Control design of an HIV-1 model

In this paper, we formulate a dynamic mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV), combined with nonlinear continuous feedback control. The detailed computations of two linearizing inputs is presented. It results in the design of a first fully linearizable system and a second partially linearizable one. The proposed controllers have the ability to drive the system close to the healthy equilibrium state. Numerical simulations demonstrate them effectiveness by maintaining virus concentration in very low levels and healthy cells in satisfactory levels

Null Controllability of a Four Stage and Age-Structured Population Dynamics Model

This paper is devoted to study the null controllability properties of a population dynamics model with age structuring and nonlocal boundary conditions. More precisely, we consider a four-stage model with a second derivative with respect to the age variable. The null controllability is related to the extinction of eggs, larvae, and female population. Thus, we estimate a time T to bring eggs, larvae, and female subpopulation density to zero. Our method combines fixed point theorem and Carleman estimate. We end this work with numerical illustrations

Sensing of Airborne Infochemicals for Green Pest Management: What Is the Challenge?

One of the biggest global challenges for our societies is to provide natural resources to the rapidly expanding population while maintaining sustainable and ecologically friendly products. The increasing public concern about toxic insecticides has resulted in the rapid development of alternative techniques based on natural infochemicals (ICs). ICs (e.g., pheromones, allelochemicals, volatile organic compounds) are secondary metabolites produced by plants and animals and used as information vectors governing their interactions. Such chemical language is the primary focus of chemical ecology, where behavior-modifying chemicals are used as tools for green pest management. The success of ecological programs highly depends on several factors, including the amount of ICs that enclose the crop, the range of their diffusion, and the uniformity of their application, which makes precise detection and quantification of ICs essential for efficient and profitable pest control. However, the sensing of such molecules remains challenging, and the number of devices able to detect ICs in air is so far limited. In this review, we will present the advances in sensing of ICs including biochemical sensors mimicking the olfactory system, chemical sensors, and sensor arrays (e-noses). We will also present several mathematical models used in integrated pest management to describe how ICs diffuse in the ambient air and how the structure of the odor plume affects the pest dynamics