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In this paper, we deal with the global dynamics of a Lotka-Volterra competition-diffusion-advection system with nonlinear boundary conditions, including the existence, nonexistence and global stability of coexistence steady states. We start with the investigation of the principal eigenvalue of linearized system to get the local stability of steady states and then discuss the global dynamics in terms of competition coefficients. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the tracking performance and antidisturbance ability of the widely used proportional-integral-derivative (PID) controllers in practice. Towards this end, we consider a basic class of second-order nonlinear stochastic control systems subject to model uncertainties and external disturbances, and focus on the ability of the classical PID controller to track time-varying reference signals. First, under some suitable conditions on the system nonlinear functions, reference signals, and external disturbances, we show that such control systems can be stabilized in the mean square sense, provided that the three PID gains are selected from a stability region constructed in the paper. Besides, it is shown that the steady-state tracking error has an upper bound proportional to the sum of the varying rates of reference signals, the varying rates of external disturbances, and the intensity of random noises. Meanwhile, its proportional coefficient depends on the selection of PID gains, which can be made arbitrarily small by choosing suitably large PID gains. Finally, by introducing a desired transient process which is shaped from the reference signal, a new PID tuning rule is presented, which can guarantee both the expected steady state and transient tracking performance. [ABSTRACT FROM AUTHOR]

A significant proportion of malaria infections in humans exhibit no symptoms, but it is a reservoir for maintaining malaria transmission. A time periodic reaction-diffusion model for malaria spread is introduced in this paper, incorporating spatial heterogeneity, incubation periods, symptomatic and asymptomatic carriers. This paper introduces the concept of the basic reproduction number R 0 , which is defined as the spectral radius of the next generation operator, and we present some preliminary results by elementary analysis. The threshold dynamic behavior analysis shows that when R 0 < 1 , the disease is extinct, and when R 0 > 1 , the disease is persistent. We investigate the case of constant system parameters, focusing on the global asymptotic stability of the disease-free steady state when R 0 = 1 . In the numerical simulation section, we validate the theoretical results obtained, and then use elasticity analysis methods to explore the influence of parameters on the output solution. In addition, sensitivity analysis of the basic reproduction number under homogeneous conditions indicates direction of controlling malaria transmission. And several control measures are evaluated in the following steps. [ABSTRACT FROM AUTHOR]

This paper investigates both the local and global stability of a system of rational difference equations and its connection to co-balancing numbers. The study delves into the intricate dynamics of mathematical models and their stability properties, emphasizing the broader implications of global stability. Additionally, the investigation extends to the role of co-balancing numbers, elucidating their significance in achieving equilibrium within the solutions of the rational difference equations. The interplay between global stability and co-balancing numbers forms a foundational aspect of the analysis. The findings contribute to a deeper understanding of the mathematical structures underlying dynamic systems and offer insights into the factors influencing their stability and equilibrium. This article serves as a valuable resource for mathematicians, researchers, and scholars interested in the intersection of global stability and co-balancing sequences in the realm of rational difference equations. Moreover, the presented examples and figures consistently demonstrate the global asymptotic stability of the equilibrium point throughout the paper. [ABSTRACT FROM AUTHOR]

This work focused on studying the effect of vaccination rate κ on reducing the outbreak of infectious diseases, especially if the infected individuals do not have any symptoms. We employed the fractional order derivative in this study since it has a high degree of accuracy. Recently, a lot of scientists have been interested in fractional-order models. It is considered a modern direction in the mathematical modeling of epidemiology systems. Therefore, a fractional order of the SEIR epidemic model with two types of infected groups and vaccination strategy was formulated and investigated in this paper. The proposed model includes the following classes: susceptible S (t) , exposed E (t) , asymptomatic infected I c (t) , symptomatic infected I η (t) , vaccinated V (t) , and recovered R (t) . We began our study by creating the existence, non-negativity, and boundedness of the solutions of the proposed model. Moreover, we established the basic reproduction number R 0 , that was used to examine the existence and stability of the equilibrium points for the presented model. By creating appropriate Lyapunov functions, we proved the global stability of the free-disease equilibrium point and endemic equilibrium point. We concluded that the free-disease equilibrium point is globally asymptotically stable (GAS) when R 0 ≤ 1 , while the endemic equilibrium point is GAS if R 0 > 1 . Therefore, we indicated the increasing vaccination rate κ leads to reducing R 0 . These findings confirm the important role of vaccination rate κ in fighting the spread of infectious diseases. Moreover, the numerical simulations were introduced to validate theoretical results that are given in this work by applying the predictor-corrector PECE method of Adams-Bashforth-Moulton. Further more, the impact of the vaccination rate κ was explored numerically and we found that, as κ increases, the R 0 is decreased. This means the vaccine can be useful in reducing the spread of infectious diseases. This work focused on studying the effect of vaccination rate on reducing the outbreak of infectious diseases, especially if the infected individuals do not have any symptoms. We employed the fractional order derivative in this study since it has a high degree of accuracy. Recently, a lot of scientists have been interested in fractional-order models. It is considered a modern direction in the mathematical modeling of epidemiology systems. Therefore, a fractional order of the SEIR epidemic model with two types of infected groups and vaccination strategy was formulated and investigated in this paper. The proposed model includes the following classes: susceptible , exposed , asymptomatic infected , symptomatic infected , vaccinated , and recovered . We began our study by creating the existence, non-negativity, and boundedness of the solutions of the proposed model. Moreover, we established the basic reproduction number , that was used to examine the existence and stability of the equilibrium points for the presented model. By creating appropriate Lyapunov functions, we proved the global stability of the free-disease equilibrium point and endemic equilibrium point. We concluded that the free-disease equilibrium point is globally asymptotically stable (GAS) when , while the endemic equilibrium point is GAS if . Therefore, we indicated the increasing vaccination rate leads to reducing . These findings confirm the important role of vaccination rate in fighting the spread of infectious diseases. Moreover, the numerical simulations were introduced to validate theoretical results that are given in this work by applying the predictor-corrector PECE method of Adams-Bashforth-Moulton. Further more, the impact of the vaccination rate was explored numerically and we found that, as increases, the is decreased. This means the vaccine can be useful in reducing the spread of infectious diseases. [ABSTRACT FROM AUTHOR]

This paper studies a delayed rumor propagation model with logistic growth and saturation incidence. The next generation matrix method, some inequality techniques, the Lyapunov-LaSalle invariance principle, and the Lyapunov method are used in this paper. Our results indicate that if the basic regeneration number (which is analogous to the basic reproduction number in disease transmission models) is less than 1, the rumor-free equilibrium point (which is analogous to the disease-free equilibrium point in disease transmission models) is globally stable. If the basic regeneration number is greater than 1, then the rumor is permanent, and some sufficient conditions are obtained for local and global asymptotic stability of the rumor prevailing equilibrium point (which is analogous to the endemic equilibrium point in disease transmission models). Finally, three examples with numerical simulations are presented to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper establishes a new fractional frSIS model utilizing a continuous time random walk method. There are two main innovations in this paper. On the one hand, the model is analyzed from a mathematical perspective. First, unlike the classic SIS infectious disease model, this model presents the infection rate and cure rate in a fractional order. Then, we proved the basic regeneration number R0 of the model and studied the influence of orders a and b on R0. Second, we found that frSIS has a disease-free equilibrium point E0 and an endemic equilibrium point E∗. Moreover, we proved frSIS global stability of the model using R0. If R0<1, the model of E0 is globally asymptotically stable. If R0>1, the model of E∗ is globally asymptotically stable. On the other hand, from the perspective of infectious diseases, we discovered that appropriately increasing a and decreasing b are beneficial for controlling the spread of diseases and ultimately leading to their disappearance. This can help us provide some dynamic adjustments in prevention and control measures based on changes in the disease. [ABSTRACT FROM AUTHOR]

In this paper, we consider a diffusive–advective predator–prey system in a spatially heterogeneous environment subject to a hostile boundary condition, where the interaction term is governed by a Holling type II functional response. We investigate the existence and global attractivity of both trivial and semi-trivial steady-state solutions and the existence and local stability of coexistence steady-state solutions, depending on the size of a key principal eigenvalue. In addition, we show that the effect of advection on the principal eigenvalue is monotonic for small advection rates, depending on the concavity of the resource distribution. For arbitrary advection rates, we consider two explicit resource distributions for which we can say precisely the behaviour of the principal eigenvalue as it depends on advection, highlighting that advection can either improve or impair a population's ability to persist, depending on the characteristics of the resource distribution. We present some numerical simulations to demonstrate the outcomes as they depend on the advection rates for the full predator–prey system. These insights highlight the intimate relationship between environmental heterogeneity, directed movement, and the hostile boundary. The methods employed include upper and lower solution techniques, bifurcation theory, spectral analysis, and the comparison principle. [ABSTRACT FROM AUTHOR]

This paper is dedicated to Jim Cushing on the occasion of his 80th birthday. It is inspired by his work on evolutionary theory. We investigate the global dynamics of discrete-time phenotypic evolutionary models, both autonomous and periodic. We developed the theory of mixed monotone maps and applied it to show that the positive equilibrium of the autonomous evolutionary Ricker model of single and multi-species is globally asymptotically stable. Then we extend this result to the corresponding evolutionary Ricker model with periodic parameters. [ABSTRACT FROM AUTHOR]

For the three-dimensional path tracking control problem of fixed-wing unmanned aerial vehicles, an inner and outer loop controller based on globally stable integral sliding mode S-plane model is proposed in this paper. The outer loop is controlled by the globally stable integral sliding mode, and the inner loop is controlled by the S-plane. Firstly, the globally stable integral sliding control law is designed for the outer loop, and the stability of the control law is proved using the Lyapunov theory. Then the S-plane controller is designed for the instruction signal of the inner loop. Due to the complexity of derivation in the S-plane controller, a second-order differentiator is introduced. The simulation results show that the proposed controller can track the ideal path accurately, which has good control performance and anti-interference performance. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global dynamics of a two-species Grindrod clustering model with Lotka–Volterra competition. The model takes the advective flux to depend directly upon local population densities without requiring intermediate signals like attractants or repellents to form the aggregation so as to increase the chances of survival of individuals like human populations forming small nucleated settlements. By imposing appropriate boundary conditions, we establish the global boundedness of solutions in two-dimensional bounded domains. Moreover, we prove the global stability of spatially homogeneous steady states under appropriate conditions on system parameters, and show that the rate of convergence to the coexistence steady state is exponential while the rate of convergence to the competitive exclusion steady state is algebraic. [ABSTRACT FROM AUTHOR]

The application of mathematical biology and dynamical systems has proven to be an effective approach for studying viral infection models. To contribute to this research, our paper proposes a new CHIKV model that takes into account an adaptive immune response and distributed time delays, which accurately reflects the time lag between initial viral contacts and the production of new active CHIKV particles. By analyzing the model’s qualitative behavior, we establish a biological threshold number that can predict whether CHIKV will be cleared from or persist in the body. We demonstrate the global stability of both CHIKV-present and CHIKV-free steady states using the Lyapunov functional method and LaSalle’s invariance principle. In addition, we conduct numerical simulations to examine how time delays can affect the stability of the steady states. Through these simulations, we gain insights into how varying time delays can influence the persistence or clearance of CHIKV within the host. [ABSTRACT FROM AUTHOR]

Mathematical models play a crucial role in controlling and preventing the spread of diseases. Based on the communication characteristics of diseases, it is necessary to take into account some essential epidemiological factors such as the time delay that takes an individual to progress from being latent to become infectious, the infectious age which refers to the duration since the initial infection and the occurrence of reinfection after a period of improvement known as relapse, etc. Moreover, age-structured models serve as a powerful tool that allows us to incorporate age variables into the modeling process to better understand the effect of these factors on the transmission mechanism of diseases. In this paper, motivated by the above fact, we reformulate an SEIR model with relapse and age structure in both latent and infected classes. Then, we investigate the asymptotic behavior of the model by using the stability theory of differential equations. For this purpose, we introduce the basic reproduction number R 0 of the model and show that this threshold parameter completely governs the stability of each equilibrium of the model. Our approach to show global attractivity is based on the fluctuation lemma and Lyapunov functionals method with some results on the persistence theory. The conclusion is that the system has a disease-free equilibrium which is globally asymptotically stable if R 0 < 1 , while it has only a unique positive endemic equilibrium which is globally asymptotically stable whenever R 0 > 1 . Our results imply that early diagnosis of latent infection with decrease in both transmission and relapse rates may lead to control and restrict the spread of disease. The theoretical results are illustrated with numerical simulations, which indicate that the age variable is an essential factor affecting the spread of the epidemic. [ABSTRACT FROM AUTHOR]

In this paper, we continue the research in Li et al. (J Differ Equ 371:353–395, 2023) and study the linear and global stability of a class of reaction-diffusion systems with general degenerate diffusion. The establishment of these systems is based on the acid-mediated invasion hypothesis, which is a candidate explanation for the Warburg effect. Our theoretical results characterize the effects of acid resistance and mutual competition between healthy cells and tumor cells on local and long-term tumor development, i.e., whether the healthy cells and tumor cells coexist or the tumor cells prevail after tumor invasion. We first consider the linear stability of the steady states and give a complete characterization by transforming the linearized analysis into an algebraic problem. In discussing global stability, the main difficulty of this model arises from density-limited diffusion terms, which can lead to degeneracy in the parabolic equations. We find that the method established in Li et al. (J Differ Equ 371:353–395, 2023) works well to overcome the degenerate problem. This method combines the Lyapunov functionals and upper/lower solutions, and it can be applied to a broader range of reaction-diffusion systems even if the diffusion terms degenerate and have very poor properties. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the global asymptotic behaviors of a mathematical susceptibleinfected(SI) age-infection-structured human immunodeficiency virus(HIV) model with heterogeneous transmission. Mathematical analysis shows that the local and global dynamics are completely determined by the basic reproductive number R 0. If R 0 < 1, disease-free equilibrium is globally asymptotically stable. If R 0 >1, it shows that diseasefree equilibrium is unstable and the unique endemic equilibrium is globally asymptotically stable. The proofs of global stability utilize Lyapunov functions. Besides, the numerical simulations are illustrated to support these theoretical results and sensitivity analysis of each parameter for R 0 is performed by the method of partial rank correlation coefficient(PRCC). [ABSTRACT FROM AUTHOR]

This paper considers the dynamical properties of a space and time discrete fractional reaction–diffusion epidemic model, introducing a novel generalized incidence rate. The linear stability of the equilibrium solutions of the considered discrete fractional reaction–diffusion model has been carried out, and a global asymptotic stability analysis has been undertaken. We conducted a global stability analysis using a specialized Lyapunov function that captures the system's historical data, distinguishing it from the integer-order version. This approach significantly advanced our comprehension of the complex stability properties within discrete fractional reaction–diffusion epidemic models. To substantiate the theoretical underpinnings, this paper is accompanied by numerical examples. These examples serve a dual purpose: not only do they validate the theoretical findings, but they also provide illustrations of the practical implications of the proposed discrete fractional system. [ABSTRACT FROM AUTHOR]

This paper analyzes an allelopathic phytoplankton competition model, which was proposed by Bandyopadhyay [Dynamical analysis of a allelopathic phytoplankton model, J Biol Syst14(02):205–217, 2006]. Our study refines the previous results and finds at most three positive equilibria for the system. The existence conditions of all positive equilibria and the corresponding stability cases are given in the paper. Interesting dynamical phenomena such as bistability, saddle-node bifurcation, and cusp bifurcation are found. It is shown that the rate of toxin releases heavily influences the positive equilibria of the system under certain conditions. Numerical simulations verify the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

We consider k-dimensional discrete-time systems of the form x n + 1 = F (x n , … , x n - k + 1) in which the map F is continuous and monotonic in each one of its arguments. We define a partial order on R + 2 k , compatible with the monotonicity of F, and then use it to embed the k-dimensional system into a 2k-dimensional system that is monotonic with respect to this poset structure. An analogous construction is given for periodic systems. Using the characteristics of the higher-dimensional monotonic system, global stability results are obtained for the original system. Our results apply to a large class of difference equations that are pertinent in a variety of contexts. As an application of the developed theory, we provide two examples that cover a wide class of difference equations, and in a subsequent paper, we provide additional applications of general interest. [ABSTRACT FROM AUTHOR]

This paper is the first to propose an allelopathic phytoplankton competition ODE model influenced by the fear effect based on natural biological phenomena. It is shown that the interplay of this fear effect and the allelopathic term cause rich dynamics in the proposed competition model, such as global stability, transcritical bifurcation, pitchfork bifurcation, and saddle-node bifurcation. We also consider the spatially explicit version of the model and prove analogous results. Numerical simulations verify the feasibility of the theoretical analysis. The results demonstrate that the primary cause of the extinction of non-toxic species is the fear of toxic species compared to toxins. Allelopathy only affects the density of non-toxic species. The discussion guides the conservation of species and the maintenance of biodiversity. [ABSTRACT FROM AUTHOR]

In a previous paper (Feng et al., J. Differential Equations (2023)), we studied a seasonally interactive model between closed seasons and open seasons with Michaelis-Menten type harvesting, in which we assumed that the harvesting quantity was relatively large (0 < κ = l G c E < 1) and obtained a length threshold of the closed season T ¯ ⁎ depending on the harvesting parameter and the seasonal fluctuation period. It was shown that the origin is globally asymptotically stable if and only if T ¯ ≤ T ¯ ⁎ , and there exists a unique globally asymptotically stable T -periodic solution if and only if T ¯ > T ¯ ⁎. In this paper, we continue to investigate the periodic dynamics of this model when the harvesting quantity is relatively small (κ = l G c E ≥ 1). By finding another smaller length threshold T ¯ ⁎ ∈ (0 , T ¯ ⁎) , we determine the number of periodic solutions and study their stability, which imply the occurrence of bifurcation of periodic solutions. Our results demonstrate that designing the closed harvesting season properly can prevent the species from extinction. Moreover, by comparing with the continuous harvesting model and combining the results in our previous paper and this article, we provide a complete understanding on the global dynamics for the periodic switching model. Some numerical simulations are also carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we derive the well-defined solutions to a θ -dimensional system of difference equations. We show that, the well-defined solutions to that system are represented in terms of Fibonacci and Lucas sequences. Moreover, we study the global stability of the solutions to that system. Finally, we give some numerical examples which confirm our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we present a survey about the latest results in global stability concerning the discrete-time evolutionary Ricker competition model with n species, in both, autonomous and periodic models. The main purpose is to convey some arguments and new ideas concerning the techniques for showing global asymptotic stability of fixed points or periodic cycles in these kind of discrete-time models. In order to achieve this, some open problems and conjectures related to the evolutionary Ricker competition model are presented, which may be a starting point to study global stability, not only in other competition models, but in predator–prey models and Leslie–Gower-type models as well. [ABSTRACT FROM AUTHOR]

In this paper, we consider an SEIS epidemic model with infectious force in latent and infected period, which incorporates by nonlinear incidence rates. The local stability of the equilibria is discussed. By means of Lyapunov functionals and LaSalle's invariance principle, we proved the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium. An application is given and numerical simulation results based on real data of COVID-19 in Morocco are performed to justify theoretical findings. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of traveling wavefronts for a three-component Lotka–Volterra system with nonlocal dispersal. This system arises in the study of three-species competition model in which there is no competition between two of these three species. It has been shown that this system admits a bistable traveling wavefront. In this paper, we further investigate the stability of bistable traveling wavefronts. By constructing suitable super- and sub-solutions and using a dynamical system approach, we obtain the globally asymptotic stability of the bistable traveling wavefronts. [ABSTRACT FROM AUTHOR]

In the present paper, we prove the existence of unique almost periodic solutions to fuzzy shunting inhibitory cellular neural networks (FSICNN) with several delays. Further, by means of Halanay inequality we analyze the global exponential stability of these solutions and obtain corresponding convergence rate. The results of this paper are new, and they are concluded with numerical simulations confirming them. [ABSTRACT FROM AUTHOR]

Vaccination is widely acknowledged as an affordable and cost-effective approach to guard against infectious diseases. It is important to take vaccination rate, vaccine effectiveness, and vaccine-induced immune decline into account in epidemic dynamical modeling. In this paper, an epidemic dynamical model of vaccination is developed. This model provides a framework of the infectious disease transmission dynamics model through qualitative and quantitative analysis. The result shows that the system may have multiple equilibria. We used the next-generation operator approach to calculate the maximum spectral radius, that is, basic reproduction number Rvac. Next, by dividing the model into infected and uninfected subjects, we can prove that the disease-free equilibrium is globally asymptotically stable when Rvac < 1, provided certain assumptions are satisfied. When Rvac > 1, there exists a unique endemic equilibrium. Using geometric methods, we calculate the second compound matrix and demonstrate the Lozinskii measure ... ≤ 0, which is equivalent to the unique endemic equilibrium, which is globally asymptotically stable. Then, using center manifold theory, we justify the existence of forward bifurcation. As the vaccination rate decreases, the likelihood of forward bifurcation increases. We also theoretically show the presence of Hopf bifurcation. Then, we performed sensitivity analysis and found that increasing the vaccine effectiveness rate can curb the propagation of disease effectively. To examine the influence of vaccination on disease control, we chose the vaccination rate as the optimal vaccination control parameter, using the Pontryagin maximum principle, and we found that increasing vaccination rates reduces the number of infected individuals. Finally, we ran a numerical simulation to finalize the theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on the S-asymptotically Periodic oscillation for a type of fractional-order fuzzy Cohen-Grossberg neural networks (CGNNs) by employing some properties of Mittag-Leffler mappings and fixed point theorems. Further, the global asymptotic stability of CGNNs is received. For CGNNs, our works in this paper not only enrich its theoretical achievements, but also expand its application scope. [ABSTRACT FROM AUTHOR]

ARS-CoV-2 can survive in different environments and remain infectious for several days, which presents challenges to eliminating infectious diseases. It encourages researchers to study the effects of SARS-CoV-2 on the environment. In this paper, we formulate an epidemic model for SARS-CoV-2, which focuses on the transmission of the virus under environmental conditions. Two distributed delays are introduced to describe the probability of the exposed and infected individuals in different infection periods based on the transmission of the virus in the environment. The positivity and boundness of solutions of model are derived. The basic reproduction number threshold theory is established and the results demonstrate that the persistence of COVID-19 depends on the basic reproduction number. Numerical simulations are presented to verify the theoretical results. Some measures are proposed to control and eliminate COVID-19 infectious diseases. [ABSTRACT FROM AUTHOR]

This paper considers stability analysis of a Susceptible-Exposed-Infected-Recovered-Virus (SEIRV) model with nonlinear incidence rates and indicates the severity and weakness of control factors for disease transmission. The Lyapunov function using Volterra–Lyapunov matrices makes it possible to study the global stability of the endemic equilibrium point. An optimal control strategy is proposed to prevent the spread of coronavirus, in addition to governmental intervention. The objective is to minimize together with the quantity of infected and exposed individuals while minimizing the total costs of treatment. A numerical study of the model is also carried out to investigate the analytical results. [ABSTRACT FROM AUTHOR]

Free-floating space robotic manipulators (FSRMs) are robotic arms mounted on space platforms, such as spacecraft or satellites which are used for the repair of space vehicles or the removal of noncooperating targets such as inactive material remaining in orbit. In this paper, a novel nonlinear optimal control method is applied to the dynamic model of FSRMs. First, the state-space model of a 3-DOF free-floating space robot is formulated and its differential flatness properties are proven. This model undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the free-floating space robot a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution of the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller's feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of setpoints under moderate variations of the control inputs and a minimum dispersion of energy by the actuators of the free-floating space robot. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a population suppression model and a population replacement model with periodic impulsive releases of Nilaparvata lugens infected with wStri. The conditions for the stability of wild- $ N.\,lugens $ N. l u g e n s -eradication periodic solution of two systems are obtained by applying the Floquet theorem and comparison theorem. And the sufficient conditions for the persistence in the mean of wild $ N.\,lugens $ N. l u g e n s are also given. In addition, the sufficient conditions for the extinction and persistence of the wild $ N.\,lugens $ N. l u g e n s in the subsystem without wLug are also obtained. Finally, we give numerical analysis which shows that increasing the release amount or decreasing the release period are beneficial for controlling the wild $ N.\,lugens $ N. l u g e n s , and the efficiency of population replacement strategy in controlling wild populations is higher than that of population suppression strategy under the same release conditions. [ABSTRACT FROM AUTHOR]

In this paper. we propose a mathematical model that describes the dynamics of transmission of COVID-19 between potential people and infected ones, as well as between bats as virus carriers and people. This article deals with optimal control applied to vaccination, treatment strategies, and the hunt for a SIR-B epidemic model with logistic growth. The global stability of the disease-free and endemic equilibrium is verified. The existence of optimal control is demonstrated. The Pontryagin maximum principle is employed to describe these optimal controls. To validate our previous theoretical results. the optimality system is numerically resolved using a Matlab algorithm based on the Runge Kutta approximation 4. [ABSTRACT FROM AUTHOR]

In this paper, we study a nonlinear mathematical model which addresses the transmission dynamics of COVID-19. The considered model consists of susceptible (S), exposed (E), infected (I), and recovered (R) individuals. For simplicity, the model is abbreviated as S E I R. Immigration rates of two kinds are involved in susceptible and infected individuals. First of all, the model is formulated. Then via classical analysis, we investigate its local and global stability by using the Jacobian matrix and Lyapunov function method. Further, the fundamental reproduction number ℛ 0 is computed for the said model. Then, we simulate the model through the Runge–Kutta method of order two abbreviated as RK2. Finally, we switch over to the fractional order model and investigate its numerical simulations corresponding to different fractional orders by using the fractional order version of the aforementioned numerical method. Finally, graphical presentations are given for the approximate solution of various compartments of the proposed model. Also, a comparison with real data has been shown. [ABSTRACT FROM AUTHOR]

This paper deals with the global boundedness and asymptotic stability of the solution of the two-predator and one-prey systems with density-dependent motion in a n-dimensional bounded domain with Neumann boundary conditions. In a previous paper, Qiu et al. (J Dyn Differ Equ, 1–25, 2021) proved the global existence and uniform boundedness of classical solution by limiting the conditions on motility functions and the coefficients of logistic source. By contrast, we relax the limitation conditions in Qiu et al. (2021) by constructing the weight function. Moreover, under diverse competition circumstances, the global stabilities of nonnegative spatially homogeneous equilibria for the special model are established. [ABSTRACT FROM AUTHOR]

In this paper the Multicompartment epidemiological model assumes that. given a contagious illness. a population can be partitioned into individuals that are susceptible to the illness. infected by the illness, and recovered from the illness.S(t) Number of individuals at time t susceptible to the illness;/(thi= 1.2.3.4 Number of individuals at time t infected with the illness.Rs(t) Total number of survivors of the illness at time t. RD(t) Total number of deaths due to the illness at time t. The stability of a disease-free status equilibrium and the existence of endemic equilibrium can be determined by the ratio called the basic reproductive number. Laplace-adomian decomposition method is used to compute an analytical solution of the model study. This paper study the equilibrium. local. global stability under certain conditions. [ABSTRACT FROM AUTHOR]