Analysis of an optimal control problem for the tridomain model in cardiac electrophysiology

In the present paper, an optimal control problem constrained by the tridomain equations in electrocardiology is investigated. The state equations consisting in a coupled reaction–diffusion system modeling the propagation of the intracellular and extracellular electrical potentials, and ionic currents, are extended to further consider the effect of an external bathing medium. The existence and uniqueness of solution for the tridomain problem and the related control problem is assessed, and the primal and dual problems are discretized using a finite volume method which is proved to converge to the corresponding weak solution. In order to illustrate the control of the electrophysiological dynamics, we present some preliminary numerical experiments using an efficient implementation of the proposed scheme.     

Optimal control applied on an HIV‐1 within‐host model

The treatment of human immunodeficiency virus (HIV) remains a major challenge, even if significant progress has been made in infection treatment by ‘drug cocktails’. Nowadays, research trend is to minimize the number of pills taken when treating infection. In this paper, an HIV‐1 within host model where healthy cells follow a simple logistic growth is considered. Basic reproduction number of the model is calculated using next generation matrix method, steady states are derived; their local, as well as global stability, is discussed using the Routh–Hurwitz criteria, Lyapunov functions and the Lozinskii measure approach. The optimal control policy is formulated and solved as an optimal control problem. Numerical simulations are performed to compare several cases, representing a treatment by Interleukin2 alone, classical treatment by multitherapy drugs alone, then both treatments at the same time. Objective functionals aim to (i) minimize infected cells quantity; (ii) minimize free virus particles number; and (iii) maximize healthy cells density in blood. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal control problem on insect pest populations

In this article we present a model of insect infestation of grape vines and consider the optimal control of the pest through egg population removal. Existence and uniqueness of solutions are proved.     

Bifurcation analysis of the HIV‐1 within host model

In this paper, a bifurcation solution's analysis is proposed for an HIV‐1 within the host model around its chronic equilibrium point, this is carried out based on Lyapunov–Schmidt approach. It is shown that the coefficient b, which represents the healthy CD4⁺ T‐cells growth rate, is a bifurcation parameter; this means that the rate of multiplication of healthy cells can have serious effects on the qualitative dynamical properties and structural stability of the infection evolution dynamics. Copyright © 2015 John Wiley & Sons, Ltd.     

An innovative multistage, physiologically structured, population model to understand the European grapevine moth dynamics

We present a multistage, physiologically structured, population model for studying the dynamics of one of the most important grapevine insect pests. Growth of the population at each stage is modeled considering the climatic variations and the grape variety. A result of existence and uniqueness of solutions is presented for this original hyperbolic system as well as simulations of experimental field data.     

Existence and uniqueness for a kinetic model of population dynamics with character dependence and spatial structure

In this work, we consider a one species population dynamics model with character dependence, spatial structure and a nonlocal renewal process arising as a boundary condition. The individual interaction are based on Boltzmann kinetic-type modeling. Using fixed point arguments and the div-rot lemma, we prove that our model admits a unique global nonnegative solution.     

Exact Null Controllability of a Stage and Age-Structured Population Dynamics System

This paper is concerned with the exact null controllability of an age-dependent life cycle dynamics with nonlocal transition processes arising as boundary conditions. We investigate the controllability for the pest by acting on eggs in a small age interval. The main method is based on the derivation of estimations for the adjoint variables related to an optimal control problem. A fixed point theorem is then used to draw conclusions.     

Exact and approximate controllability of the age and space population dynamics structured model

We prove exact and approximate controllability for a linear age-dependent and spatially structured population dynamics problem. The birth process is nonlocal, and the demographic functions depends on age, time, and space. Our method relies on the derivation of a Carleman inequality for the backward nonlocal adjoint system.     

Exact null controllability of the Lobesia botrana model with diffusion

This paper is devoted to analyze the exact null controllability of the diffusive Lobesia botrana model with nonlocal boundary condition. We study the null controllability of butterfly population by acting on eggs, larvas and female moths in a small age interval. We assume that the control of female moths is in a certain given region of the vineyard. The main result is established by combining some estimations and the Carleman inequality for the backward system related to an optimal control problem. A fixed point theorem is then used to draw the conclusion.     

A one-pot synthesis of 7-phenylindolo[3,2-a]carbazoles from indoles and β-nitrostyrenes, via an unprecedented reaction sequence

A six-step one-pot reaction was designed for synthesizing homodimeric 7-phenylindolo[3,2-a]carbazoles from 1H-indoles and β-nitrostyrenes, in the presence of SnCl(2)·2H(2)O. The reactions proceeded under very mild conditions and the desired heterocycles were obtained in moderate to good yields. An unprecedented mechanism involving sequential indole dimerization, regioselective nucleophilic conjugate addition of the resulting 2,3'-biindole to β-nitrostyrene and formal intramolecular [4 + 2]-cycloaddition is proposed.