengue and other arboviral infections. When deliberately infected withWolbachia, major vector species, such as Aedes aegypti females, lose their vectorial competence and become less capable of transmitting the virus to humans. Thus, Wolbachia-based biocontrol aims to replace wild vectors (fully capable of transmitting arboviral infections) by Wolbachia-carrying insects that bear a reduced transmission capacity. The population replacement can be achieved by releasing mosquitoes that were transinfected with Wolbachia during the process of mass-rearing.In this presentation, we propose a sex-structured model describing the dynamics of two sup-populations of adult mosquitoes: the wild insects (males and females that are Wolbachia- free), and those deliberately infected with Wolbachia. This model is biologically viable, well-posed, and reflects the two significant features of Wolbachia: maternal transmission and cytoplasmic incompatibility. The model also exhibits bistability that agrees with the principle of competitive exclusion.Using this mosquito population dynamics model, we further construct a dengue transmission system of SEIR-SEI type to perform an epidemiological assessment of Wolbachia-based control for prevention of dengue morbidity. As an example, we simulate this type of preventive control applied to Cali, a sizeable Colombian city commonly considered a hyperendemic area regarding dengue morbidity

A sex-structured model of Wolbachia invasion to design sex-biased release strategies in Aedes spp mosquitoes populations

Laboratory experiments as well as some field essays have revealed that the intracellular bacterium Wolbachia, deliberately introduced in Aedes spp female mosquitoes, drastically reduces their vector competence for dengue virus and other pathogens. However, female mosquitoes infected with Wolbachia still need to ingest human blood while male mosquitoes, either wild or Wolbachia-carrying, do not bite people. Moreover, Wolbachia-carrying females may transmit the virus to people during blood-feeding, even though with a far less probability than the wild ones. Therefore, massive releases of Wolbachia-carrying females may increase both the nuisance and the epidemiological risk among human residents. In this paper, we propose a sex-structured model of Wolbachia invasion that brings forward the possibility of developing male-biased release strategies of Wolbachia-carriers leading to Wolbachia invasion. Thanks to this model, we study the minimal amount of mosquitoes necessary to complete this task, according to the relative sex-ratio of the released mosquitoes and to the release schedule. We also pay attention to the estimate of the time needed to achieve the ultimate population replacement

New Feedback Laws for Stabilization of Unstable Periodic Orbits

International audienceIn this note a gain tuning scheme for prediction-based chaos control of discrete-time systems is proposed, extending previous work by T. Ushio and S. Yamamoto. The derived control laws are proved to be stabilizing. Three different time-invariant or time-varying laws are proposed, leading to different convergence rates and sizes for the basins of attraction. The results are illustrated by numerical simulations. A parallel between finding unstable periodic orbits and chaos control is done

A sex-structured model of Wolbachia invasion to design sex-biased release strategies in Aedes spp mosquitoes populations

Laboratory experiments as well as some field essays have revealed that the intracellular bacterium Wolbachia, deliberately introduced in Aedes spp female mosquitoes, drastically reduces their vector competence for dengue virus and other pathogens. However, female mosquitoes infected with Wolbachia still need to ingest human blood while male mosquitoes, either wild or Wolbachia-carrying, do not bite people. Moreover, Wolbachia-carrying females may transmit the virus to people during blood-feeding, even though with a far less probability than the wild ones. Therefore, massive releases of Wolbachia-carrying females may increase both the nuisance and the epidemiological risk among human residents. In this paper, we propose a sex-structured model of Wolbachia invasion that brings forward the possibility of developing male-biased release strategies of Wolbachia-carriers leading to Wolbachia invasion. Thanks to this model, we study the minimal amount of mosquitoes necessary to complete this task, according to the relative sex-ratio of the released mosquitoes and to the release schedule. We also pay attention to the estimate of the time needed to achieve the ultimate population replacement

A sex-structured model of Wolbachia invasion to design sex-biased release strategies in Aedes spp mosquitoes populations

Laboratory experiments as well as some field essays have revealed that the intracellular bacterium Wolbachia, deliberately introduced in Aedes spp female mosquitoes, drastically reduces their vector competence for dengue virus and other pathogens. However, female mosquitoes infected with Wolbachia still need to ingest human blood while male mosquitoes, either wild or Wolbachia-carrying, do not bite people. Moreover, Wolbachia-carrying females may transmit the virus to people during blood-feeding, even though with a far less probability than the wild ones. Therefore, massive releases of Wolbachia-carrying females may increase both the nuisance and the epidemiological risk among human residents. In this paper, we propose a sex-structured model of Wolbachia invasion that brings forward the possibility of developing male-biased release strategies of Wolbachia-carriers leading to Wolbachia invasion. Thanks to this model, we study the minimal amount of mosquitoes necessary to complete this task, according to the relative sex-ratio of the released mosquitoes and to the release schedule. We also pay attention to the estimate of the time needed to achieve the ultimate population replacement

Sex-structured model of Wolbachia invasion and design of sex-biased release strategies in Aedes spp mosquitoes populations

DATA AVAILABILITY : No data was used for the research described in the article.Laboratory experiments as well as some field essays have revealed that the intracellular bacterium Wolbachia, deliberately introduced in Aedes spp female mosquitoes, drastically reduces their vector competence for dengue virus and, also, other mosquito-borne viral diseases. However, female mosquitoes infected with Wolbachia still need to ingest human blood while male mosquitoes, either wild or Wolbachia-carrying, do not bite people. As such, Wolbachia-carrying females may transmit the virus to people during blood-feeding, even though with far less probability than the wild ones. Therefore, massive releases of Wolbachia-carrying females may increase both the nuisance and the epidemiological risk among human residents. With the goal of exploring in depth the practical aspects of sex-biased releases, we introduce in this paper a simple sex-structured model of Wolbachia invasion that brings forward the possibility of developing male-biased release strategies of Wolbachia-carriers leading to Wolbachia invasion. Thanks to this model, we study at length the minimal amount of mosquitoes necessary to complete this task, according to the relative sex-ratio of the released mosquitoes and the release schedule. We also pay attention to the estimate of the time needed to achieve the ultimate population replacement.The National Fund for Science, Technology, and Innovation; Autonomous Heritage Fund Francisco José de Caldas; Colombian Ministry of Science, Technology, and Innovation – Minciencias; Universidad del Valle; the DST/NRF SARChI Chair in Mathematical Models and Methods in Biosciences and Bioengineering at the University of Pretoria; DST/NRF Incentive Grant and the support of the Conseil Régional de la Réunion, the Conseil Départemental de la Réunion, the European Agricultural Fund for Rural Development (EAFRD) and the Centre de Coopération Internationale en Recherche Agronomique pour le Développement (CIRAD).http//www.elsevier.com/locate/apm2024-03-11hj2023Mathematics and Applied MathematicsNon