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Studying the interplay of phytoplankton–zooplankton–fish (PP–ZP–F) in an aquatic system is crucial for better understanding of nutrient cycling, assessing ecosystem health, predicting and mitigating harmful algal blooms, and managing fisheries in the water bodies. In order to investigate the effectiveness of nanoparticles (NPs), fear, and harvesting, this paper focuses on exploring the dynamics of a food chain model among PP–ZP–F species. We consider the fear of fish on zooplankton species (which reduces the reproduction rate of ZPs) with saturated fear cost in the presence of nanoparticles (NPs) and harvesting in fish. The system dynamics are studied from the viewpoint of proving positivity, boundedness, and uniqueness, followed by analysing the existence and local stability of biologically feasible equilibria. Conditions for the global stability of the interior equilibrium point are also found. Furthermore, we established the transversality conditions for the occurrence of Hopf, transcritical, and saddle–node bifurcations. To validate our theoretical results, we made numerous phase portraits, time-series graphs, tables showing the extinction of species, and bifurcation diagrams. It is numerically observed that increasing the contact rate of NPs with PPs makes the system stable from chaos, and further increase of contact rate may lead to extinction. Chaos at a low contact rate can also be managed by increasing the fear level, and the chaotic behaviour at a low fear level can again be controlled by enhancing the harvesting of fish species. Over-exploitation may result in the extinction of fish, whereas fear may promote coexistence, stability, and long-term survival of the species. Increased saturated fear cost can make the system chaotic from stable dynamics. Therefore, the theoretical as well as numerical findings of our paper may be of great interest in estimating the behaviour of aquatic systems biologically and practically. [ABSTRACT FROM AUTHOR]

The spreading of HIV or HTLV-I among the cells has received the great attention in recent modelling study to explore the virus infection dynamics. The co-infection of HIV and HTLV-I with the effect of Cytotoxic T-lymphocytes (CTLs) immune response is also important from epidemiological point of view. To identify the co-infection scenario of HIV and HTLV-I with the CTLs effect we proposed in this paper a six compartmental ODE-model with uninfected, HIV-infected, HTLV-I infected CD4+T cells and free HIV virus particles with HIV specific CTLs and HTLV-I specific CTLs. The rates of infection of the cases are considered here saturated type and proliferation rate of uninfected and HIV infected CD4+ T-cells are of logistic terms. To establish the well-posedness of the model we have shown that the solution of the proposed model is non-negative and bounded. We obtain the basic reproduction number which is the maximum of the HIV-related reproduction and the HTLV-I related reproduction number. Along with the disease free equilibrium point the system contains other seven endemic equilibrium points containing infection by single disease or both. Analytically, we establish the local and global stability conditions of the equilibrium points and also we establish that the system experiences transcritical bifurcation by the generation of only HIV or HTLV-I infected endemic equilibrium point. Using numerical simulations, we validate the theoretical results and found two infection paths, one initiating with HIV and other with HTLV-I, both cases ultimately become co-infected. Finally, using the optimal control analysis we found the optimal policy for treatment using AVR, RTI & PI for HIV or AZT for HTLV-I control and lastly concluded by some recommendations. • A co-infected HIV & HTLV-I infection model in vivo. • Proliferation of CD4+ T-cells are taken in logistic form. • Incidence rate is taken as saturated type. • Verified competitive exclusive principle. • Spreading path has been studied using Flow-diagram. • Three types of control strategies are investigated. [ABSTRACT FROM AUTHOR]

This paper studies the global dynamics of an SEIR (Susceptible–Exposed–Infectious–Recovered) model with nonlocal diffusion. We show the model's well-posedness, proving the solutions' existence, uniqueness, and positivity, along with a disease-free equilibrium. Next, we prove that the model admits the global threshold dynamics in terms of the basic reproduction number R 0 , defined as the spectral radius of the next-generation operator. We show that the solution map has a global compact attractor, offering insights into long-term dynamics. In particular, the analysis shows that for R 0 < 1 , the disease-free equilibrium is globally stable. Using the persistence theory, we show that there is an endemic equilibrium point for R 0 > 1. Moreover, by constructing an appropriate Lyapunov function, we establish the global stability of the unique endemic equilibrium in two distinct scenarios. [ABSTRACT FROM AUTHOR]

This paper aims to study an HIV model with age structure and latently in a spatially homogeneous environment. By applying the fixed point theorem, we obtain the existence of the global solution and the global attractor for the model. We also identify the explicit formula of the basic reproduction number by the mean of the Laplace transformation, and confirm that this number predicts whether the infection occurs or not. Through analyzing the root distribution of the characteristic equation, the local stability of the equilibrium is obtained. By appealing to the appropriate Lyapunov functionals, we further study the global stability of the equilibrium. Numerical simulations also validate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an age-structured infectious disease dynamical model that considers two diseases simultaneously but with limited medical resources is proposed and analyzed. The asymptotic smoothness and persistence of the solution semi-flow are investigated. Then conditions for the existence of a global attractor are derived, which means that disease persists when ℜ 0 > 1. By using a Lyapunov function, it is shown that the infection-free equilibrium is globally asymptotically stable if ℜ 0 < 1 and the infection equilibrium is globally asymptotically stable if ℜ 0 > 1. In the presence of limited medical resources, the results suggest that equitable distribution for the limited medical resources is significant when treating low-risk and high-risk diseases and that keeping a resource sharing coefficient at a moderate level helps to eliminate the disease. • We proposed an age-structured infectious disease model with limited medical resources. • some important parameters were included in ℜ 0. • ℜ 0 determines the global stability of the equilibria. • Discussions of the effects of the parameters and biological significance were provided. [ABSTRACT FROM AUTHOR]

It is well known that the mathematical biology and dynamical systems give very important information for the study and research of viral infection models such as HIV, HBV, HCV, Ebola and Influenza. This paper deals with the global dynamics of generalized virus model with logistic growth rate for target cells, general incidence rate and cellular immunity. The results will be obtained by using Lyapunov's second method and LaSalle's invariance principle. We prove the global stability of the rest points of the system by the value of basic reproduction number (R 0) and the immune response reproduction number (R CTL). We have found that if R 0 < 1 , then the infection-free equilibrium is globally asymptotically stable. For R 0 > 1 and R CTL < 1 , under certain conditions on incidence rate function, immune-free equilibrium is globally asymptotically stable. Finally, we prove that if R 0 > 1 and R CTL > 1 , then under certain conditions on incidence rate function the endemic equilibrium is globally asymptotically stable. Since the logistic growth rate for target cells and general incidence rate have been included in this manuscript, our obtained results are the generalization of those in the previous literatures. Moreover, the results have been obtained with weaker assumptions in comparison with the previous ones. Numerical simulations are presented to support and illustrate our analytical results. [ABSTRACT FROM AUTHOR]

This paper aims to explore the behavior of malware propagation on mobile wireless sensor networks (MWSNs). A new malware propagation model with nonlinear incidence rate and sigmoid type removal rate is established, and its global stability, spatiotemporal stability, and optimal control are analyzed. Specifically, the theoretical analysis shows that (i) a forward transcritical bifurcation occurs when the basic reproduction number R 0 > 1 ; (ii) time and space affect the spreading behavior of malware due to spatial distribution; (iii) the optimization technology can effectively control the malware spreading on MWSNs. Finally, some numerical simulations are performed to verify the obtained theoretical results, and the experimental results confirm that the generated patterns are consistent with the field observations of actual MWSNs. Our study helps in controlling the propagation of malware and applicable to design and prediction of the security and robustness of a sensor network. • A new malware propagation model with nonlinear incidence rate and sigmoid type removal rate is studied. • Global stability, spatiotemporal stability, and optimal control are analyzed. • Optimal control technique is employed to reduce the malware propagation. • Stability switching phenomena are obtained via Hopf bifurcation. • Spatio-temporal dynamics depends on transmission rate, time movement of nodes and its initial deployment. [ABSTRACT FROM AUTHOR]

A mathematical model for the CD8+ T-cell response to Human T cell leukemia/lymphoma virus type I (HTLV-I) infection is investigated in this paper. The proposed model, which involves four coupled nonlinear ordinary differential equations, describes the interaction of uninfected CD4+T cells, latently infected CD4+T cells, actively infected CD4+T cells and HTLV-I specific cytotoxic T-lymphocytes (CTLs). Our model exhibits three biologically feasible equilibria, namely infection-free steady state, HTLV-I free steady state and an endemic steady state. Our mathematical analysis establishes that the local and global dynamics are determined by the two threshold parameters R 0 and R 1 , basic reproduction number for HTLV-I viral infection and for CTL response, respectively. For R 0 < 1 , the infection-free steady state E 0 is globally asymptotically stable, and HTLV-I viruses are cleared. For R 1 ≤ 1 < R 0 , the HTLV-I free singular point E 1 is globally asymptotically stable, and the HTLV-I infection becomes chronic but no CTL response can be established, and most of the HTLV-I infected individual remains as an asymptomatic carrier. Mathematical analysis shows that a unique endemic steady state E ∗ is globally asymptotically stable for R 1 > 1 in the interior of the feasible region. We perform the sensitivity analysis to find out the key parameters of the HTLV-I infection model with respect to R 0 and R 1. Implications of our findings to the dynamics of CTL response to HTLV-I infections in vivo and pathogenesis of HTLV-I associated myelopathy/tropical spastic paraparesis (HAM/TSP) are discussed. • We investigate a model for HTLV-I infection with CTL response. • Local and global dynamics are determined by the threshold parameters R 0 and R 1. • For R 1 ≤ 1 < R 0 , E 1 is globally asymptotically stable and HTLV-I infection becomes chronic. • Performed global asymptotic stability for E ∗ using Lyapunov function and by geometric approach. • Sensitivity analysis has been done with respect to R 0 and R 1. [ABSTRACT FROM AUTHOR]

In this paper, a fully discrete θ -method with 0 ≤ θ ≤ 1 is suggested to solve the initial–boundary value problem of semi-linear reaction–diffusion equations with time-variable delay. Under some appropriate conditions, a novel global stability criterion of the method is derived and it is shown that this method has the computational accuracy O (τ 2 + h 2) (resp. O (τ + h 2)) when θ = 1 2 (resp. θ ≠ 1 2) , where h and τ denote spatial and temporal stepsizes, respectively. Moreover, with some numerical experiments, the theoretical accuracy and global stability of the method are further illustrated. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical solutions of nonlinear functional-differential and functional equations (FDFEs) with constant delay. The block boundary value methods (BBVMs) are extended to solve the FDFEs. Under the suitable conditions, it is shown that the extended BBVMs are uniquely solvable and globally stable. Moreover, the method can be convergent of order p whenever the Lipschitz condition holds and this method is preconsistent and p -order consistent. With several numerical examples, the theoretical results and computational validity of the extended BBVMs are further confirmed. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we analyze the Zika virus transmission dynamics on human and mosquito populations. Mosquitoes play a role of infectious agents and vector of the Zika virus (ZIKV). In this sense, we set out a mathematical model assuming constant size population for the evolution of the infected humans with ZIKV and analyze its qualitative dynamics. The epidemic threshold parameter R 0 for the extinction of disease is computed. Numerical simulations of the model varying the numerical values of the parameters corroborate the theoretical results regarding R 0. The values of the parameters related to the mathematical model of the Zika epidemic are estimated using real data from Zika prevalence in Colombia for year 2016. We find a R 0 = 0. 88 for this particular case which allows us to understand and explain some aspects of the Zika epidemic in Colombia. These results are valuable since they can be compared with Zika epidemics in other countries and from other years, and enrich the knowledge about the dynamics of the spread of Zika virus. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies stationary oscillation for a time-varying recurrent cellular neural network with time delays and impulses. In a recent paper, the authors claim that they obtain a criterion of existence, uniqueness, and global exponential stability of periodic solution (i.e. stationary oscillation) for a recurrent cellular neural network with time delays and impulses. We point out that the main result of their paper is incorrect, and present a sufficient condition of stationary oscillation for a time-varying recurrent cellular neural networks with time delays and impulses. An numerical example is given to illustrate the effectiveness of the obtained result. [Copyright &y& Elsevier]

In this paper, a within-host chikungunya virus infection model with two delays is considered. The basic reproductive number R 0 is formulated. If R 0 < 1 , the virus-free equilibrium is globally asymptotically stable and the disease always dies out. If R 0 > 1 , the global stability of the unique endemic equilibrium E 1 is proved for the case without the time delay of antigenic stimulation, which can change the stability of E 1 and lead to the existence of Hopf bifurcation. Furthermore, explicit formulae for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are established. Finally, some numerical simulations are presented to illustrate the results. [ABSTRACT FROM AUTHOR]

HIV can infect different cell populations such as CD4+ T cells and macrophages. In this paper, we study the global property of the solution of an HIV model with two target cell populations. The model includes general nonlinear rates of viral infection and cell death. For each class of target cells, the time delay between viral entry into cells and viral production is included in the model. We obtain the basic reproductive number of the model, which is shown to provide a threshold condition determining the long-term behavior of the solution of the model. Specifically, we show that the infection-free equilibrium is globally asymptotically stable when the basic reproductive number is less than or equal to 1, and that the infected equilibrium is globally asymptotically stable when the basic reproductive number is greater than 1. We also extend the model with two target cell populations to a general model with n populations. Similar global properties are obtained for the general model. Numerical simulations are performed to illustrate the stability results and to evaluate the relative contribution to viral production from the two cell populations. [ABSTRACT FROM AUTHOR]

This paper deals with dynamic behaviors of Hopfield type neural network model of n ( ≥ 3 ) identical neurons with two time-delayed connections coupled in a star configuration. Delay dependent as well as independent local stability conditions about trivial equilibrium is found. Considering synaptic weight and time delay as parameters Hopf-bifurcation, steady-state bifurcation and equivariant steady state bifurcation criteria are given. The criterion for the global stability of the system is presented by constructing a suitable Lyapunov functional. Also conditions for absolute synchronization about the trivial equilibrium are also shown. Using normal form method and the center manifold theory the direction of the Hopf-bifurcation, stability and the properties of Hopf-bifurcating periodic solutions are determined. Numerical simulations are presented to verify the analytical results. The effect of synaptic weight and delay on different types of oscillations, e.g. in-phase, phase-locking, standing wave and oscillation death, has been shown numerically. [ABSTRACT FROM AUTHOR]

Abstract: We focus on an epidemic model which incorporates a non-linear force of infection and two controls: an imperfect preventive vaccine given to susceptible individuals and therapeutic treatment given to infectious. We study both the cases of constant and non constant controls. In the case of constant controls we perform a qualitative analysis based on Lyapunov stability which allows to integrate the bifurcation analysis performed in a previous paper. The occurrence of a backward bifurcation is discussed in the perspective of disease control. The case of time-dependent controls is studied by means of the optimal control theory. The strategy is to minimize both the disease burden and the intervention costs. We derive the optimality system and solve it numerically. The characterization of the optimal time profile of the controls, together with the qualitative analysis provides a rather complete picture of the possible outcomes of the model. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the dynamical behavior of a virus infection model with general incidence rate and humoral immunity. By using suitable Lyapunov functional and the LaSalle's invariance principle, we establish the global stability of the three equilibria. The uninfected equilibrium E 0 is globally asymptotically stable if R 0 ≤1, the infected equilibrium without immunity E 1 is globally asymptotically stable if R 1 ≤1 and R 0 >1, the infected equilibrium with humoral immunity E 2 is globally asymptotically stable if R 1 >1. We check our theorems with numerical simulation in the end. [Copyright &y& Elsevier]

Abstract: In this paper, an SEIS epidemiological model with a saturation incidence rate and a time delay representing the latent period of the disease is investigated. By means of Lyapunov functional, LaSalle''s invariance principle and comparison arguments, it is shown that the global dynamics is completely determined by the basic reproduction number. It is proven that the basic reproduction number is a global threshold parameter in the sense that if it is less than unity, the disease-free equilibrium is globally asymptotically stable and therefore the disease dies out; whereas if it is greater than unity, there is a unique endemic equilibrium which is globally asymptotically stable and thus the disease becomes endemic in the population. Numerical simulations are carried out to illustrate the main results. [Copyright &y& Elsevier]

Abstract: This paper describes a prey–predator model with Holling type II functional response incorporating prey refuge. The equilibria of the proposed system are determined and the behavior of the system is investigated around equilibria. Density-dependent mortality rate for the predator is considered as bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighborhood of the co-existing equilibrium point. Discrete-type gestational delay of predators is also incorporated on the system. The dynamics of the delay induced prey–predator system is analyzed. Delay preserving stability and direction of the system is studied. Global stability of the delay preserving system is shown. Finally, some numerical simulations are given to verify the analytical results, and the system is analyzed through graphical illustrations. [Copyright &y& Elsevier]

Abstract: In this paper, we incorporate the periodic therapy from antiretroviral drugs for HIV into the standard within-host virus model, and study the stability and bifurcation of the system. It is shown that when the basic reproduction number of virus is less than one, there is an infection-free equilibrium which is globally stable. Further, if it is greater than one, the HIV infection is uniformly persistent. Besides, subharmonic bifurcation occurs under suitable conditions, and chaotic attractor may emerge through period doubling routes, which can be used to explain the HIV patients’ unpredictable unstable health states, even after a long and hard treatment. [Copyright &y& Elsevier]

Abstract: A nonlinear predictive controller (NPC) for a permanent magnet synchronous motor (PMSM) is proposed in this paper. Its objective is high performance tracking of the rotor speed trajectory while maintaining the d-axis component of the armature current at zero. The load torque and the mismatched parameters are considered to be unknown perturbations. To ensure robustness against these perturbations, a disturbance observer is designed using a new gain function, and integrated into the control law. The combination of the nonlinear predictive controller and the disturbance observer works as a nonlinear controller. The overall closed-loop system is proved to be globally asymptotically stable depending on the design parameters. The validity of the proposed controller was tested by simulations. Satisfactory results were obtained with respect to the tracking of the speed trajectory and disturbance rejection. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates a viral infection model with periodic immune response and nonlinear cytotoxic T lymphocyte (CTL) response. Using the periodic rhythms of human immune system, the model can avoid the unreasonable equilibrium in the basic viral model with nonlinear CTL response introduced by Nowak et al. We obtain the global stability of the infection-free equilibrium and the immune-exhausted equilibrium. Numerical simulations show that the oscillation of immune system can affect the pattern of the viral dynamical behaviors. Period doubling bifurcations of the system are observed via simulations. This can provide a possible interpretation for the viral oscillation behaviors, which were observed in chronic HBV and HCV infection patients. [ABSTRACT FROM AUTHOR]