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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.

Made available in DSpace on 2019-10-06T17:02:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-08-01 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) This paper presents an age structured problem modelling mosquito blood-feeding plasticity in a natural environment. We first investigate the analytical asymptotic solution through studying the spectrum of an operator A which is the infinitesimal generator of a C 0 -semigroup. Indeed, the study of the spectrum of A per se is interesting. Additionally, we get the existence and nonexistence of nonnegative steady solutions under some conditions. Institut de Mathématiques de Bordeaux Université de Bordeaux Department of Biostatistics Institute of Biosciences São Paulo State University (UNESP) Department of Biostatistics Institute of Biosciences São Paulo State University (UNESP) FAPESP: 14/07615-3

The aim of this paper is to study a general class of $ SIRI $ age infection structured model where infectivity depends on the age since infection and where some individuals from the $ R $ class, also called quarantaine class in this work, can return to the infectiousness class after a while. Using classical technics we compute a basic reproductive number $ R_0 $ and show that the disease dies out when $ R_0 1 $. Some Lyapunov suitable functions are derived to prove global stability for the disease free equilibrium (DFE) when $ R_0 1 $. Using numerical results we show that the non homogeneous infectivity combined with the feedback to the infectiousness class of a part of the quarantaine population modifies drastically the behavior of the epidemic.

In this paper, we model a mosquito plasticity problem and investigate the large time behavior of matured population under different control strategies. We prove that when the control is small, then the matured population will become large for large time and when the control is large, then the matured population will become small for large time. In the intermediate case, we derive a time-delayed model for the matured population which can be governed by a sub-equation and a super-equation. We prove the existence of traveling fronts for the sub-equation and use it to prove that the matured population will finally be between the positive states of the sub-equation and super-equation. At last, we present numerical simulations.

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.

We consider a linear system coming from a population dynamics model with age structuring and nonlocal boundary conditions. Our population dynamics model is a four-stage model with a second derivative with respect to the age variable. Using Banach fixed point theorem, we show the existence and unicity of a non negative solution and illustrations of numerical simulations are given.

International audience; This work is dedicated to study the cardiac defibrillation problem by using an optimal thoracic electroshock treatment. The problem is formulated as an optimal control problem in a 3D domain surrounded by the bath and including the heart. The control corresponds to the thoracic electroshock and the model describing the electrical activity in the heart is the bidomain model. The bidomain model is coupled with the quasi-static Maxwell's equation to consider the effect of an external bathing medium. The existence and uniqueness of a weak solution for the direct problem is assessed as well as the existence of a weak solution for the adjoint problem. The numerical discretization is realized using a finite element method for the spatial discretization and linearly implicit Runge-Kutta methods for the temporal discretization of the partial differential equations. The numerical results are demonstrated for the termination of re-entry waves.

A system of nonlinear integro-differential equations is investigated. The model describes an age structured S.I.S system of a disease with horizontal and vertical transmission. Global well-posedness is proved in L 1 space. The method is based on the contraction fixed point theorem. We exhibit a closed subset of a Banach space, on which a certain mapping is a strict contraction.

In this paper, an age structured epidemic Susceptible-Infected-Quarantined-Recovered-Infected (SIQRI) model is proposed, where we will focus on the role of individuals that leave the R-class before being completely recovered and thus will participate again to the disease transmission. We investigate the asymptotic behavior of solutions by studying the stability of both trivial and positive equilibria. In order to see the impact of the different model parameters like the relapse rate on the qualitative behavior of our system, we firstly, give an explicit expression of the basic reproduction number R0, which is a combination of the classical basic reproduction number for the SIQR model and some other model parameters, corresponding to the individuals infected by the relapsed ones. It will be shown that, if R0 ≤ 1, the disease free equilibrium is globally asymptotically stable and becomes unstable for R0 > 1. Secondly, while R0 > 1, a suitable Lyapunov functional is constructed to prove that the unique endemic equilibrium is globally asymptotically stable on some subset Ω0.

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.

Made available in DSpace on 2019-10-06T16:50:53Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-02-01 In this paper, we study an age-structured model which has strong biological background about mosquito plasticity. Firstly, we prove the existence of solutions and the comparison principle for a generalized system. Then, we prove the existence of the optimal control for the best harvesting. Finally, we establish necessary optimality conditions. Institut de Mathématiques de Bordeaux Université de Bordeaux São Paulo State University (UNESP) Institute of Biosciences Department of Biostatistics São Paulo State University (UNESP) Institute of Biosciences Department of Biostatistics

In this paper, we revisit the model by Guedj et al. [J. Guedj, R. Thibaut and D. Commenges, Maximum likelihood estimation in dynamical models of HIV, Biometrics 63 (2007) 198–206; J. Guedj, R. Thibaut and D. Commenges, Practical identifiability of HIV dynamics models, Bull. Math. Biol. 69 (2007) 2493–2513] which describes the effect of treatment with reverse transcriptase (RT) inhibitors and incorporates the class of quiescent cells. We prove that there is a threshold value [Formula: see text] of drug efficiency [Formula: see text] such that if [Formula: see text], the basic reproduction number [Formula: see text] and the infection is cleared and if [Formula: see text], the infectious equilibrium is globally asymptotically stable. When the drug efficiency function [Formula: see text] is periodic and of the bang–bang type we establish a threshold, in terms of spectral radius of some matrix, between the clearance and the persistence of the disease. As stated in related works [L. Rong, Z. Feng and A. Perelson, Emergence of HIV-1 drug resistance during antiretroviral treatment, Bull. Math. Biol. 69 (2007) 2027–2060; P. De Leenheer, Within-host virus models with periodic antiviral therapy, Bull. Math. Biol. 71 (2009) 189–210.], we prove that the increase of the drug efficiency or the active duration of drug must clear the infection more quickly. We illustrate our results by some numerical simulations.

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.

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.

We present a model for describing the spread of an infectious disease with public screening measures to control the spread. We want to address the problem of determining an optimal screening strategy for a disease characterized by appreciable duration of the infectiveness period and by variability of the transmission risk. The specific disease we have in mind is the HIV infection. However the model will apply to a disease for which class-age structure is significant and should not be disregarded.

In this work, we construct and analyse an ovine brucellosis mathematical model. In this model, the population is divided into susceptible and infected subclasses. Susceptible individuals can contract the disease in two ways: (i) direct mode - caused by contact with infected individuals; (ii) indirect mode - related to the presence of virulent organisms in the environment. We derive a net reproductive number and analyse the global asymptotic behaviour of the model. We also perform some numerical simulations, and investigate the effect of a slaughtering policy.

The internal zero-stabilization of the nonnegative solutions to some parabolic equations is investigated. We provide a necessary and a sufficient condition for nonnegative stabilizability in terms of the sign of the principal eigenvalue of a certain elliptic operator. This principal eigenvalue is related to the rate of the convergence of the solution. We give some evaluations of this principal eigenvalue with respect to the geometry of the domain and of the support of the control. A stabilization result for an age-dependent population dynamics with diffusion is also established.

International audience; In this paper, we study the stability result for the conductivities diffusion coefficients to a strongly reaction-diffusion system modeling electrical activity in the heart. To study the problem, we establish a Carleman estimate for our system. The proof is based on the combination of a Carleman estimate and certain weight energy estimates for parabolic systems. 1. Introduction. Let Ω ⊂ R N (N ≥ 1) be a bounded connected open set whose boundary ∂Ω is regular enough. Let T > 0 and ω be a small nonempty subset of Ω. We will denote (0, T) × Ω by Q T and (0, T) × ∂Ω by Σ T. To state the model of the cardiac electric activity in Ω (Ω ⊂ R 3 being the natural domain of the heart), we set u i = u i (t, x) and u e = u e (t, x) to represent the spacial cellular and location x ∈ Ω of the intracellular and extracellular electric potentials respectively. Their difference v = u i − u e is the transmembrane potential. The anisotropic properties of the two media are modeled by intracellular and extracellular conductivity tensors M i (x) and M e (x). The surface capacitance of the membrane is represented by the constant c m > 0. The transmembrane ionic current is represented by a nonlinear function h(v). The equations governing the cardiac electric activity are given by the coupled reaction-diffusion system: c m ∂ t v − div(M i (x)∇u i) + h(v) = f χ ω , in Q T , c m ∂ t v + div(M e (x)∇u e) + h(v) = gχ ω , in Q T , (1) where f and g are stimulation currents applied to Ω. We complete this model with Dirichlet boundary conditions for the intra-and extracellular electric potentials

In this work we consider a 2 × 2 system of semilinear partial differential equations of parabolic-type describing interactions between a prey population and a predator population, featuring a Holling-type II functional response to predation. We address the question of stabilizing the predator population to zero, upon using a suitable internal control supported on a small subdomain ω of the whole spatial domain Ω , and acting on predators. We give necessary and sufficient conditions for this stabilizability result to hold.

A nonlinear and nonlocal reaction-diffusion system of population growth is investigated which allows for consideration of both age-size and spatial effects. The mortality and fertility processes of the population are assumed to be linear to simplify the exposition. Local existence, continuation property, positivity, and global existence are obtained. This theory is applied to some specific reaction-diffusion epidemic model including the SI system, the SIS system with vertical transmission, and the SIR system.

International audience; In this study, we consider a model of T cell homeostasis based on the Smith-Martin model. This nonlinear model is structured by age and CD44 expression. First, we establish the mathematical well-posedness of the model system. Next, we prove the theoretical identifiability regarding the up-regulation of CD44, the proliferation time phase and the rate of entry into division, by using the experimental data. Finally, we compare two versions of the Smith-Martin model and we identify which model fits the experimental data best.

International audience; In the inverse problem en electrocardiology, the goal is to recover electrophysiological activity in the heart without measuring directly on its surface (without using catheter interventions). Note that today the inverse computation is frequently used by solving the quasi-static model. This model doesnt take into account the heart dynamic in time and may result in considerable errors in the reconstruction of the solution on the heart. In this paper, a 3D numerical inverse problem constrained by the bidomain equations in electrocardiology is investigated. The state equations consisting in a coupled reaction-diffusion system modelling the propagation of the intracelullar and extracellular electrical potentials, and ionic currents, are extended to further consider the effect of an external bathing medium. Thus, we demonstrate that the novel concept of applying electrophysiological data might be useful to improve noninvasive reconstruction of electrical heart activity. Finally, we present numerical experiments representing the effect of the heart dynamic on the inverse solutions.

In this paper, we study a mathematical model of leukemia diseases. We find sufficient conditions for existence and local stability of steady states.

We are interested in partial differential equations and systems of partial differential equations arising in some population dynamics models, for populations living in heterogeneous spatial domains. Discontinuities appear in the coefficients of divergence form operators and in reaction terms as well. Global posedness results are given. For models offering a great a degree of heterogeneity we derive simpler models with constant coefficients by applying homogenization method. Long term behavior is then analyzed.

The number of T Lymphocytes (T cells) in the body is under homeostatic control. At equilibrium, the majority of naive T cells are non-dividing and express low levels of the surface protein CD44. In conditions of T cell deficiency (lymphopenia), naive T cells enter into a proliferative phase, undergoing cell division accompanied by a subtle change in their surface expression of CD44. In this study, we use a mathematical modelling approach to analyse the proliferative response of transgenic T cells in lymphopenic conditions. Our nonlinear model is composed of ordinary differential equations and partial differential equations structured by age (maturity of cell) and CD44 expression. To better understand the evolution of CD44 expression on the surface of T cells during cell division, we present a numerical analysis to solve a parameter identification problem. Finally, we show the parameters and the simulations that we obtain from the model and compare them to experimental data.

We consider the control problem for a population dynamics model with age dependence, spatial structure, and a nonlocal birth process arising as a boundary condition. We examine the controllability at a given time T and show that approximate controllability holds for every fixed finite time T. As a consequence a new uniqueness condition continuation result is proved.

In this study, we consider a model of T cell proliferation in vivo which is structured by age and CD44 expression. This model is rewritten as an age-structured model system without the CD44 structure, and we investigate its asymptotic behavior. We find that there exists one or three stationary solutions when cells undergo at least five divisions and only one stationary solution when cells undergo at most three divisions. The limiting case with four divisions is numerically handled. By applying the Lyapunov method, we prove that the stationary solution is globally asymptotically stable in some regions of parameter space.

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.

In this paper, we are interested in the null controllability of a linear population dynamics model with degenerate dispersion coefficient. We develop first a Carleman-type inequality for its adjoint system, and then an observability inequality which allows us to establish the existence of a control acting on a subset of the space domain which steers the population of a certain age to extinction in a finite time.

This article shows the creation of a software that allows simulating the voltage in the epicardium by using inverse problems theory, and Tikhonov regularization. The software takes a mesh file containing two surfaces (heart and thorax) and calculates a transfer matrix using the volume conductor model. Then, with the selection of the Tikhonov regularization parameter gives a possible heart voltage distribution for a given data in the thorax.