Search

Rotating an axially symmetric rigid body on a horizontal plane is rather a common and simple experience, but this experience has attracted a great deal of interests due to it exhibiting novel features and containing fairly complicated mechanics. This paper is concerned with the threedimensional rotational motion of a rigid tube on a plane.We present the governing dynamical equations of this motion and give a numerical treatment, based on which we discuss the nutation of tube and simulate the trajectory of tube end. We also discuss how fast the angular velocity should be in order to initiate an uninterrupted, steady rotational motion. Then the air lift related to such a three-dimensional rotation of tube is modeled by using Kutta-Joukowski law. By employing this model, we show that the air lift indeed "lift" the tube head during rotating. [ABSTRACT FROM AUTHOR]

This paper is concerned with a stochastic population model with Allee effect and jumps. First, we show the global existence of almost surely positive solution to the model. Next, exponential extinction and persistence in mean are discussed. Then, we investigated the global attractivity and stability in distribution. At last, some numerical results are given. The results show that if attack rate a is in the intermediate range or very large, the population will go extinct. Under the premise that attack rate a is less than growth rate r, if the noise intensity or jump is relatively large, the population will become extinct; on the contrary, the population will be persistent in mean. The results in this paper generalize and improve the previous related results. [ABSTRACT FROM AUTHOR]

Because of mutations and selection, pathogens can manage to resist to drugs. However, the evolution of an asexual population (e.g., viruses, bacteria and cancer cells) depends on some external factors (e.g., antibiotic concentrations), and so understanding the impact of the environmental changes is an important issue. This paper is devoted to model this problem with a nonlocal diffusion PDE, describing the dynamics of such a phenotypically structured population, in a changing environment. The large-time behaviour of this model, with particular forms of environmental changes (linear or periodically fluctuations), has been previously developed. A new mathematical approach (limited to isotropic mutations) has been developed recently for this problem, considering a very general form of environmental variations, and giving an analytic description of the full trajectories of adaptation. However, recent studies have shown that an anisotropic mutation kernel can change the evolutionary dynamics of the population: some evolutive plateaus can appear. Thus the aim of this paper is to mix the two previous studies, with an anisotropic mutation kernel, and a changing environment. The main idea is to study a multivariate distribution of (2n) "fitness components". Its generating function solves a transport equation, and describes the distribution of fitness at any time. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a control strategy for applying the Sterile Insect Technique (SIT) to eliminate the population of Aedes mosquitoes which are vectors of various deadly diseases like dengue, zika, chikungunya... in a wide area. We use a system of reaction-diffusion equations to model the mosquito population and study the effect of releasing sterile males. Without any human intervention, and due to the so-called hair-trigger effect, the introduction of only a few individuals (eggs or fertilized females) can lead to the invasion of mosquitoes in the whole region after some time. To avoid this phenomenon, our strategy is to keep releasing a small number of sterile males in the treated zone and move this release forward with a negative forcing speed c to push back the invasive front of wild mosquitoes. By using traveling wave analysis, we show in the present paper that the strategy succeeds in repulsing the population while consuming a finite amount of mosquitoes in any finite time interval even though we treat a moving half-space {x > ct}. Moreover, we succeed in constructing a 'forced' traveling wave for our system moving at the same speed as the releases. We also provide some numerical illustrations for our results. [ABSTRACT FROM AUTHOR]

Many researchers began doing studies about pandemic COVID-19 which began to spread from Wuhan, China in 2019 to all around the world and so far, numerous researches have been done around the world to control this contagious disease. In this paper, we proposed a MSIlIhR-V mathematical model to study the spreading of pandemic COVID-19. This paper is aimed to study the vaccination effect in the control of the disease propagation rate. Another goal of this paper is to find the maximum number of susceptible people, minimum number of infected people, and the best value for number of vaccination people. The Jacobian matrix was obtained in the virus absenteeism equilibrium point for the proposed dynamical system. The spectral radius method was applied to find the analytical formula for the reproductive number. Reproductive number is one of the most benefit and important tools to study of epidemic model's stability and instability. In the following, by adding a controller to the model and also using the optimal control strategy, model performance was improved. To validate of the proposed models with controller and without controller we use the real data of COVID-19 from 4 January, 2021 up to 14 June, 2021 in Iran. Maple and MATLAB software's will be used for programming. We will use Maple software for analytical parts and MATLAB software for numerical and simulation parts. [ABSTRACT FROM AUTHOR]

In this paper, we consider a stochastic SIRS epidemic model with nonlinear incidence and Markovian switching. By using the stochastic calculus background, we establish that the stochastic threshold ℜswt can be used to determine the compartment dynamics of the stochastic system. Some examples and numerical simulations are presented to confirm the theoretical results established in this paper. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model for tumour-immune response interactions in the perspective of immunotherapy by immune checkpoint inhibitors (ICIs). The model is of the nonlocal integro-differential Lotka-Volterra type, in which heterogeneity of the cell populations is taken into account by structuring variables that are continuous internal traits (aka phenotypes) present in each individual cell. These represent a lumped "aggressiveness", i.e., for tumour cells, malignancy understood as the ability to thrive in a viable state under attack by immune cells or drugs – which we propose to identify as a potential of de-differentiation–, and for immune cells, ability to kill tumour cells, in other words anti-tumour efficacy. We analyse the asymptotic behaviour of the model in the absence of treatment. By means of two theorems, we characterise the limits of the integro-differential system under an a priori convergence hypothesis. We illustrate our results with a few numerical simulations, which show that our model reproduces the three Es of immunoediting: elimination, equilibrium, and escape. Finally, we exemplify the possible impact of ICIs on these three Es. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in modeling the production of mucus by diatoms under the constraint of a nutrient limitation and carbon overabundance. The initial questioning comes from the observation of the so-called "liga" on the Acquitaine coast. The biological origin of the phenomenon is presented and discussed based on the existing literature. An original mathematical model incorporating mucus secretion is proposed and its theoretical properties are analized: well-posedness and differentiability with respect to the model parameters. Finally, numerical experiments are provided, investigating the possibility of parameter identification for the model using chemostat-type experiments. [ABSTRACT FROM AUTHOR]

We consider the governing equations for the motion of the viscous fluids in two moving domains and an evolving surface from both energetic and thermodynamic points of view. We make mathematical models for multiphase flow with surface flow by our energetic variational and thermodynamic approaches. More precisely, we apply our energy densities, the first law of thermodynamics, and the law of conservation of total energy to derive our multiphase flow system with surface tension and flow. We study the conservative forms and conservation laws of our system by using the surface transport theorem and integration by parts. Moreover, we investigate the enthalpy, the entropy, the Helmholtz free energy, and the Gibbs free energy of our model by applying the thermodynamic identity. The key idea of deriving surface tension and viscosities is to make use of both the first law of thermodynamics and our energy densities. [ABSTRACT FROM AUTHOR]

New technologies play a central role in damage prevention of artistic and cultural heritage. The literature is ourishing of mathematical models that describe the process of corrosion due to weathering and exposition to pollutants. These models consist of differential equations or partial differential equations that need to be solved approximately by numerical methods. This paper aims to describe the mathematical models in the literature and the numerical methods used for their solution. We focus in particular on the studies of corrosion of pieces of art made of stone, lime mortar concrete and metal. [ABSTRACT FROM AUTHOR]

Cocoa mirid, Sahlbergella singulars, is the major pest of cocoa (Theobroma cacao) responsible of several damage in plots in West Africa and particularly in Cameroon. Occasional damage accounts for 30 40% of pod losses. However, when miridae affect the foliage, gradual wilting occurs and eventually, tree death. A few studies have focused on describing the time evolution of Miridae in the plot in Cameroon, yet numerous questions remain. The aim of this paper is to estimate and control the losses of production caused by the bites of miridea. To do this, we will formulate and study a mathematical model for the dynamics of pods that takes into account the feeding and egg-laying of adults miridae on pods. We present the theoretical analysis of the model. More precisely, we compute equilibria and derive a threshold parameter that determines the presence or not of miridae in the plot. Throughout numerical simulations, we found that miridae can cause approximately 39.21% of production losses (which represents approximatively USD 1276.8 revenue losses) when initially, one has 1200 plants in the plot. After, we aim to increase cocoa production through optimal control. Optimal control consists in reducing density the number of nymphs and adults miridae in the plot. We studied the controlled model and we found that losses with control shrink to 20.58% which corresponds to USD670.32 income revenue. [ABSTRACT FROM AUTHOR]

In this paper, we consider a steady state multi-anticipative traffic model and we provide necessarily and sufficient conditions for the existence of traveling solutions. In our work, the word "traveling" means that the distance between two consecutive vehicles travels continuously between two different states. As application to our result, we show that taking a strictly concave optimal velocity, we can construct a traveling solution such that the distance between two vehicles decreases. The existence, uniqueness and the study of the asymptotic behavior of such solutions is done at the level of the Hamilton-Jacobi equation. [ABSTRACT FROM AUTHOR]

This paper investigates a three-strategy (cooperators, toxin producers, and cheaters) N-player division of labor game in bacterial populations. We construct the replicator equation to discuss the evolution of the frequency of the three strategies. Firstly, we prove that the interior equilibrium is always unstable, the three strategies cannot coexist. Secondly, according to Sotomayor's theorem, the system undergoes transcritical bifurcation. Furthermore, the sensitivity of the two-dimensional evolutionary state diagrams to the third parameter (toxin rate, absorption rate, toxin quantity, etc) is analyzed. In summary, high toxicity rates, high levels of toxins, and low levels of competition tend to promote cooperation. All players choose to perform the task, and the cheater disappears. When the absorption rate of cooperators is high enough, only cooperators exist in the population over time. When the absorption rate of the cooperator is low, and the absorption rate of the toxin producer is greater than the threshold, the cooperator and the toxin producer coexist. All players perform the task. Finally, the triangle diagrams and three-dimensional diagrams are presented, which show the initial conditions of the three strategies also affect the dynamic results. As the amount of toxin increases, the range of players who choose to perform tasks widens. [ABSTRACT FROM AUTHOR]

Developing new approaches that help control the spread of infectious diseases is a critical issue for public health. Such approaches must consider the available resources and capacity of the healthcare system. In this paper, we present a new mathematical approach to controlling an epidemic model by investigating the optimal control that aims to bring the output of the epidemic to target a desired disease output yd = (ydi)i∈{0,...,N}. First, we use the state-space technique to transfer the trajectory controllability to optimal control with constraints on the final state. Then, we use the fixed point theorems to determine the set of admissible controls and solve the output trajectory controllability problem. Finally, we apply our method to the model of a measles epidemic, and we give a numerical simulation to illustrate the findings of our approach. [ABSTRACT FROM AUTHOR]

In this paper, we present and analyze an age-structured tumor immune model. Based on the fact that tumor cells of different ages tend to exhibit different physiological behaviors, we consider the age structure of tumor cells, age-based proliferation function and age-dependent death function in the model. The threshold R0 for the existence of tumor-free steady state is derived. It is found that if R0 > 1, the tumor-free steady state is not only locally stable but also globally stable. Moreover, numerical simulation shows that the threshold R0 may be regarded as an index to reflect the ability of "tumor immune surveillance", that is, the smaller the R0, the better the ability of tumor immune surveillance. If R0 > 1, it is proved that the tumor steady state is existent and uniformly persistent. The local stability of the tumor steady state is investigated under some further conditions besides R0 > 1. In the end, we estimate the system parameters, verify the theoretical results and analyze some system parameters' sensitivities. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic SEIR epidemic model is studied with alertness and vaccination. The goal is to stabilize the infectious disease system quickly. The dynamic behavior of the model is analyzed and an integral sliding mode controller with distributed compensation is designed. By using Lyapunov function method, the sufficient conditions for the existence and uniqueness of global positive solutions and the existence of ergodic stationary distributions are obtained. The stochastic center manifold and stochastic average method are used to simplify the system into a one-dimensional Markov diffusion process. The stochastic stability and Hopf bifurcation are analyzed using singular boundary theory. An integral sliding mode controller with non-parallel distributed compensation is designed by linear matrix inequality (LMI) method, which realizes the stability of system and prevents the outbreak of epidemic disease. The correction of theoretical analysis and the effectiveness of controller are validated using numerical simulation performed in MATLAB/Simulink. [ABSTRACT FROM AUTHOR]

The Spatio-temporal pattern induced by self-diffusion of a predator-prey model with Boiling type III functional response that incorporates the hunting cooperation between predators has been investigated in this paper. For the local model without structure, the stability of non-negative equilibria with or without collaborative hunting in predators is studied. For the Spatio-temporal model, we analyze the effect of hunting cooperation term on diffusion-driven Turing instability of the homogeneous positive equilibria. To get an idea about patterns formation near the Turing bifurcation, we derive and give a detailed study of the amplitude equation using the multiple-scale analysis. Our result shows that hunting cooperation plays a crucial role in determining the stability and the Turing bifurcation of the model, which is in sharp contrast to the case without cooperation in hunting. Furthermore, some numerical simulations are illustrated to visualize the complex dynamic behavior of the model. [ABSTRACT FROM AUTHOR]

A large necrotic core increases the risk of atherosclerotic plaque instability. Statins can delay the growth of necrotic core in plaques, but the kinetic mechanism of statins in slowing down the necrotic core has not yet been addressed in detail. In this paper, a mathematical model is governed by a system of advection-diffusion-reaction equations coupling of the porous nature of vessel wall is established and applied to illustrate the plaque growth with lipid-rich necrotic core (LRNC) with and without statins using finite element method. We study the influence of LRNC plaque growth for different drug concentrations at different time intervals. The results showed that the drug use at different time points has a significant impact on the treatment efficacy. Compared with short-term, low-dose treatment, early statin treatment with high dose showed more pronounced effects on reducing the low-density lipoprotein (LDL) cholesterol, decreasing the volume of necrotic core, changing the characteristics of plaques, and improving the plaque stability. The model is validated by comparing with the clinical data, and may be used to predict the progression of LRNC plaque and the effects of statin therapy. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the convergence of the Faedo-Galerkin approximations, in a strong sense, to a strong T-periodic solution of the torso-coupled bidomain model where T is the period of activation of the inner wall of the heart. First, we define the torso-coupled bidomain operator and prove some of its more important properties for our work. After, we define the abstract evolution system of the equations that are associated with torso-coupled bidomain model and give the definition of a strong solution. We prove that the Faedo-Galerkin's approximations have the regularity of a strong solution, and we find that some restrictions can be imposed over the initial conditions, so that this sequence of Faedo-Galerkin fully converges to a strong solution of the Cauchy problem. Finally, these results are used for showing the existence a strong T-periodic solution. [ABSTRACT FROM AUTHOR]

This research paper proposes and discusses a conceptual modelling of both growth of tumours in presence of immortal multipotent cancer stem cells (CSCs) and of several lineages of differentiated tumour cells (CCs). The replication of CSCs is assumed symmetric or asymmetric with a prescribed mean ratio and mitosis and apoptosis are taken into account for the CCs aging. Replication can be hindered by the local crowding of the cells in the vicinity of the mother cell. The model is implemented in the framework of 3D cellular automata (CA) whose dynamics is governed by stochastic rules. Some simulations are displayed showing the growth of a tumour and the fractions of different lineages and age classes of CCs. Then, an approach that considers the same dynamics of aging, replication, and apoptosis, but with the aim to study the time evolution of the fractions of the different lineages and age classes of cells averaged over the total volume is presented. The dynamics is governed by a system of ordinary differential equations (ODEs), hence by deterministic rules. Numerical simulations of the solution of this system show qualitative similarity with the CA results, although the crowding effect is no longer a local effect, but also averaged over the total volume. The Appendix provides the proof of the mathematical well-poscdness of this model in a general framework. [ABSTRACT FROM AUTHOR]

This research is devoted to Fornasnisi-Marchesini model (FM). More precisely, the investigation of the control problem for the second model discrete-time FM. The model takes into account the random packet loss and quantization errors in the network environment. So our modelling method has the potential to achieve a better stabilization effects. Random packet dropouts, time delays and quantization are taken into consideration in the feedback control problem simultaneously. Measured signals are quantized before being communicated. A logarithmic quantizer is utilized and quantized signal measurements are handled by a sector bound method. The random packet dropouts are modeled as a Bernoulli process. A control law model which depends on packet dropouts and quantization is formulated. Notably, we lighten the assumptions by using the Schur complement. Besides, both a state feedback controller and an observer-based output feedback controller are designed to ensure corresponding closed-loop systems asymptotically stability. Sufficient conditions on mean square asymptotic stability in terms of LMIs have been obtained. Finally, two numerical example show the feasibility of our theoretical results. [ABSTRACT FROM AUTHOR]

A nonlocal theory for thermoelastic materials with voids based on Mindlin's strain gradient theory was derived in this paper with some qualitative properties. We have also established the size effect of nonlocal heat conduction with the aids of extended irreversible thermodynamics and generalized free energy. The obtained system of equations is a coupling of three equations with higher gradients terms due to the length scale parameters ϖ and l. This poses some new mathematical difficulties due to the lack of regularity. Based on nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions to the one dimensional problem. By an approach based on the Gearhart-Herbst-Prüss-Huang theorem, we prove that the associated semigroup is exponentially stable; but not analytic. [ABSTRACT FROM AUTHOR]

As cyber attacks have become more frequent, cyber insurance premiums have increased, resulting in the need for better modeling of cyber risk. Toward this direction, Jevtić and Lanchier [Insur. Math. Econ.91 (2020) 209–223] proposed a dynamic structural model of aggregate loss distribution for cyber risk of small and medium-sized enterprises under the assumption of a tree-based local-area-network topology that consists of the combination of a Poisson process, homogeneous random trees, bond percolation processes, and cost topology. Their model assumes that the contagion spreads through the edges of the network with the same fixed probability in both directions, thus overlooking a dynamic cyber security environment implemented in most networks, and their results give an exact expression for the mean of the aggregate loss but only a rough upper bound for the variance. In this paper, we consider a bidirectional version of their percolation model in which the contagion spreads through the edges of the network with a certain probability of moving toward the lower level assets of the network but with another probability of moving toward the higher level assets of the network, which results in a more realistic cyber security environment. In addition, our mathematical approach is quite different and leads to exact expressions for both the mean and the variance of the aggregate loss, and therefore an exact expression for the insurance premiums. [ABSTRACT FROM AUTHOR]

A hyperbolic model for diffusion, nonlfnear transport (or advection) and production of a scalar quantity, is considered. The model is based on a constitutive law of Cattaneo-Maxwell type expressing non-Fickian diffusion by means of a relaxation time relation. The production or source term is assumed to be of logistic type. This paper studies the existence and spectral stability properties of spatially periodic traveling wave solutions to this system. It is shown that a family of subcharacteristic periodic waves emerges from a local Hopf bifurcation around a critical value of the wave speed. These waves have bounded fundamental period and small-amplitude. In addition, it is shown that these waves are spectrally unstable as solutions to the hyperbolic system. For that purpose, it is proved that the Floquet spectrum of the linearized operator around a wave can be approximated by a linear operator whose point spectrum intersects the unstable half plane of complex numbers with positive real part. [ABSTRACT FROM AUTHOR]

In this paper, we establish a rigorous connection between a microscopic and a macroscopic pedestrians model on a convergent junction. At the microscopic level, we consider a "follow the leader" model far from the junction point and we assume that a rule to enter the junction point is imposed. At the macroscopic level, we obtain the Hamilton-Jacobi equation with a flux limiter condition at x = 0 introduced in Imbert and Monneau [Ann. Sci. l'École Normale Supér. 50 (2017) 357-414], To obtain our result, we inject using the "cumulative distribution functions" the microscopic model into a non-local PDE. Then, we show that the viscosity solution of the non-local PDE converges locally uniformly towards the solution of the macroscopic one. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study of spatial transformations of a radially symmetric flow in a shallow fluid-filled cylindrical cavity partially covered by a solid non-deformable film. The upper central part of the liquid has a free surface where an intense light beam is focused to produce a hot spot on the symmetry axis. The heating generates a divergent thermocapillary motion on the free surface, which causes the fluid to flow under the immovable solid film. The edge of this film induces thermal perturbations, which, at specific heat generation values, begin to increase and give rise to a gradual radial flow symmetry breakdown that visually demonstrates the onset of vorticity in the azimuthal plane. Three-dimensional calculations have been carried out based on the interfacial hydrodynamics equations using Comsol Multiphysics software. The results of numerical calculations confirm that the instability occurs in the area corresponding to the boundary between the free surface and the solid film. The motion in the azimuthal direction becomes more evident with the growth of heating intensity. The vorticity in the azimuthal plane makes the flow structure significantly more complex compared to the axisymmetric radial flow. Thus, there is a predominantly radial flow in the area of free surface and, at the same time, the vortices with the azimuthal velocity component are observed under the film. As in the experiment, the number of vortices is determined by the ratio of the area of free surface to the covered area. It is shown that the appearance of motion in the azimuthal direction depends on the joint action of several physical mechanisms, which have been initialized in the theoretical model by means of various piecewise thermal and mechanical conditions at the upper boundary. [ABSTRACT FROM AUTHOR]

Analysis of longitudinal vibration in a nanorod is an important subject in science and engineering due to its vast application in nanotechnology. This paper introduces a port-Hamiltonian formulation for the longitudinal vibrations in a nanorod, which shows that this model is essentially hyperbolic. Furthermore, it investigates the spectral properties of the associated system operator. Standard distributed control and feedback are shown not to be controllable nor stabilizing. [ABSTRACT FROM AUTHOR]

The Sterile Insect Technique (SIT) is a classic vector control method that has been successfully applied to fight against diverse insect plagues since the 1950s. In recent years, this strategy has been used to control mosquito populations, in order to limit the spread of the diseases they transmit. In this paper, we consider a system of reaction-diffusion equations to model the mosquito population and study the effect of the release of sterile mosquito males. Then, we propose to analyze the release in a limited area inside a wider area containing a natural mosquito population. We are interested in protecting a mosquito free region from invasion by mosquitoes from an exterior domain by controlling the population in a release band at the border between the two regions: we construct a barrier blocking the invasion of mosquitoes from the exterior. We adapt the geometric method of Lewis and Keener (see Lewis and Keener [SIAM J. Appl. Math.61 (2000) 293-316]) in this framework and extend their main result to find relations on the size of the release region and the density of the released sterile males that allow us to block the invasion. Numerical simulations are also performed to illustrate our results. [ABSTRACT FROM AUTHOR]

Atherosclerosis is a chronic disease which involves the build up of cholesterol and fatty deposits within the inner lining of the artery. It is associated with a progressive thickening and hardening of the arterial wall that result in narrowing of the vessel lumen and restriction of blood flow to vital organs. These events may cause heart attack or stroke, the commonest causes of death worldwide. In this paper we study the early stages of atherosclerosis via a mathematical model of partial differential equations of reaction-diffusion type. The model includes several key species and identifies endothelial hyperpermeability, believed to be a precursor on the onset of atherosclerosis. For simplicity, we reduce the system to a monotone system and provide a biological interpretation for the stability analysis according to endothelial functionality. We investigate as well the existence of solutions of traveling waves type along with numerical simulations. The obtained results are in good agreement with current biological knowledge. Likewise, they confirm and generalize results of mathematical models previously performed in literature. Then, we study the non monotone reduced model and prove the existence of perturbed solutions and perturbed waves, particularly in the bistable case. Finally, we extend the study by considering the complete model proposed initially, perform numerical simulations and provide more specific results. We study the consistency between the reduced and complete model analysis for a certain range of parameters, we elaborate bifurcation diagrams showing the evolution of inflammation upon endothelial permeability and LDL accumulation and we consider the effect of anti-inflammatory process on the system behavior. In this model, the regulation of atherosclerosis progression is mediated by anti-inflammatory responses that, up to certain extent, lead to plaque regression. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, by using the new concepts of monotonicity, pseudomonotonicity and hemicontinuity associated with the considered curvilinear integral functional, we investigate the well-posedness and well-posedness in generalized sense for a class of controlled variational inequality problems. More precisely, by introducing the approximating solution set of the considered class of controlled variational inequality problems, we formulate and prove some characterization results on well-posedness and well-posedness in generalized sense. Also, the theoretical developments presented in the paper are accompanied by illustrative examples. [ABSTRACT FROM AUTHOR]

The current paper is devoted to stochastic damped higher order KdV equation driven by Poisson process. We establish the well-posedness of stochastic damped higher-order KdV equation, and prove that there exists an unique invariant measure for non-random initial conditions. Some discussion on the general pure jump noise case are also provided. Some numerical simulations of the invariant measure are provided to support the theoretical results. [ABSTRACT FROM AUTHOR]

Acute Lymphoblastic Leukemia (ALL) accounts for the 80% of leukemias when coming down to pediatric ages. Survival of these patients has increased by a considerable amount in recent years. However, around 15 20% of treatments are unsuccessful. For this reason, it is definitely required to come up with new strategies to study and select which patients are at higher risk of relapse. Thus the importance to monitor the amount of leukemic cells to predict relapses in the first treatment phase. In this work, we develop a mathematical model describing the behavior of ALL, examining the evolution of a leukemic clone when treatment is applied. In the study of this model it can be observed how the risk of relapse is connected with the response in the first treatment phase. This model is able to simulate cell dynamics without treatment, representing a virtual patient bone marrow behavior. Furthermore, several parameters are related to treatment dynamics, therefore proposing a basis for future works regarding childhood ALL survival improvement. [ABSTRACT FROM AUTHOR]

Rayleigh-Taylor instability (RTI) is of critical important in a broad range of natural and industrial processes and is an intellectual challenge for theoretical studies. In this work, we analyze the scale-dependent linear and nonlinear Rayleigh{Taylor (RT) dynamics within the group theory approach. We link the governing equations, through an associated dynamical system based on space groups, to a momentum model based on scaling transformations. In doing so, we precisely derive expressions for the buoyancy and drag parameters of the momentum model, exactly integrate the model equations and determine solutions for bubbles and for spikes in both early-time and late-time regimes. In particular, we focus on the general situation in which the instability is driven by an acceleration having power-law time dependence. Our analysis provides extensive benchmarks for future research. [ABSTRACT FROM AUTHOR]

Ferromagnetic materials such as the ferrites are used in the electronic and energy industries. Here, we concentrate on a complex Kraenkel-Manna-Merle system in a ferrite, under some coefficient constraints. An N-fold Darboux transformation of that system is presented via an existing Lax pair, where N is a positive integer. An N-fold generalized Darboux transformation, which admits one spectral parameter, is proposed through a limit procedure. One-, two- and three-soliton solutions of that system are determined via that N-fold Darboux transformation. The second-order and third-order degenerate soliton solutions of that system are derived via that N-fold generalized Darboux transformation. Those solitons are graphically represented for the magnetization and external magnetic field related to a ferrite. [ABSTRACT FROM AUTHOR]

The steady state Stokes-Brinkman equations in a thin tube structure is considered. The Brinkman term differs from zero only in small balls near the ends of the tubes. The boundary conditions are: given pressure at the inflow and outflow of the tube structure and the no slip boundary condition on the lateral boundary. The complete asymptotic expansion of the problem is constructed. The error estimates are proved. The method of partial asymptotic dimension reduction is introduced for the Stokes-Brinkman equations and justified by an error estimate. This method approximates the main problem by a hybrid dimension problem for the Stokes-Brinkman equations in a reduced domain. [ABSTRACT FROM AUTHOR]

Antibiotic resistance is one of the greatest public health threats today, mainly due to the non-rational use of antibiotics. Acinetobacter baumannii is an example of a microorganism with high antibiotic resistance that has developed rapidly in recent years. Consequently, only a few lastresort antibiotics, such as colistin, are currently effective against it. In this work, we propose a random agent-based computational model to describe the evolution of colistin-resistant A. baumannii in the population of Valencia (Spain) and to predict its impact both on the whole population and by age groups. The agent- based model uses a synthetic population of individuals with a vector of characteristics or state variables. These variables change over time based on a series of random events with certain conditional probabilities. The synthetic population statistical features and the probabilities have been found in demographic and hospital databases. One of these probabilities, the probability of infection by a resistant strain, has been modeled using random differential equations. The model takes into account antibiotic consumption as the primary driving force of variation and assumes non-rewersibility of resistance as the worst-case scenario. The agent-based model calibration and the selection of a real-world representative set of solutions have been carried out using the Partide Swarm Optimization evolutionary algorithm. This approach takes into account the inherent stochasticity of the model and the uncertainty of the data. Finally, projections of the incidence and absolute cases of colistin-resistant A. baumannii have been performed. Our results suggest that, if the same consumption pattern continues, the ervolution of the colistin-resistant strain proportion will be exponential, exceeding 50% in 2025. Additionally, the results reveal that, despite the low incidence in Valencian hospitals, the impact on people over 60 years old will be more significant in terms of the number of cases. Based on these findings, it can be deduced that colistin will cense to be an effective antibiotic in the coming years, negatively impacting the human population, especially the most advanced age groups. [ABSTRACT FROM AUTHOR]

In the study of cancer evolution and therapeutic strategies, scientific evidence shows that a key dynamics lies in the tumour-environment interaction. In particular, oxygen concentration plays a central role in the determination of the phenotypic heterogeneity of cancer cell populations, whose qualitative and geometric characteristics are predominant factors in the occurrence of relapses and failure of eradication. We propose a mathematical model able to describe the eco-evolutionary spatial dynamics of tumour cells in their adaptation to hypoxic microenvironments. As a main novelty with respect to the existing literature, we combine a phenotypic indicator reflecting the experimentally-observed metabolic trade-off between the hypoxia-resistance ability and the proliferative potential with a 2d geometric domain, without the constraint of radial symmetry. The model is settled in the mathematical framework of phenotype-structured population dynamics and it is formulated in terms of systems of coupled non-linear integro-differential equations. The computational outcomes demonstrate that hypoxia-induced selection results in a geometric characterization of phenotypic-defined tumour niches that impact on tumour aggressiveness and invasive ability. Furthermore, results show how the knowledge of environmental characteristics provides a predictive advantage on tumour mass development in terms of size, shape, and composition. [ABSTRACT FROM AUTHOR]

In this article we derive the equations that constitute the mathematical model of the full von Kármán beam with temperature and microtemperatures effects. The nonlinear governing equations are derived by using Hamilton principle in the framework of Euler–Bernoulli beam theory. Under quite general assumptions on nonlinear damping function acting on the transversal component and based on nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions to the derived problem. Then using the multiplier method, we show that solutions decay exponentially. Finally we consider the case of zero thermal conductivity and we show that the dissipation given only by the microtemperatures is strong enough to produce exponential stability. [ABSTRACT FROM AUTHOR]

This work presents a model of a harvested population in a multisite environment. Locally it has the shape of the Gordon-Schaefer model. This model gives rise, placing us in the case of a fishery, to an equilibrium of the stock and the fishing effort and, therefore, of the yield that is obtained per unit of time. Considering that the management of the fishery can act on the fishing costs, the yield is optimized as a function of the cost. The objective of the work is to compare the maximum obtained yield in two extreme cases: unconnected sites and connected sites with rapid movements of both the stock and the fishing effort. The analysis of the model, first in an environment with two sites and later with any number of them, makes it possible to establish the conditions for one of the two cases to be more favorable from the point of view of the yield. In this way, it is proposed towards which of the two compared cases management should be directed. [ABSTRACT FROM AUTHOR]

Two models of recrystallization are proposed taking into account the convective flux of impurity exchange between the polycrystalline and the thin-film coating. The special boundary modes of recrystallization described by the single-phase and two-phase Stefan problems with the boundary condition at coated surface containing the convective term. The exact solutions of the formulated problems corresponding to the grain-boundary concentration of impurities are obtained. The detail theoretical analysis focused on the third type problem shows that the concentration of impurities and the width of the recrystallized layer increase with an increase in the annealing time. An increase in intensity of impurity exchange between the polycrystalline and the coating promotes an increase in the width of the recrystallized layer. The recrystallization front position increases with an increase in the surface concentration of impurities and it decreases with an increase in the intensity of the impurity flux from the surface. The rate of recrystallization kinetics increases with an increase in the intensity of impurity exchange between the polycrystalline and the coating. [ABSTRACT FROM AUTHOR]

Epidemic source detection is the problem of identifying the network node that originated an epidemic from a partial observation of the epidemic process. The problem finds applications in different contexts, such as detecting the origin of rumors in online social media, and has been studied under various assumptions. Different from prior studies, this work considers an epidemic process on a finite graph that starts on a random node (epidemic source) and terminates when all nodes are infected, yielding a rooted and directed epidemic tree that encodes node infections (i.e., a directed spanning tree of the graph with every edge directed away from the epidemic source). Assuming knowledge of the underlying graph and the undirected spanning tree (i.e., the infection edges but not their directions), can the epidemic source be accurately identified? This work tackles this problem by introducing the epicenter, an efficient estimator for the epidemic source, and thus, the direction of every edge in the epidemic tree. When the underlying graph is vertex-transitive the epicenter can be computed in linear time and it coincides with the well-known distance center of the epidemic tree. Moreover, on a complete graph the epicenter is also the most likely estimator for the source. Finally, the accuracy of the epicenter is evaluated numerically on five different graph models and the performance strongly depends on the graph structure, varying from 31% (on complete graphs) to 13% (on sparse power-law graphs). However, for all graph models considered the epicenter exhibited an accuracy higher than the distance center, being three times more accurate on sparse power-law graphs. [ABSTRACT FROM AUTHOR]

It is now recognized that the personal well-being of an individual can be evaluated numerically. The related utility ("happiness") profile would give at each instant t the degree u(t) of happiness. The moment-based approach to the evaluation of happiness introduced by the Nobel laureate Daniel Kahneman establishes that the experienced utility of an episode can be derived from real-time measures of the pleasure and pain that the subject experienced during that episode. Since these evaluations consist of two types of utility concepts: instant utility and remembered utility, a dynamic model of happiness based on this approach must be defined by a delay differential equation. Furthermore, the application of the peak-end rule leads to a class of delay-differential equations called differential equations with maxima. We propose a dynamical model for happiness based on differential equations with maxima and provide results which shed some new light on important experimental observations. In particular, our model supports the U-shaped profile of the age-happiness curve, which is a widely observed pattern: well-being is high in youth, falls to a minimum in midlife (midlife crisis), and rises again in old age. [ABSTRACT FROM AUTHOR]

Here we re-examine experimental in vitro data for the EMT6/Ro tumor volume and viable rim thickness. This shows that the growth speed is constant in time, and independent of nutrient concentration at large concentrations, but that the viable rim thickness increases in this high concentration regime. We then present a simple mechanistic reaction-diffusion equation that includes crowding and starvation effects, and show that the model qualitatively captures the experimental observations. Moreover, the model predicts that the cancer cell concentration is characterised by a wave pulse (soliton), and the pulse shape is explored through zero'th order perturbation analysis corresponding to large wave speeds. It is shown that this zero'th order term is dominant for the experimental condition, further indicating that the non-linear reaction governs the pulse characteristic shape. Finally, at low nutrient concentrations we find that the front is a pulled-front, that is, the growth speed is determined by the cell multiplication at the wave front edge in accordance with earlier modelling approaches. [ABSTRACT FROM AUTHOR]

There are several phenomena in nature governed by simultaneous or intermittent diffusion and advection processes. Many of these systems are networked by their own nature. Here we propose a degree-biased advection processes to undirected networks. For that purpose we define and study the degree-biased advection operator. We then develop a degree-biased advection-diffusion equation on networks and study its general properties. We give computational evidence of the utility of this new model by studying artificial graphs as well as a real-life patched landscape network in southern Madagascar. In the last case we show that the foraging movement of the species L. catta in this environment occurs mainly in a diffusive way with important contributions of advective motions in agreement with previous empirical observations. [ABSTRACT FROM AUTHOR]

An ecological system comprehended by a pest and its natural enemy, the predator, is considered. Parameters of system are time dependent in order to accompany their variations associated to climate evolutions. Combining the use of pesticides and of extra supply of food to predators, we propose the eradication of pest through optimal control having those two measures as controls. Is established that the resulting problem has a unique solution. Uniqueness is obtained on the whole interval using a recursive argument. The usefulness of model to tackle the pest population is backed by numerical simulation results. [ABSTRACT FROM AUTHOR]

Early vaccination efforts and non-pharmaceutical interventions (NPIs) were insufficient to prevent a surge of COVID-19 cases triggered by the Delta variant. A compartment model that includes age, vaccination, and variants was developed. We estimated the transmission rates using maximum likelihood estimation, and phase-dependent NPIs according to government policies from 26 February to 8 October 2021. Simulations were done to examine the effects of varying dates of initiation and intensity of eased NPIs, arrival timing of Delta, and speed of vaccine administration. The estimated transmission rate matrices show distinct patterns, with transmission rates of younger groups (0-39 years) much larger with Delta. Social distancing (SD) level 2 and SD4 in Korea were associated with transmission reduction factors of 0.63-0.70 and 0.70-0.78, respectively. The easing of NPIs to a level comparable to SD2 should be initiated not earlier than 16 October to keep the number of severe cases below Korea's healthcare capacity. Simulations showed that a surge prompted by Delta can be prevented if the number of people vaccinated daily or SD level when Delta arrived was higher. The timing of easing, intensity of NPIs, vaccination speed, and screening measures are key factors in preventing another epidemic wave. [ABSTRACT FROM AUTHOR]

The use of external enzymes provides an alternative way of reducing communication in pathogenic bacteria that may lead to the degradation of their signal and the loss of their pathogeneity. The present study considers an optimal control problem for the semilinear reaction-diffusion model of bacterial quorum sensing under the impact of external enzymes. Estimates of the solution of the controlled system are obtained, on the basis of which the solvability of the extremal problem is proved and the necessary optimality conditions of the first-order are derived. A numerical algorithm to find a solution of the optimal control problem is constructed and implemented. The conducted numerical experiments demonstrate an opportunity to build an effective strategy of the enzymes impact for treatment. [ABSTRACT FROM AUTHOR]