Paul Georgescu

Gheorghe Asachi Technical University of Iasi | TU Iasi · Department of Mathematics and Computer Science

There is an increasing realization that industrial, large-scale agriculture can negatively impact both food quality and the environment, and that alternatives should be thoroughly considered. Consisting of various participants with distinct and often competing interests, organic food chains have a dynamic structure. We consider an evolutionary game...

The global economic trends and the winds of technological change have elevated the status of integration between industry and education for innovation and entrepreneurship to that of being a national strategic priority of China. However, for a long time prior to that, the many differences between the industrial and educational systems have caused a...

In this paper, we assess the relevance of social and cognitive factors such as self-efficacy, locus of control and exposure to negative social influence in relation to undergraduate student dropout. To this purpose, we analyze a compartmental model involving a system of nonlinear ODEs, which is loosely based upon the SIR model of mathematical epide...

We model a common teller–customer interaction occurring in the Ghanaian banking sector via a Double-X queuing network consisting of three single servers with infinite-capacity buffers. The servers are assumed to face independent general renewal of customers and independent identically distributed general service times, the inter-arrival and service...

Distance Education

We examine the effectiveness and sustainability of the distance teacher education program established by the University of Education, Winneba, Ghana, by investigating the differences in the academic performance of students who are trained in the teacher education program via traditional and distance education modes, respectively, from 2011 to 2015....

This paper proposes and investigates a model for rumor spreading and control which accounts for different attitudes and for a distinct type of variable, related to the strength and effectiveness of rumor inhibiting mechanisms. The control mechanisms essentially amount to budgeting and to adjusting the attitude of spreaders. The existence and stabil...

In this paper, we propose and analyze from a stability viewpoint a deterministic, ODE-based class of rumor spreading models with two distinct inhibiting and adjusting mechanisms, together with its corresponding stochastic counterpart. For the deterministic model, a threshold parameter R 0 defined ad hoc, called the basic influence number, is us...

This study examines the influence of certain academic and demographic variables upon the academic performance of Chinese students enrolled in a cooperative Bachelor’s degree program in Pure and Applied Mathematics. The program is English taught and jointly organised by Jiangsu University, China and Arcadia University, USA. Data from a sample of 166...

Cigarette smoking on college campuses has become a significant public health issue, which in turn led to an increasing focus on establishing programs to reduce its prevalence. In this paper, a compartmental model depicting the spread and cessation of the smoking habit on college campuses, obtained using theoretical principles often employed in math...

We model a multi-divisional firm as a queueing system consisting in interconnected nodes, each project passing through queues, processing and quality assurance checks. It is assumed that the uptake of projects into processing is delayed by the availability of resources and by the size of the queue. The costs of delays are linearly dependent on queu...

A metapopulation model which explicitly integrates vector-borne and sexual transmission of an epidemic disease with passive and active movements between an urban city and a satellite city is formulated and analysed. The basic reproduction number of the disease is explicitly determined as a combination of sexual and vector-borne transmission paramet...

We formulate a model of HIV transmission which keeps track of two interacting high-risk groups, namely female sex workers (FSW) and male injecting drug users (IDU), along with a third “bridge” group of male drug-free clients (DFC). To determine the global asymptotic behaviour of the model, we first consider the dynamics of an n-group SIR model feat...

Mutualism refers to any species interaction in which the presence of one species benefits the others. While many specific models of two-species mutualism have been developed and analyzed, comparatively, more attention has been devoted to antagonistic interactions among species (i.e., predation and competition). However, recent work revisited the pr...

Many models of mutualism have been proposed and studied individually. In this paper, we develop a general class of models of facultative mutualism that covers many of such published models. Using mild assumptions on the growth and self-limiting functions, we establish necessary and sufficient conditions on the boundedness of model solutions and pro...

We establish boundedness results for a model of mutualism with an arbitrary number of species which encompasses several classic two-species models, even when extended to their respective multidimensional versions. These conditions are obtained under fairly general assumptions on the mathematical form of the functions modelling the mutualistic inter...

The goal of a future free from schistosomiasis in Ghana can be achieved through integrated strategies, targeting simultaneously several stages of the life cycle of the schistosome parasite. In this paper, the transmission of schistosomiasis is modeled as a multi-scale 12-dimensional system of ODEs that includes vector-host and within-host dynamics...

In this paper, deterministic and stochastic SEIRI epidemic models featuring a distributed latent period and general, unspecified nonlinear incidence and growth rates for the susceptible class are proposed and investigated from a stability viewpoint. By applying Lyapunov–LaSalle invariance principle, we first obtain sufficient conditions for the glo...

Predation is a major cause of early-stage mortality for prey individuals, which are often forced to use refuges in order to reduce the risk of being consumed. The ability of certain genotypes in a prey population to reach a size refuge from predation may contribute significantly to the preservation of community diversity. We investigate how the spe...

We analyze the dynamics of three models of mutualism, establishing the global stability of coexisting equilibria by means of Lyapunov's second method. This further establishes the usefulness of certain Lyapunov function-als of an abstract nature introduced in an earlier paper. As a consequence, it is seen that the use of higher order self-limiting...

This paper proposes and investigates a delayed model for the dynamics and control of a mosquito population which is subject to an integrated strategy that includes pesticide release, the use of mechanical controls and the use of the sterile insect technique (SIT). The existence of positive equilibria is characterized in terms of two threshold quant...

We analyze the global stability of the coexisting equilibria for several models of commensalism, first by devising a procedure to modify several Lyapunov functionals which were introduced earlier for corresponding models of mutualism, further confirming their usefulness. It is seen that commensalism promotes global stability, in connection with hig...

This paper proposes and investigates a model for the spread of an infection into a plant population, considering the effects of both primary and secondary infections. We determine the basic reproduction number of the plant pathogens R 0 and prove that if R 0 > 1, then the positive equilibrium is globally stable, provided that several auxiliary ineq...

It is conceivable that genetically modified mosquitoes could stop the spread of malaria, by outcompeting the wild mosquitoes and interfering with their reproductive processes, and genetically inheriting and further transmitting a diminished potential to carry Plasmodium.To get insight into the possible outcomes, we formulate an ODE model for the in...

It is conceivable that genetically modified mosquitoes could stop the spread of malaria, by outcompeting the wild mosquitoes and interfering with their reproductive processes, and genetically inheriting and further transmitting a diminished potential to carry Plasmodium. To get insight into the possible outcomes, we formulate an ODE model for the i...

Motivated by considerations on the success of integrated pest management strategies and on the associated economically relevant thresholds, this paper is concerned with the finite time dynamics of a class of impulsive functional differential systems with delay. By using an approach based on the Lyapunov–Razumikhin method, we determine sufficient co...

This paper deals with the dynamics of a class of hybrid dynamical systems, which are subject to time-dependent impulsive perturbations within a finite-time interval and describe control strategies for integrated pest management. By using suitably defined Lyapunov functionals, sufficient conditions for the finite-time contractive stability of the nu...

This paper investigates the behavior of a Cohen-Grossberg neural network composed of two neurons which are subject to periodic impulsive perturbations. By employing Mawhin's continuation theorem, we determine sufficient conditions for the existence of semi-trivial periodic solutions. The asymptotic stability of these solutions is then investigated...

We analyze the dynamics of a disease propagation model with relapse under the assumption that the incidence of infection is given in an abstract, possibly bi-nonlinear form. Sufficient conditions for the local stability of equilibria are obtained by means of Lyapunov’s second method and it is shown that global stability can be attained under suitab...

A single species model which is subject to periodic impulsive perturbations is investigated from the viewpoint of finding sufficient conditions for permanence, for the existence of periodic solutions, and for their global asymptotic stability. First, an auxiliary equation, whose solutions are continuous functions but which incorporates the effects...

By the superficial grafting of monochlorotriazinyl-β-cyclodextrin (MCT-β-CD) on a special paper (Japanese veil), hosting nanocavities are generated, which can include certain guest chemicals for special protection effects (antibacterial nanocoatings, deodorants, UV protector etc). The original results obtained in the experimental research have been...

A two-prey one-predator food web model with an abstract functional response of the predator is considered as being subject to impulsive controls, in the form of periodic predator release and pesticide spraying. Sufficient conditions for the local and global stability of the prey-free periodic solution are established by using Floquet theory and com...

The dynamics of a n-prey one-predator food web model which is subject to impulsive controls is studied from the viewpoint of finding suffi-cient conditions for the extinction of prey and for prey and predator perma-nence. Using the Floquet theory of impulsively perturbed systems of ordinary differential equations, the local and global stability of...

We consider the dynamics of a general stage-structured predator–prey model which generalizes several known predator–prey, SEIR, and virus dynamics models, assuming that the intrinsic growth rate of the prey, the predation rate, and the removal functions are given in an unspecified form. Using the Lyapunov method, we derive sufficient conditions for...

We consider a two-patch SI model of integrated pest management with dispersal of both susceptible and infective pests between patches. A biological control, consisting of the periodic release of infective pests and a chemical control, consisting of periodic and impulsive pesticide spraying, are employed in order to maintain the size of the pest pop...

Insect pests are common but undesirable elements in ecosystems and represent thorny problems for most developing countries. To prevent pest outbreaks, growers often resort to insect–pathogenic viruses rather than to pesticides which affect human health and the environment. The purpose of this paper is to investigate a new age-structured pest manage...

This paper investigates a compartmental pest management model which divides the pest population into a susceptible and an infective class, while also including a class of pathogenic viruses. The model is age-structured, in the sense that it accounts for the differences in the amounts of pathogenic viruses released by infective pests at various infe...

In this paper, we consider an integrated pest management model with disease in the pest and a stage structure for its natural predator, which is subject to impulsive and periodic controls. A nonlinear incidence rate expressed in an abstract form, is used to describe the propagation of the disease, which is spread through the periodic release of inf...

In this paper, we consider a variable yield model of a single-species growth in a well-stirred tank containing fresh medium, assuming the instances of time as triggering factors in which the nutrient refilling process and the removal of microorganisms by the uptake of lethal external antibiotic are initiated. It is also assumed that the periodic nu...

In this paper, the bifurcation of nontrivial periodic solutions for an impulsively perturbed system of ordinary differential equations which models an integrated pest management strategy is studied by means of a fixed point approach. A biological control, consisting in the periodic release of infective pests, and a chemical control, consisting in p...

We consider the global dynamics of a virus propagation model in which infective cells pass through several successive stages, assuming that the incidence of infection and the removal rate of the virus are nonlinear func-tions given in an abstract, unspecified form. Suitable Lyapunov functionals are constructed to establish the existence of a thresh...

We hereby consider a two-patch SI integrated pest man-agement model with dispersal of susceptible pests between patches, which is subject to periodic impulsive biological and chemical controls. The biological control consists in the periodic release of infective pests, in a constant amount, while the chemical control consists in periodic pesticide...

The dynamics of an impulsively controlled three-trophic food chain system with general nonlinear functional responses for the intermediate consumer and the top predator are analyzed using the Floquet theory and comparison techniques. It is assumed that the impulsive controls act in a periodic fashion, the constant impulse (the biological control) a...

From a practical point of view, the most efficient strategy for pest control is to combine an array of techniques to control the wide variety of potential pests that may threaten crops in an approach known as integrated pest management (IPM). In this paper, we propose a predator–prey (pest) model of IPM in which pests are impulsively controlled by...

This paper investigates the onset of nontrivial periodic solutions for an integrated pest management model which is subject to pulsed biological and chemical controls. The biological control consists in the periodic release of infective individuals, while the chemical control consists in periodic pesticide spraying. It is assumed that both controls...

This paper deals with an impulsive predator-prey model with Beddington–DeAngelis functional response and time delay, in which the evolution of the predators takes them through two stages, juvenile and mature. It is assumed that only mature predators are able to hunt for prey and reproduce and the time delay is understood as being the time spent by...

Let X be a real Banach space, let A:D(A)⊂X→X be a linear operator which is the infinitesimal generator of a (C0)-semigroup and let B:D⊂X→X be a nonlinear perturbation which is continuous on level sets of D with respect to a lower semicontinuous (l.s.c.) functional φ. We discuss the existence of a nonlinear semigroup S providing mild solutions to th...

Given a linear operator A which satises a generalized dissipativity condition in terms of a \uniqueness function" w and its nonlinear continuous perturbation B in a real Banach space X, we discuss the construction of a nonlinear semigroup S providing mild solutions for the semilinear abstract Cauchy problem (SP) u 0 = (A + B)u(t);t > 0 and u(0) = x...

In this paper, we propose two impulsive differential systems concerning biological and, respectively, integrated pest management strategies. In each case, it is observed that there exists a globally asymptotically stable susceptible pest-eradication periodic solu-tion on condition that the amount of infective pests released periodically is larger t...

In this paper, we consider an integrated pest management model which is impulsively controlled by means of biological and chemical controls. These controls are assumed to act in a periodic fashion, a nonlinear incidence rate being used to account for the dynamics of the disease caused by the application of the biological control. The Floquet theory...

The global properties of a predator-prey model with nonlinear functional response and stage structure for the predator are studied using Lyapunov functions and LaSalle’s invariance principle. It is found that, under hypotheses which ensure the uniform persistence of the system and the existence of a unique positive steady state, a feasible a priori...

Global dynamics of a compartmental model which describes virus propagation in vivo is studied using the direct Lyapunov method, where the incidence rate of the infection and the removal rate of the virus are assumed to be nonlinear. In the case where the functional quotient between the force of infection and the removal rate of the virus is a nonin...

The asymptotic behavior of a stage-structured predator-prey system is studied using the theory of finite dimensional competitive systems. Using natural conditions on the persistency constant for prey and on the reproduction rate of the mature predators, it is found that the system under consideration has a unique positive equilibrium, which is glob...

Let X be a real Banach space, let A : D(A) X ! X be the generator of a (C0)-contraction semigroup on X and let B : D (0,T)◊X ! X be a continuous operator. Under a combination of Pavel's subtangential condition, a semilinear stability condition defined in terms of a uniqueness function w : (0,T) ◊ R ! R and suitable connectedness and closedness asum...

If ＄￥alpha￥in(0,1)＄ is given and ＄T_{1}=￥{T_{1}(t);t￥geq 0￥},＄ ＄T_{2}=￥{T_{2}(t);t￥geq 0￥}＄ are ＄C_{0}＄-semigroups defined on a real Banach space (X, ＄|￥cdot|＄ ), we indicate sufficient conditions for the existence of ＄x_{￥alpha}￥in X＄ such that |T_{1}(t)x_{￥alpha}-T_{2}(t)x_{￥alpha}|=O(t^{￥alpha})＄ and ＄|T_{1}(t)x_{￥alpha}-T_{2}(t)x_{￥alpha}|￥neq...

The initial value problem for the generalized Kortweg-deVries equa- tion ut + (f(u))x + uxxx = 0, t,x 2 R is treated in terms of a recent theory of nonlinear operator semigroups associated with semilinear evolution equations in Banach spaces. Two operators A and B are introduced to represent the linear and nonlinear dierential operators in the equa...

An approximation theory for semilinear evolution equations is treated in terms of convergence theorems of nonlinear operator semigroups and three types of fundamental results are established. For a semilinear evolution problem in a general Banach space, a se- quence of approximate evolution problems is formulated and so-called consistency and stabi...

From a practical point of view, the most efficient strategy for pest control is to combine an array of techniques to control the wide variety of potential pests that may threaten crops in an ap-proach known as integrated pest management (IPM). In this paper, we propose a predator-prey (pest) model of IPM in which pests are impulsively controlled by...

Given a semilinear problem of the form (SP) u0(t) = (A + B)u(t),t > 0; u(0) = x 2 D X, where X is a real Banach space and B is its nonlinear perturbation, whose continuity is localized using a lower semicontinuous functional ', a sequence of approximating semilinear problems is formulated and the convergence of the associated approximating nonlinea...

RESUMEN RESUMEN Global dynamics of a compartmental model which describes virus propagation in vivo is studied using the direct Lyapunov method , where the incidence rate of the infection and the removal rate of the virus are assumed to be nonlinear . In the case where the functional quotient between the force of infection and the removal rate of...