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In this paper, a new delayed fractional-order model including susceptible migratory birds, infected migratory birds and predators is proposed to discuss the spread of diseases among migratory birds. Fear of predators is considered in the model, as fear can reduce the reproduction rate and disease transmission rate among prey. First, some basic mathematical results of the proposed model are discussed. Then, time delay is regarded as a bifurcation parameter, and the delay-induced bifurcation conditions for such an uncontrolled system are established. A novel periodic pulse feedback controller is proposed to suppress the bifurcation phenomenon. It is found that the control scheme can successfully suppress the bifurcation behavior of the system, and the pulse width can be arbitrarily selected on the premise of ensuring the control effect. Compared with the traditional time-delay feedback controller, the control scheme proposed in this paper has more advantages in practical application, which not only embodies the advantages of low control cost and easy operation but also caters to the periodic changes of the environment. The proposed control scheme, in particular, remains effective even after the system has been disrupted by a constant. Numerical simulation verifies the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the host–parasitoid model, where the logistic equation governs the host population growth, and a proportion of the host population can find refuge. The equilibrium points' existence, number, and local character are discussed. Taking the parameter regulating the parasitoid's growth as a bifurcation parameter, we prove that Neimark–Sacker and period-doubling bifurcations occur. Despite the complex behavior, it can be proved that the system is permanent, ensuring the long-term survival of both populations. Furthermore, it was observed that the presence of the proportional refuge does not significantly influence the system's behavior compared to the system without a proportional refuge. [ABSTRACT FROM AUTHOR]

This work investigates a prey–predator model featuring a Holling-type II functional response, in which the fear effect of predation on the prey species, as well as prey refuge, are considered. Specifically, the model assumes that the growth rate of the prey population decreases as a result of the fear of predators. Moreover, the detection of the predator by the prey species is subject to a delay known as the fear response delay, which is incorporated into the model. The paper establishes the preliminary conditions for the solution of the delayed model, including positivity, boundedness and permanence. The paper discusses the existence and stability of equilibrium points in the model. In particular, the paper considers the discrete delay as a bifurcation parameter, demonstrating that the system undergoes Hopf bifurcation at a critical value of the delay parameter. The direction and stability of periodic solutions are determined using central manifold and normal form theory. Additionally, the global stability of the model is established at axial and positive equilibrium points. An extensive numerical simulation is presented to validate the analytical findings, including the continuation of the equilibrium branch for positive equilibrium points. [ABSTRACT FROM AUTHOR]

This paper studies the global exponential p -norm stability of bidirectional associative memory (BAM) neural networks with unbounded time-varying delays. A novel method based on the representation of solutions is put forward to deduce a global exponential p -norm stability criterion. This method does not need to set up any Lyapunov–Krasovskii functionals (LKF), which can greatly reduce a large amount of computations and is simpler than the existing methods. In the end, representative numerical examples are given to illustrate the availability of the method. [ABSTRACT FROM AUTHOR]

In this paper, a stage structure predator–prey model consisting of three nonlinear ordinary differential equations is proposed and analyzed. The prey populations are divided into two parts: juvenile prey and adult prey. From extensive experimental data, it has been found that prey fear of predators can alter the physiological behavior of individual prey, and the fear effect reduces their reproductive rate and increases their mortality. In addition, we also consider the presence of constant ratio refuge in adult prey populations. Moreover, we consider the existence of intraspecific competition between adult prey species and predator species separately in our model and also introduce the gestation delay of predators to obtain a more realistic and natural eco-dynamic behaviors. We study the positivity and boundedness of the solution of the non-delayed system and analyze the existence of various equilibria and the stability of the system at these equilibria. Next by choosing the intra-specific competition coefficient of adult prey as bifurcation parameter, we demonstrate that Hopf bifurcation may occur near the positive equilibrium point. Then by taking the gestation delay as bifurcation parameter, the sufficient conditions for the existence of Hopf bifurcation of the delayed system at the positive equilibrium point are given. And the direction of Hopf bifurcation and the stability of the periodic solution are analyzed by using the center manifold theorem and normal form theory. What's more, numerical experiments are performed to test the theoretical results obtained in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of solutions and analyze the large-time behavior for Gurtin–Maccamy population model involving conformable fractional derivatives. As a preliminary step, we construct a generic structure of the solution associated with our proposed model by utilizing some basic properties and tools of conformable fractional calculus. We establish the existence of a unique solution of the given model with the given initial conditions. At last, by using the upper and lower solutions for the characteristic equation, we define the upper and lower boundaries for the obtained solution and describe the large-time behavior of the total population. [ABSTRACT FROM AUTHOR]

This paper is concerned with the sustained periodic oscillation phenomenon in a three-species delayed predation system with Holling type II functional response and age structure in top predator. The top predator fertility function is regarded as a piecewise continuous smooth function with regard to their maturation period τ 2 . The complicated dynamic behavior is proved by integrated semigroup theory and Hopf bifurcation theorem for semilinear equations with non-dense domain. Through qualitative analysis and bifurcation study of the system, we yield that this system has a nontrivial periodic solution that bifurcates from the positive equilibrium age distribution when bifurcation parameter τ passes through some critical values. Numerical simulations are also provided to illustrate theoretically analytical results. [ABSTRACT FROM AUTHOR]

In this paper, an SIRS epidemic model using Grunwald–Letnikov fractional-order derivative is formulated with the help of a nonlinear system of fractional differential equations to analyze the effects of fear in the population during the outbreak of deadly infectious diseases. The criteria for the spread or extinction of the disease are derived and discussed on the basis of the basic reproduction number. The condition for the existence of Hopf bifurcation is discussed considering fractional order as a bifurcation parameter. Additionally, using the Grunwald–Letnikov approximation, the simulation is carried out to confirm the validity of analytic results graphically. Using the real data of COVID-19 in India recorded during the second wave from 15 May 2021 to 15 December 2021, we estimate the model parameters and find that the fractional-order model gives the closer forecast of the disease than the classical one. Both the analytical results and numerical simulations presented in this study suggest different policies for controlling or eradicating many infectious diseases. [ABSTRACT FROM AUTHOR]

This paper investigates a nonlocal dispersal epidemic model under the multiple nonlocal distributed delays and nonlinear incidence effects. First, the minimal wave speed c ∗ and the basic reproduction number R 0 are defined, which determine the existence of traveling wave solutions. Second, with the help of the upper and lower solutions, Schauder's fixed point theorem, and limiting techniques, the traveling waves satisfying some asymptotic boundary conditions are discussed. Specifically, when ℛ 0 > 1 , for every speed c > c ∗ there exists a traveling wave solution satisfying the boundary conditions, and there is no such traveling wave solution for any 0 < c < c ∗ when ℛ 0 > 1 or c > 0 when ℛ 0 < 1. Finally, we analyze the effects of nonlocal time delay on the minimum wave speed. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model for a solid spherically symmetric vascular tumor growth with nutrient periodic supply and time delays is studied. Compared to the apoptosis process of tumor cells, there is a time delay in the process of tumor cell division. The cells inside the tumor obtain nutrient σ(r,t) through blood vessels, and the tumor attracts blood vessels at a rate proportional to α(t). So, the boundary value condition ∂σ ∂r + α(t)(σ − ψ(t)) = 0,r = R(t),t > 0, holds on the boundary, where the function ψ(t) is the concentration of nutrient externally supplied to the tumor. Considering that the nutrients provided by the outside world are often periodic, the research in this paper assumes that ψ(t) is a periodic function. Sufficient conditions for the global stability of zero steady state are presented. Under certain conditions, we prove that there exists at least one periodic solution to the model. The results are illustrated by computer simulations. [ABSTRACT FROM AUTHOR]

Zika is a mosquito-transmitted viral disease which may spread directly by the vector or sexual transmission. Zika virus may persist in semen and urine for a long time after disappearance from the blood, those persons are known as the convalescent humans. It can also be transmitted vertically among mosquitoes. In this paper, we have considered an eight-compartment Zika model to study the effect of all the said aspects on the virus dynamics in deterministic as well as stochastic environment. In analytic part, we have computed basic reproduction number and discussed stability of different equilibria. We have shown the proposed model undergoes through transcritical bifurcation when the reproduction number is unity and validate the model with real infection data of Dominican Republic in 2016. To study the model in stochastic environments, the additive noise is taken into consideration which is formulated considering the standard Brownian white noises proportional to each class. We have obtained the condition for disease extinction and persistence in mean. All theoretical findings are justified by numerical simulations. Lastly, the paper is ended with some conclusions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the dynamic behaviors of fractional- order logistic model with Allee effects in Caputo–Fabrizio sense. First of all, we apply the two-step Adams–Bashforth scheme to discretize the fractional-order logistic differential equation and obtain the two-dimensional discrete system. The parametric conditions for local asymptotic stability of equilibrium points are obtained by Schur–Chon criterion. Moreover, we discuss the existence and direction for Neimark–Sacker bifurcations with the help of center manifold theorem and bifurcation theory. Numerical simulations are provided to illustrate theoretical discussion. It is observed that Allee effect plays an important role in stability analysis. Strong Allee effect in population enhances the stability of the coexisting steady state. In additional, the effect of fractional-order derivative on dynamic behavior of the system is also investigated. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors of a discrete-time fractional-order population model are considered. The stability analysis and the topological classification of the model at the fixed point have been investigated. It is shown that the model undergoes flip and Neimark–Sacker bifurcations around the co-existence fixed point by using the bifurcation and the normal form theory. These bifurcations lead to chaos when the parameter changes at critical point. In order to control chaotic behavior in the model result from Neimark–Sacker bifurcation, the OGY feedback method has been used. Furthermore, some numerical simulations, including bifurcation diagrams, phase portraits and maximum Lyapunov exponents of the presented model are plotted to support the correctness of the analytical results. The positive Lyapunov exponents demonstrate that chaotic behavior exists in the considered model. [ABSTRACT FROM AUTHOR]

In this paper, a new generalized non-monotonic and saturated incidence rate was introduced into a susceptible-infected-susceptible (SIS) epidemic model to account for inhibitory effect and crowding effect. The dynamic properties of the model were studied by qualitative theory and bifurcation theory. It is shown that when the influence of psychological factors is large, the model has only disease-free equilibrium point, and this disease-free equilibrium point is globally asymptotically stable; when the influence of psychological factors is small, for some parameter conditions, the model has a unique endemic equilibrium point, which is a cusp point of co-dimension two, and for other parameter conditions the model has two endemic equilibrium points, one of which could be weak focus or center. In addition, the results of the model undergoing saddle-node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation as the parameters vary were also proved. These results shed light on the impact of psychological behavior of susceptible people on the disease transmission. [ABSTRACT FROM AUTHOR]

In recent years, the epidemic model with anomalous diffusion has gained popularity in the literature. However, when introducing anomalous diffusion into epidemic models, they frequently lack physical explanation, in contrast to the traditional reaction–diffusion epidemic models. The point of this paper is to guarantee that anomalous diffusion systems on infectious disease spreading remain physically reasonable. Specifically, based on the continuous-time random walk (CTRW), starting from two stochastic processes of the waiting time and the step length, time-fractional space-fractional diffusion, time-fractional reaction–diffusion and fractional-order diffusion can all be naturally introduced into the SIR (S: susceptible, I: infectious and R: recovered) epidemic models, respectively. The three models mentioned above can also be applied to create SIR epidemic models with generalized distributed time delays. Distributed time delay systems can also be reduced to existing models, such as the standard SIR model, the fractional infectivity model and others, within the proper bounds. Meanwhile, as an application of the above stochastic modeling method, the physical meaning of anomalous diffusion is also considered by taking the SEIR (E: exposed) epidemic model as an example. Similar methods can be used to build other types of epidemic models, including SIVRS (V: vaccine), SIQRS (Q: quarantined) and others. Finally, this paper describes the transmission of infectious disease in space using the real data of COVID-19. [ABSTRACT FROM AUTHOR]

Pine wilt disease is a destructive forest disease with strong infectivity, a wide spread range and high difficulty in prevention and control. Since controlling Monochamus alternatus, the vector of pine wood nematode (Bursaphelenchus xylophilus) can reduce the occurrence of pine wilt disease efficiently, the parasitic natural enemy of M. alternatus, Dastarcus helophoroides, is introduced in this paper. Considering the influence of parasitic time of D. helophoroides on the control effect, based on the mutualistic symbiosis and parasitic relationship among pine wood nematode, M. alternatus and D. heloporoides, this paper establishes a pine wood nematode prevention and control model with delay. Then, the stability of positive equilibrium and the existence of Hopf bifurcation are discussed. Besides, we obtain the normal form of Hopf bifurcation by applying the multiple time scales method. Finally, numerical simulations with two sets of meaningful parameters selected by means of statistical analysis are carried out to support the theoretical findings. Through the comparative analysis of numerical simulations, the factors affecting the control effect of pine wilt disease are obtained, and some suggestions are put forward for practical control in the forest. [ABSTRACT FROM AUTHOR]

In this paper, we mainly investigate the dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria. We first establish the existence of spreading speed, and show that the spreading speed coincides with the minimal wave speed of traveling wavefronts. Moreover, a lower bound estimate of the spreading speed is given. Then, we prove that the traveling wavefronts with large speeds are globally exponentially stable, when the initial perturbation around the traveling wavefronts decays exponentially as x → − ∞ , but the initial perturbation can be arbitrarily large in other locations. The adopted methods are the weighted energy and the squeezing technique. [ABSTRACT FROM AUTHOR]

Self-diffusion prerequisite is obtained as the spreading approach of biological populations. Cooperative hunting is a common behavior in predator populations that promotes predation and the coexistence of the prey–predator system. On the other side, the Allee effect among prey may cause the system to become unstable. In this paper, a diffusive prey–predator system with cooperative hunting and the weak Allee effect in prey populations is discussed. The linear stability and Hopf-bifurcation analysis had been used to examine the system's stability. From the spatial stability of the system, the conditions for Turing instability have been derived. The multiple-scale analysis has been used to derive the amplitude equations of the system. The stability analysis of these amplitude equations leads to the formation of Turing patterns. Finally, numerical simulations are used to analyze spatial patterns forming in 1-D and 2-D. The studies indicate that the model can generate a complex pattern structure and that self-diffusion has a drastic impact on species distribution. [ABSTRACT FROM AUTHOR]

This paper investigates the global dynamics of a reaction–diffusion–advection Leslie–Gower predator–prey model in open advective environments. We find that there exist critical advection rates, intrinsic growth rates, diffusion rates and length of the domain, which classify the global dynamics of the Leslie–Gower predator–prey system into three scenarios: coexistence, persistence of prey only and extinction of both species. The results reveal some significant differences with the classical specialist and generalist predator–prey systems. In particular, it is found that the critical advection rates of prey and predator are independent of each other and the parameters about predation rate have no influence on the dynamics of system. The theoretical results provide some interesting highlights in ecological protection in streams or rivers. [ABSTRACT FROM AUTHOR]

The primary varicella-zoster virus (VZV) infection that causes chickenpox (also known as varicella), spreads quickly among people and, in severe circumstances, can cause to fever and encephalitis. In this paper, the Mittag-Leffler fractional operator is used to examine the mathematical representation of the VZV. Five fractional-order differential equations are created in terms of the disease's dynamical analysis such as S: Susceptible, V: Vaccinated, E: Exposed, I: Infectious and R: Recovered. We derive the existence criterion, positive solution, Hyers–Ulam stability, and boundedness of results in order to examine the suggested fractional-order model's wellposedness. Finally, some numerical examples for the VZV model of various fractional orders are shown with the aid of the generalized Adams–Bashforth–Moulton approach to show the viability of the obtained results. [ABSTRACT FROM AUTHOR]

Many discrete systems have more distinctive dynamical behaviors compared to continuous ones, which has led lots of researchers to investigate them. The discrete predator–prey model with two different functional responses (Holling type I and II functional responses) is discussed in this paper, which depicts a complex population relationship. The local dynamical behaviors of the interior fixed point of this system are studied. The detailed analysis reveals this system undergoes flip bifurcation and Neimark–Sacker bifurcation. Especially, we prove the existence of Marotto's chaos by analytical method. In addition, the hybrid control method is applied to control the chaos of this system. Numerical simulations are presented to support our research and demonstrate new dynamical behaviors, such as period-10, 19, 29, 39, 48 orbits and chaos in the sense of Li–Yorke. [ABSTRACT FROM AUTHOR]

In this paper, we aim to minimize the epidemic size of tungiasis disease and economic costs simultaneously, with terminal demands for infected humans. A human–jigger parasite control system with four control schemes for humans and jiggers is established. We propose a multi-objective optimal control problem with terminal constraints, in which the accumulated number of infected humans and control costs are involved. By applying the modified normal boundary intersection algorithm and the interior point scheme, numerical simulations for different combinations of control schemes are carried out, and actual data in Madagascar are used. Effective combination schemes are indicated from the perspectives of disease eradication, cost saving and time saving. Once these effective combinations are properly performed, the disease can be controlled. When only minimizing the epidemic size, the combination of the optimal treatments and adulticiding efforts is the best choice in the rainy season; the combination of the optimal personal protections and treatments is the preferential option in the dry season. When only minimizing the economical cost, the combination of the optimal adulticide and larvicide is the better selection in the rainy season; the combination of the optimal personal protections, treatments and adulticiding efforts is the prior choose in the dry season. Thus, there is a trade-off between the two objectives for all the effective combinations, decision-makers may choose an appropriate one to control the disease. [ABSTRACT FROM AUTHOR]

For food chain system with three populations, direct predation is the basic interaction between species. Different species often have different predation functional responses, so a food chain system with Holling-II response for middle predator and Beddinton–DeAngelis response for top predator is proposed. Apart from direct predation, predator population can significantly impact the survival of prey population by inducing the prey's fear, but the impact often possesses a time delay. This paper is concentrated to explore how the fear and time delay affect the system stability and the species persistence. By use of Lyapunov functional method and bifurcation theory, the positiveness and boundedness of solutions, local and global behavior of species, the system stability around the equilibrium states and various kinds of bifurcation are investigated. Numerically, some simulations are carried out to validate the main findings and the critical values of the bifurcation parameters of fear and conversion rate are obtained. It is observed that fear and delay can not only stabilize, but also destabilize the system, which depends on the magnitude of the fear and delay. The system varies from unstable to stable due to the continuous increase of the prey's fear by middle predator. Small fear induced by top predator or small delay of the prey's fear can stabilize the system, while they are sufficiently large, the system stability is to be destroyed. Simultaneously, the conversion rate can also change the stability and even make the species to be extinct. Some rich dynamics like multiple stabilities and various types of bistability behaviors are also exhibited, which results in the convergence of the species from one stable equilibrium to another. [ABSTRACT FROM AUTHOR]

This paper handles with a time-space SIR model in two regions which have a common interface. The model is defined as coupled reaction–diffusion system with a robin boundary in interface to predict the immigration between the two regions. As known, the immigration has an influence on the spread of disease, this is caused by immigrants who could carry the disease from their areas to other places. For this reason, this paper deals with the existence of solutions to SIR model with disease spread between different regions by the Fadeo–Galerkin method and validate this result by the numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the long-term sustainability of the northeast Korean pine. We propose a class of natural Korean pine population system with time delay and diffusion term. First, by analyzing the roots distribution of the characteristic equation, we study the stability of the model system with diffusion terms and prove the occurrence of Hopf bifurcation. Second, we introduce lactation time delay into a population model with a diffusion term, based on stability theory of ordinary differential equation, norm form methods and center manifold theorem, the stability of bifurcating periodic solutions and the relevant formula for the direction of Hopf bifurcation are given. Finally, some numerical simulations are given. [ABSTRACT FROM AUTHOR]

In this paper, we propose and investigate a delayed diffusive predator–prey model affected by toxic substances. We first study the boundedness and persistence property of the model. By analyzing the associated characteristic equation, we obtain the conditions for the existence of steady state bifurcation, Hopf bifurcation and Turing bifurcation. Furthermore, we also study the Hopf bifurcation induced by the delay. Finally, our theoretical results are verified by numerical simulation. The numerical observation results are in good agreement with the theoretically predicted results. Theoretical and numerical simulations indicate that toxic substances have a great impact on the dynamics of the system. [ABSTRACT FROM AUTHOR]

Traditional biological neural networks cannot simulate the real situation of the abrupt synaptic connections between neurons while modeling associative memory of human brains. In this paper, the memristive multidirectional associative memory neural networks (MAMNNs) with mixed time-varying delays are investigated in the sense of Filippov solution. First, three steps are given to prove the existence of the almost periodic solution. Two new lemmas are proposed to prove the boundness of the solution and the asymptotical almost periodicity of the solution by constructing Lyapunov function. Second, the uniqueness and global exponential stability of the almost periodic solution of memristive MAMNNs are investigated by a new Lyapunov function. The sufficient conditions guaranteeing the properties of almost periodic solution are derived based on the relevant definitions, Halanay inequality and Lyapunov function. The investigation is an extension of the research on the periodic solution and almost periodic solution of bidirectional associative memory neural networks. Finally, numerical examples with simulations are presented to show the validity of the main results. [ABSTRACT FROM AUTHOR]

The spread of infectious diseases often presents the emergent properties, which leads to more difficulties in prevention and treatment. In this paper, the SIR model with both delay and network is investigated to show the emergent properties of the infectious diseases' spread. The stability of the SIR model with a delay and two delay is analyzed to illustrate the effect of delay on the periodic outbreak of the epidemic. Then the stability conditions of Hopf bifurcation are derived by using central manifold to obtain the direction of bifurcation, which is vital for the generation of emergent behavior. Also, numerical simulation shows that the connection probability can affect the types of the spatio-temporal patterns, further induces the emergent properties. Finally, the emergent properties of COVID-19 are explained by the above results. [ABSTRACT FROM AUTHOR]

The sterile insect technique (SIT) has been applied as an alternative method to reduce or eradicate mosquito-borne diseases. To explore the impact of the sterile mosquitoes on controlling the wild mosquito populations, in this paper, we further extend the work in [J. Li, New revised simple models for interactive wild and sterile mosquito populations and their dynamics, J. Biol. Dyn. 11(S2) (2017) 316–333] and formulate delayed models for interactive wild and sterile mosquitoes, which can depict wild mosquito population undergoing distinct stages of development during a lifetime. By performing mathematical analysis, the threshold dynamics of the proposed models are explored, respectively. In particular, Hopf bifurcation phenomena are observed as the delay τ is varying. Numerical examples illustrate our 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]

Szemerédi’s Regularity Lemma (SRL) is a crucial tool in the analysis of large graphs, having made significant contributions in the proof of some sensational results in mathematics. Traditional methods for studying proteins in Protein–Protein Interaction (PPI) networks typically only extract the first-order or second-order neighbor information of proteins, ignoring the potential third-order or higher-order neighbor information between proteins, which may hide certain relationships between proteins. To explore more in-depth insights for PPI networks, we take into account the fourth-order neighbor information of proteins and reconstruct the network in this paper, naming it the weighted dense PPI network. We then partition it using SRL, which primarily utilizes the structural information and corresponds to a unique partition of the original network. Bioinformatics analyses such as those for pathway enrichment analysis and multiple sequence alignment show that our method can classify interacting protein pairs, grouping proteins with functional association, disease association, and sequence similarity together. Overall, this paper has three essential contributions: (1) we present a new model to overcome the astronomically large demand of vertices in applying SRL, and achieve protein classification; (2) we reconstruct a weighted dense PPI network which can make SRL work and mine potential interactions more efficiently; and (3) proteins in the same class partitioned by our method not only have sequence similarity, but also have functional associations. [ABSTRACT FROM AUTHOR]

In this paper, we study the pulsating traveling fronts for a spatially discrete periodic reaction–diffusion system with a quiescent stage. It is known that there exists a critical number c∗ > 0 (called minimal wave speed) such that a pulsating traveling front exists if and only if its speed is above c∗. In this paper, we derive a uniqueness theorem for supercritical pulsating traveling fronts. Further, we show that all supercritical pulsating traveling fronts are exponentially stable. [ABSTRACT FROM AUTHOR]

In this paper, we study a diffusive predator–prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition. We first analyze the influence of prey-taxis on the local stability of constant equilibria. It turns out that prey-taxis has influence on the stability of the unique positive constant equilibrium, but has no influence on the stability of the trivial equilibrium and the semi-trivial equilibrium. We then derive Hopf bifurcation and steady state bifurcation related to prey-taxis, which imply that the prey-taxis plays an important role in the dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear ratio-dependent prey–predator model with constant prey refuge in the prey population. Both Allee and fear phenomena are incorporated explicitly in the growth rate of the prey population. The qualitative behaviors of the proposed model are investigated around the equilibrium points in detail. Hopf bifurcation including its direction and stability for the model is also studied. We observe that fear of predation risk can have both stabilizing and destabilizing effects and induces bubbling phenomenon in the system. It is also observed that for a fixed strength of fear, an increase in the Allee parameter makes the system unstable, whereas an increase in prey refuge drives the system toward stability. However, higher values of both the Allee and prey refuge parameters have negative impacts and the populations go to extinction. Further, we explore the variation of densities of the populations in different bi-parameter spaces, where the coexistence equilibrium point remains stable. Numerical simulations are carried out to explore the dynamical behaviors of the system with the help of MATLAB software. [ABSTRACT FROM AUTHOR]

The study of rumor propagation dynamics is of great significance to reduce false news and ensure the authenticity of news information. In this paper, a SI reaction-diffusion rumor propagation model with nonlinear saturation incidence is studied. First, through stability analysis, we obtain the conditions for the existence and local stability of the positive equilibrium point. By selecting suitable variable as the control parameter, the critical value of Turing bifurcation and the existence theorem of Turing bifurcation are obtained. Then, using the above theorem and multi-scale standard analysis, the expression of amplitude equation around Turing bifurcation point is obtained. By analyzing the amplitude equation, different types of Turing pattern are divided such as uniform steady-state mode, hexagonal mode, stripe mode and mixed structure mode. Further, in the numerical simulation part, by observing different patterns corresponding to different values of control variable, the correctness of the theory is verified. Finally, the effects of different network structures on patterns are investigated. The results show that there are significant differences in the distribution of users on different network structures. [ABSTRACT FROM AUTHOR]

A nonlinear infectious disease model with information-influenced vaccination behavior and contact patterns is proposed in this paper, and the impact of information related to disease prevalence on increasing vaccination coverage and reducing disease incidence during the outbreak is considered. First, we perform the analysis for the existence of equilibria and the stability properties of the proposed model. In particular, the geometric approach is used to obtain the sufficient condition which guarantees the global asymptotic stability of the unique endemic equilibrium E e when the basic reproduction number R 0 > 1. Second, mathematical derivation combined with numerical simulation shows the existence of the double Hopf bifurcation around E e . Third, based on the numerical results, it is shown that the information coverage and the average information delay may lead to more complex dynamical behaviors. Finally, the optimal control problem is established with information-influenced vaccination and treatment as control variables. The corresponding optimal paths are obtained analytically by using Pontryagin's maximum principle, and the applicability and validity of virous intervention strategies for the proposed controls are presented by numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we propose a size-stage-structured cooperation model which has two distinct life stages in facultative cooperator. The primary feature of this model is to consider size structure, stage structure and obligate and facultative symbiosis at the same time in a cooperation system. We use the method of characteristic to show that this new model can be reduced to a threshold delay equations (TDEs) model, which can be further transformed into a functional differential equations (FDEs) model by a simple change of variables. Such simplification allows us to apply the classical theory of FDEs and establish a set of sufficient conditions to investigate the qualitative analysis of solutions of the FDEs model, including the global existence and uniqueness, positivity and boundedness. What's more, we use the geometric criteria to get the conclusions about stability and Hopf bifurcation of positive equilibrium because the coefficients of the characteristic equation depend on the bifurcation parameter. Finally, numerical simulations are carried out as supporting evidences of our analytical results. Our results show that the presence of size structure and stage structure plays an important role in the dynamic behavior of the model. [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]

This paper has been motivated by the following ecological question: how influential is the water stress on plants production? The aim of this paper is to investigate the impact of water stress and irrigation on plants production. We propose a mathematical model for the dynamics growth of plants that takes into account the concentration of available water in the soil, the absorption of water by plants, water stress, the plants production and the plants compensation. We present the theoretical analysis of the model. More precisely, we show that the model is well-posed. We also compute trivial equilibria and derive a threshold parameter that determines the outcome of water stress within a plantation. Further, we perform a numerical simulation in the case of banana-plantain plant to support and valid theoretical results. We found that the Hopf bifurcation occurs for a specific value of the water absorption rate of unstressed plants. The impact of the water stress on the banana-plantain production is also numerically investigated. We found that the water stress can cause about 62.57% tons of loss of banana-plantain production within a plantation with 1600 rejects initially planted. We also consider the irrigation as a control parameter of water stress. We found that the irrigation increases the stressed plant production to more than 60% for 1600 rejects initially planted. This suggests that climate change may play a detrimental role on banana-plantains production. We also investigate the role of the type of soil in banana-plantain production. Our finding suggests that the Fine Sandy Loam soil is more resilient to water stress than Silty Clay and Loamy soils. [ABSTRACT FROM AUTHOR]

Optimal control technique is crucial to improve the yield of microbial fermentation production. In this paper, we propose a nonlinear control system with state-dependent impulses, where the impulsive volume of feeding glycerol and the critical concentration of glycerol for occurring impulse are the control variables, to formulate 1,3-propanediol (1,3-PD) fed-batch production process. We also discuss a quantity of important properties for this control system. Then, we analyze the sensitivity of system state with respect to the kinetic parameters. We further propose a constrained optimal control model governed by the control system with state-dependent impulses. The existence of the optimal impulsive controls is established. For solving this problem, we utilize an exact penalty method to transform the problem into an optimization problem with only box constraints. Moreover, an improved differential evolution method is developed to seek the optimal impulsive strategy. Finally, numerical simulation results demonstrate that, by using the optimal impulsive strategies, final 1,3-PD concentration is considerably increased under the nominal parameter values and disturbances of kinetic parameters have significant effects on the optimal final 1,3-PD yield. [ABSTRACT FROM AUTHOR]

This paper considered a multi-stage sheep brucellosis model with incomplete immunity. First, we established a deterministic model, calculated the basic reproduction number ℛ 0 , set out the conditions for the global stability of the disease-free equilibrium and endemic equilibrium. Second, considering the influence of environmental white noise on brucellosis infection, we further established the stochastic version of the model. By constructing a suitable Lyapunov function, we proved the existence and uniqueness of the global positive solution. Further, we got the sufficient conditions for disease extinction and the existence of ergodic stationary distribution. Finally, we carried out some numerical simulations to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Waterborne disease threatens public health globally. Previous studies mainly consider that the birth of pathogens in water sources arises solely by the shedding of infected individuals. However, for free-living pathogens, intrinsic growth without the presence of hosts in environment could be possible. In this paper, a stochastic waterborne disease model with a logistic growth of pathogens is investigated. We obtain the sufficient conditions for the extinction of disease and also the existence and uniqueness of an ergodic stationary distribution if the threshold ℛ 0 s > 1. By solving the Fokker–Planck equation, an exact expression of probability density function near the quasi-endemic equilibrium is obtained. Results suggest that the intrinsic growth in bacteria population induces a large reproduction number to determine the disease dynamics. Finally, theoretical results are validated by numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates multiple bifurcations analyses and strong resonances of the Bazykin–Berezovskaya predator–prey model in depth using analytical and numerical bifurcation analysis. The stability conditions of fixed points, codim-1 and codim-2 bifurcations to include multiple and generic bifurcations are studied. This model exhibits transcritical, flip, Neimark–Sacker, and 1 : 2 , 1 : 3 , 1 : 4 strong resonances. The normal form coefficients and their scenarios for each bifurcation are examined by using the normal form theorem and bifurcation theory. For each bifurcation, various types of critical states are calculated, such as potential transformations between the one-parameter bifurcation point and different bifurcation points obtained from the two-parameter bifurcation point. To validate our analytical findings, the bifurcation curves of fixed points are determined by using MatcontM. [ABSTRACT FROM AUTHOR]

In this paper, a discrete-time SIR epidemic model with nonlinear incidence and recovery rates is obtained by using the forward Euler's method. The existence and stability of fixed points in this model are well studied. The center manifold theorem and bifurcation theory are applied to analyze the bifurcation properties by using the discrete time step and the intervention level as control parameters. We discuss in detail some codimension-one bifurcations such as transcritical, period-doubling and Neimark–Sacker bifurcations, and a codimension-two bifurcation with 1:2 resonance. In addition, the phase portraits, bifurcation diagrams and maximum Lyapunov exponent diagrams are drawn to verify the correctness of our theoretical analysis. It is found that the numerical results are consistent with the theoretical analysis. More interestingly, we also found other bifurcations in the model during the numerical simulation, such as codimension-two bifurcations with 1:1 resonance, 1:3 resonance and 1:4 resonance, generalized period-doubling and fold-flip bifurcations. The results show that the dynamics of the discrete-time model are richer than that of the continuous-time SIR epidemic model. Such a discrete-time model may not only be widely used to detect the pathogenesis of infectious diseases, but also make a great contribution to the prevention and control of infectious diseases. [ABSTRACT FROM AUTHOR]

Recent evidences show that individuals who recovered from COVID-19 can be reinfected. However, this phenomenon has rarely been studied using mathematical models. In this paper, we propose an SEIRE epidemic model to describe the spread of the epidemic with reinfection. We obtain the important thresholds R 0 (the basic reproduction number) and R c (a threshold less than one). Our investigations show that when R 0 > 1 , the system has an endemic equilibrium, which is globally asymptotically stable. When R c < R 0 < 1 , the epidemic system exhibits bistable dynamics. That is, the system has backward bifurcation and the disease cannot be eradicated. In order to eradicate the disease, we must ensure that the basic reproduction number R 0 is less than R c . The basic reinfection number is obtained to measure the reinfection force, which turns out to be a new tipping point for disease dynamics. We also give definition of robustness, a new concept to measure the difficulty of completely eliminating the disease for a bistable epidemic system. Numerical simulations are carried out to verify the conclusions. [ABSTRACT FROM AUTHOR]

In this paper, a class of non-autonomous stochastic Nicholson's blowflies systems with patch structure and time delays is formulated and studied. By constructing suitable Lyapunov functions and using the stochastic technical, the pth moment boundedness and almost sure growth bounds are discussed, which reveal that solutions of the system do not exceed the time value t and the sample Lyapunov exponent is no more than zero. Then, the system is proved to be exponentially stable (or extinct) if the production rate is less than the mortality rate, which provides an effective reference for the population control. Moreover, taking into account the specific form of time-varying coefficients, related results for several classical stochastic Nicholson's blowflies systems are studied, and they show the significant improvement of this paper. Finally, numerical simulations for several specific examples are carried out to illustrate our theoretical conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamics behavior of stochastic hybrid switching staged progression model for the transmission of HIV. The method used in this paper is Lyapunov functions analysis. We establish sufficient conditions for extinction of disease. Especially, we conclude that there is a stationary distribution for the stochastic system and it has ergodicity under appropriate conditions. Finally, some examples and their simulations are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The aim of this research paper is to model the effects of misidentification in the transmission dynamics of the super yeast, Candida auris (or C. auris), among patients receiving treatment in the Intensive Care Units (ICUs). The mathematical analysis is carried out by obtaining the reproduction number of the C. auris model using the next generation matrix and utilizing it as a threshold value to establish the local and global stability properties at the points of equilibria. The numerical investigations carried out in this paper establish the outcomes of the effect of variations in the values of important parameters on the dynamics of C. auris colonization and infections in the health care settings. The corresponding results from the numerical simulations are illustrated graphically. [ABSTRACT FROM AUTHOR]

Considering the prevailing situations, the mathematical modeling and dynamics of novel coronavirus (2019-nCoV) particularly in India are studied in this paper. The goal of this work is to create an effective SEIRS model to study about the epidemic. Four different SEIRS models are considered and solved in this paper using an efficient homotopy perturbation method. A clear picture of disease spreading can be obtained from the solutions derived using this method. We parametrized the model by considering the number of infection cases from 1 April 2020 to 30 June 2020. Finally, numerical analysis and graphical representations are provided to interpret the spread of virus. [ABSTRACT FROM AUTHOR]

In this paper, a reaction–diffusion SEI epidemic model with nonlinear incidence rate is proposed. The well-posedness of solutions is studied, including the existence of positive and unique classical solution and the existence and the ultimate boundedness of global solutions. The basic reproduction numbers are given in both heterogeneous and homogeneous environments. For spatially heterogeneous environment, by the comparison principle of the diffusion system, the infection-free steady state is proved to be globally asymptotically stable if R 0 < 1 , if R 0 > 1 , the system will be persistent and admit at least one positive steady state. For spatially homogenous environment, by constructing a Lyapunov function, the infection-free steady state is proved to be globally asymptotically stable if R 0 < 1 , and then the unique positive steady state is achieved and is proved to be globally asymptotically stable if R 0 > 1. Finally, two examples are given via numerical simulations, and then some control strategies are also presented by the sensitive analysis. [ABSTRACT FROM AUTHOR]