Search

We consider a class of forced continuous-time Lur'e systems obtained by applying nonlinear feedback to a higher-order linear differential equation which defines an input-output system in the sense of behavioural systems theory. This linear system directly relates the input and output signals and does not involve any internal, latent or state variables. A stability theory subsuming results of circle criterion type is developed, including criteria for input-to-output stability and strong integral input-to-output stability, concepts which are very much reminiscent of input-to-state stability and strong integral input-to-state stability, respectively. The methods used in the paper combine ideas from the behavioural approach to systems and control, absolute stability theory and input-to-state stability theory. [ABSTRACT FROM AUTHOR]

In this paper, a SIS epidemic model with nonlinear incidence and ratio dependent pulse control is proposed and analyzed. Firstly, for the system that ignores the effect of pulses, the basic reproductive number R 0 is derived using the next-generation matrix method, and the stability of the equilibria of the system is analyzed. And then the dynamics of the system containing pulse effects was investigated. The existence of periodic solutions has been proven by constructing appropriate Poincaré mappings and using the fixed point theorem. We found that pulses have a significant impact on system dynamics. Under the influence of pulses, the system trajectory undergoes periodic oscillations, which are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a predator–prey model with fear-induced group defense and Monod–Haldane functional response is considered. We establish a connection between fear effect and group defense by incorporating anti-predator sensitivity and emphasizing their impact on the dynamics of the model. Our analysis shows that increasing anti-predator sensitivity lowers the threshold for initiating group defense, leading to faster adoption of prey defense strategies. The preliminary results include positivity, boundedness, and persistence. We find that under certain thresholds, anti-predator sensitivity can sustain species persistence; otherwise, predators may face extinction. Changes in anti-predator sensitivity significantly influence system dynamics, notably affecting the quantity and stability of equilibrium points. We provide a comprehensive analysis of the global properties of both boundary and interior equilibrium points. Additionally, the system undergoes Transcritical, Saddle-node and Hopf bifurcation by considering the anti-predator sensitivity as a bifurcation parameter and Bogdanov–Takens bifurcation with respect to the prey birth rate and the anti-predator sensitivity. Numerical simulations support our theoretical findings. Our study highlights the complex interplay of fear effect, group defense, and anti-predator sensitivity in predator–prey dynamics. These results may provide valuable biological insights into predator–prey interactions. [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, a multi-patch and multi-group vector-borne disease model is proposed to study the effects of host commuting (Lagrangian approach) and/or vector migration (Eulerian approach) on disease spread. We first define the basic reproduction number of the model, R 0 , which completely determines the global dynamics of the model system. Namely, if R 0 ≤ 1 , then the disease–free equilibrium is globally asymptotically stable, and if R 0 > 1 , then there exists a unique endemic equilibrium which is globally asymptotically stable. Then, we show that the basic reproduction number has lower and upper bounds which are independent of the host residence times matrix and the vector migration matrix. In particular, nonhomogeneous mixing of hosts and vectors in a homogeneous environment generally increases disease persistence and the basic reproduction number of the model attains its minimum when the distributions of hosts and vectors are proportional. Moreover, R 0 can also be estimated by the basic reproduction numbers of disconnected patches if the environment is homogeneous. The optimal vector control strategy is obtained for a special scenario. In the two-patch and two-group case, we numerically analyze the dependence of the basic reproduction number and the total number of infected people on the host residence times matrix and illustrate the optimal vector control strategy in homogeneous and heterogeneous environments. [ABSTRACT FROM AUTHOR]

In this paper we study a modified SEIR model with general incidence function of the form f (s) [ g (I 1) + h (I 2) ] where I 1 and I 2 are two infection categories different and the migration is constant in all compartments. The model admits neither a disease-free equilibrium point nor a basic reproduction number. Using a suitable Lyapunov function and under sufficient conditions on the functions f, g and h we show that the endemic equilibrium point is globally asymptotically stable. The considered model without migration has a disease-free equilibrium, at least one endemic equilibrium and a basic reproduction number. We show according to the values of R 0 that these equilibria are globally asymptotically stable. To illustrate the results obtained we use a non-linear incidence function given by β S I 1 1 + α 1 I 1 + η I 2 1 + α 2 I 2 where I 1 modeling uneducated infected individuals and I 2 modeling educated infected individuals. Next, we performed sensitivity analysis to determine how each parameter of the model may affect disease transmission. Finally, using reasonably chosen numerical data, we confirm our analytical results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop and investigate a novel mathematical model of the dynamical behaviors of chronic hepatitis B virus infection. The model includes exposed infected hepatocytes, intracellular HBV DNA-containing capsids, uses a general incidence function for viral infection covering a variety of special cases available in the literature, and describes the interaction of cytotoxic T lymphocytes that kill the infected hepatocytes and the magnitude of B-cells that send antibody immune defense to neutralize free virions. Further, one time delay is incorporated to account for actual capsids production. The other time delays are used to account for maturation of capsids and free viruses. We start with the analysis of the proposed model by establishing the local and global existence, uniqueness, non-negativity and boundedness of solutions. After defined the threshold parameters, we discuss the stability properties of all possible steady state constants by using the crafty Lyapunov functionals, the LaSalle’s invariance principle and linearization methods. The impacts of the three time delays on the HBV infection transmission are discussed through local and global sensitivity analysis of the basic reproduction number and of the classes of infected states. Finally, an application is provided and numerical simulations are performed to illustrate and interpret the theoretical results obtained. It is suggested that, a good strategy to eradicate or to control HBV infection within a host should concentrate on any drugs that may prolong the values of the three delays. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes a five-dimensional tuberculosis model incorporating slow-fast progression, endogenous reactivation, exogenous reinfection, and the assumption that infectives pass the smear microscopy test. This study disseminates information regarding how the presence and infectiousness of smear-negative patients in a tuberculosis epidemic significantly affect the threshold epidemic quantity R 0 (basic reproduction number). Stability and bifurcation analysis is carried out, and we find that the exogenous reinfection causes backward bifurcation and multiple endemic steady states in the system. We analytically and numerically explored the case of the periodic oscillations in the population via Hopf bifurcation for R 0 < 1 as well as R 0 > 1. [ABSTRACT FROM AUTHOR]

In this paper, we propose a diffusive prey-predator model with saturated hunting cooperation and predator-taxis. We first establish the global classical solvability and boundedness, and provide some sufficient conditions to assure the existence of a unique positive homogeneous steady state and the global uniform asymptotic stability of the predator-free homogeneous steady state. Secondly, we study the pattern formation mechanism and reveal that pattern formation is driven by the joint effect of predator-taxis, hunting cooperation, and slow diffusivity of predators. Moreover, we find that a strong predator-taxis can annihilate the spatiotemporal patterns, but a weak predator-taxis supports the pattern formation when diffusion-driven instability is present in the model without predator-taxis. However, if diffusion-driven instability is absent, predator-taxis cannot destabilize the unique positive spatially homogeneous steady state. Additionally, we highlight that spatially heterogeneous steady states do not exist when the diffusion coefficient ratio of predators to prey is sufficiently large under specific parametric conditions. To explore the various types of spatially heterogeneous steady states, we derive amplitude equations based on the weakly nonlinear analysis theory. Finally, numerical simulations, including the hexagonal pattern, stripe pattern, a mixed pattern combining hexagons and stripes, and the square pattern, are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Considering that HBV belongs to the DNA virus family and is hepatotropic, we model the HBV DNA-containing capsids as a compartment. In this paper, a delayed HBV infection model is established, where the general incidence function and two infection routes including cell-virus infection and cell-cell infection are introduced. According to some preliminaries, including well-posedness, basic reproduction number and existence of two equilibria, we obtain the threshold dynamics for the model. We illustrate numerical simulations to verify the above theoretical results, and furthermore explore the impacts of intracellular delay and cell-cell infection on the global dynamics of the model. [ABSTRACT FROM AUTHOR]

The anthropogenic carbon dioxide (C O 2) emission from the burning of fossil fuels is the prime cause behind the menace of global warming. Over the past few decades, fossil fuel consumption has increased drastically to fulfill the energy demand of the growing population and economy. The population pressure has not only contributed to the increase in fossil fuel consumption but also accelerated the deforestation for industrial, agricultural, and infrastructure expansion. This paper presents a nonlinear mathematical model to study the effect of an increase in fossil fuel use and deforestation due to population pressure on atmospheric carbon dioxide concentration. Further, the effect of economic efforts applied to reduce the population pressure over the control of atmospheric C O 2 levels is explored. The model analysis shows that an increase in the fossil fuel consumption rate causes an increase in the equilibrium level of carbon dioxide. Further, it is found that an increase in the deforestation rate coefficient has a destabilizing effect on the stability of positive state of the system. If the deforestation rate crosses a critical threshold, the positive state of the system loses stability and the periodic solutions arise via Hopf-bifurcation. It is shown that at high deforestation rates, an increase in the implementation rate of economic efforts applied to reduce the population pressure may cause reduction in the amplitude of periodic oscillations. The periodic oscillations may disappear if the implementation rate of economic effort increased beyond a critical threshold and the concentration of carbon dioxide gets stabilized. [ABSTRACT FROM AUTHOR]

This paper explores the effect of immigration in a generalized model that considers susceptibles, infected, chronic carriers, and recovered, the incidence rate is considered as a general function and the immigration as a constant in all its populations. This model has the characteristic that carriers and infected can transmit the disease, besides it has not a disease-free equilibrium point and no basic reproductive number when the immigration is considered. Using an appropriate Lyapunov function and with suitable conditions on the functions involved in the general incidence, we show that the endemic equilibrium point is globally asymptotically stable. When the immigration is not considered the model has a disease-free equilibrium point, endemic equilibrium and basic reproductive number which are globally asymptotically stable depending on the magnitude of this threshold. Through numerical simulations we show that even having a good vaccination rate, recovery rate, diagnosis rate cannot stop the transmission of the disease if migration or immigration is considered. [ABSTRACT FROM AUTHOR]

With the development of intelligent recommendation technology on the Internet, new challenges have been brought to the research of rumor spreading. To study the influence of multiple contact mechanism and incentive effect on rumor spreading, we propose a rumor propagation dynamics model with multiple contact mechanism, which is based on the traditional SIR rumor propagation model and has divided the susceptible people into n S 1 S 2... S n categories. Firstly, in the system, without considering the population movement, we calculate the threshold and the final rumors spread scale of the system. Secondly, we consider population immigration and emigration in the new system. The existence of the equilibrium of the system is analyzed, and the basic reproduction number is obtained based on the next generation matrix method. The local asymptotic stability of the rumor free equilibrium is proved by the Hurwitz criterion, and the global asymptotic stability is proved according to LaSalle's Invariance Principle. Finally, numerical simulation verifies the theoretical results, and the research shows that the multiple contact mechanism and incentive effect proposed in this paper are more similar to the rumor propagation law of social networks in the new era. [ABSTRACT FROM AUTHOR]

We propose a population dynamical model for SARS-CoV-2 that takes into account mask compliance and effectiveness, in the context of saturated treatment. This model also considers reinfection and relapse among individuals with comorbidities. Our findings indicate that global mask usage, in conjunction with other public health measures, effectively reduces the basic reproduction number ( R 0 ). We establish the local and conditional global stability of the disease-free equilibrium point. Notably, the model exhibits intriguing behavior due to saturated treatment and reinfection. Under specific parameter conditions, it demonstrates multiple endemic equilibria when R 0 < 1 resulting and backward and forward bifurcation. We conduct sensitivity analysis to pinpoint the key factors influencing disease spread. The existence of multiple equilibria contributes to intricate and diverse dynamics, showcasing a variety of bifurcations and oscillations through Hopf bifurcation. Under specific conditions, global asymptotic stability for the unique endemic equilibrium, when it exists, is established. Among further nonlinear dynamics exhibited by the proposed model, we establish backward Hopf bifurcation, Hopf–Hopf bifurcation and saddle-node bifurcation. Bistability of the equilibrium points is also observed through forward hysteresis. Additionally we provide the impact of parameters most effective in reducing in COVID-19 spread. Numerical simulations of the theoretical findings are offered to validate the results. [ABSTRACT FROM AUTHOR]

Heterogeneity in susceptibility and infectivity is a central issue in epidemiology. Although the latter has received some attention recently, the former is often neglected in modeling of epidemic systems. Moreover, very few studies consider both of these heterogeneities. This paper is concerned with the characterization of epidemic models with differential susceptibility and differential infectivity under a general setup. Specifically, we investigate the global asymptotic behavior of equilibria of these systems when the network configuration of the Susceptible-Infectious interactions is strongly connected. These results prove two conjectures by Bonzi et al. (J Math Biol 62:39–64, 2011) and Hyman and Li (Math Biosci Eng 3:89–100, 2006). Moreover, we consider the scenario in which the strong connectivity hypothesis is dropped. In this case, the model exhibits a wider range of dynamical behavior, including the rise of boundary and interior equilibria, all based on the topology of network connectivity. Finally, a model with multidirectional transitions between infectious classes is presented and completely analyzed. [ABSTRACT FROM AUTHOR]

The paper mainly studies globally pth moment exponentially ultimate boundedness and pth moment exponential stability of impulsive stochastic functional differential equations. By using the Lyapunov direct method of Razumikhin-type condition and principle of comparison, this article first gives a lemma, discusses the simple system that does not consider impulse in the original system, then directly apply the conclusion of the lemma and use mathematical induction to get the main results of the theorem. In this paper, when allowing the original system to be unbounded and unstable, some sufficient conditions for pth moment globally exponentially ultimate boundedness and pth moment globally exponential stability are presented, and the linear coefficient of the upper bound of Lyapunov differential operator is time-varying function, and is not required to be negative definite. Finally, we use an example to illustrate the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the h-stability analysis with respect to part of the variables of nonlinear non-autonomous systems. With the help of the notion of practical h-stable functions, input-to-state practical partial h-stability (h-ISppS), integral input-to-state practical partial h-stability (h-iISppS) and practical partial h-stability are considered. Moreover, some sufficient Lyapunov-like conditions are derived to check the partial input-to-state practical h-stability of two important classes of nonlinear systems, namely perturbed and cascaded systems. Furthermore, two numerical examples are given to illustrate the effectiveness and the superiority of the results. [ABSTRACT FROM AUTHOR]

This paper studies the dynamical behaviors of a diffusion epidemic SIRI system with distinct dispersal rates. The overall solution of the system is derived by using L p theory and the Young’s inequality. The uniformly boundedness of the solution is obtained for the system. The asymptotic smoothness of the semi-flow and the existence of the global attractor are discussed. Moreover, the basic reproduction number is defined in a spatially uniform environment and the threshold dynamical behaviors are obtained for extinction or continuous persistence of disease. When the spread rate of the susceptible individuals or the infected individuals is close to zero, the asymptotic profiles of the system are studied. This can help us to better understand the dynamic characteristics of the model in a bounded space domain with zero flux boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study a three-patch two-species Lotka–Volterra competition patch model over a stream network. The individuals are subject to both random and directed movements, and the two species are assumed to be identical except for the movement rates. The environment is heterogeneous, and the carrying capacity is lager in upstream locations. We treat one species as a resident species and investigate whether the other species can invade or not. Our results show that the spatial heterogeneity of environment and the magnitude of the drift rates have a large impact on the competition outcomes of the stream species. [ABSTRACT FROM AUTHOR]

This paper is concerned with the formulation and analysis of an epidemic model of COVID-19 governed by an eight-dimensional system of ordinary differential equations, by taking into account the first dose and the second dose of vaccinated individuals in the population. The developed model is analyzed and the threshold quantity known as the control reproduction number R 0 is obtained. We investigate the equilibrium stability of the system, and the COVID-free equilibrium is said to be locally asymptotically stable when the control reproduction number is less than unity, and unstable otherwise. Using the least-squares method, the model is calibrated based on the cumulative number of COVID-19 reported cases and available information about the mass vaccine administration in Malaysia between the 24th of February 2021 and February 2022. Following the model fitting and estimation of the parameter values, a global sensitivity analysis was performed by using the Partial Rank Correlation Coefficient (PRCC) to determine the most influential parameters on the threshold quantities. The result shows that the effective transmission rate (α) , the rate of first vaccine dose (ϕ) , the second dose vaccination rate (σ) and the recovery rate due to the second dose of vaccination (η) are the most influential of all the model parameters. We further investigate the impact of these parameters by performing a numerical simulation on the developed COVID-19 model. The result of the study shows that adhering to the preventive measures has a huge impact on reducing the spread of the disease in the population. Particularly, an increase in both the first and second dose vaccination rates reduces the number of infected individuals, thus reducing the disease burden in the population. [ABSTRACT FROM AUTHOR]

Our earlier work in Nguyen et al. (Maximizing metapopulation growth rate and biomass in stream networks. arXiv preprint , 2023) shows that concentrating resources on the upstream end tends to maximize the total biomass in a metapopulation model for a stream species. In this paper, we continue our research direction by further considering a Lotka–Volterra competition patch model for two stream species. We show that the species whose resource allocations maximize the total biomass has the competitive advantage. [ABSTRACT FROM AUTHOR]

In this article, we are working on an SEIR-SI type model for dengue disease in order to better observe the dynamics of infection in human beings. We calculate the basic reproduction number R 0 and determine the equilibrium points. We then show the existence of global stability in each of the different states depending on the value of R 0 . Moreover, to support the theoretical work, we present numerical simulations obtained using Python. We also study the sensitivity of the parameters included in the expression of R 0 with the aim of identifying the most influential parameters in the dynamics of dengue disease spread. Finally, we introduce two functions u and v, respectively indicating the treatment of the infected people and any prevention system minimizing contact between humans and the disease causing vectors. We present the curves of the controlled system after calculating the optimal pair of controls capable of reducing the dynamics of the disease spread, still using Python. [ABSTRACT FROM AUTHOR]

A mechanistic model that incorporates public health enlightenment, treatment, and snake developmental stages is developed and rigorously analyzed. The model is used to gain more insights into the dynamics and control of snakebite envenoming (SBE). Some interesting equilibrium points that demonstrate the presence and absence of snakes in a given population were computed. It has been shown that the existence or extinction of snakes in a given community depends on snake existence threshold (RS). Whenever the threshold is greater than one, snakes exist in the community, while if the threshold is exactly equal to one, then snakes seize to exist. Furthermore, a rigorous qualitative study of the model revealed that each of the snake-free, SBE-free, and SBE-endemic equilibrium points is globally asymptotically stable. In addition, a sensitivity analysis of the model parameters was conducted in order to identify the most influential parameters on SBE transmission dynamics. It is shown that an effective contact rate is the most important parameter. Therefore, preventive strategies that focus on reducing contact between humans and snakes, such as the use of snakebite repellent and protective gloves, are very important in controlling SBE. Finally, simulations have indicated that public health education on the use of snakebite preventive measures in combination with treatment of SBE victims is critical in reducing the number of new cases and deaths, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we first formulate a system of ODEs–PDE to model diseases with latency-age and differential infectivity. Then, based on the ways how latent individuals leave the latent stage, one ODE and two DDE models are derived. We only focus on the global stability of the models. All the models have some similarities in the existence of equilibria. Each model has a threshold dynamics for global stability, which is completely characterized by the basic reproduction number. The approach is the Lyapunov direct method. We propose an idea on constructing Lyapunov functionals for the two DDE and the original ODEs–PDE models. During verifying the negative (semi-)definiteness of derivatives of the Lyapunov functionals along solutions, a novel positive definite function and a new inequality are used. The idea here is also helpful in applying the Lyapunov direct method to prove the global stability of some epidemic models with age structure or delays. [ABSTRACT FROM AUTHOR]

This paper concentrates on the problem of H ∞ state estimation for quaternion-valued inertial neural networks (QVINNs) with nonidentical time-varying delay. Without reducing the original second order system into two first order systems, a non-reduced order method is developed to investigate the addressed QVINNs, which is different from the majority of existing references. By constructing a new Lyapunov functional with tuning parameters, some easily checked algebraic criteria are established to ascertain the asymptotic stability of error-state system with the desired H ∞ performance. Moreover, an effective algorithm is provided to design the estimator parameters. Finally, a numerical example is given out to illustrate the feasibility of the designed state estimator. [ABSTRACT FROM AUTHOR]

In this paper, we study the practical exponential stability of nonlinear nonautonomous differential equations under nonlinear perturbations. By introducing a new method, we obtain some explicit criteria for the practical exponential stability of these equations. Furthermore, several characterizations for the exponential stability of a class of nonlinear differential equations are also presented. The obtained results generalize some existing results in the literature. Applications to neutral networks are investigated. Some examples are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

The Belousov–Zhabotinsky reaction is a well-known family of nonlinear oscillating biochemical systems. It is an example of a homogeneous non-equilibrium reaction that is widely used in biological structure, chemistry and physics. As a reaction kinetic model, it can be represented by multi-dimensional autonomous systems which contain only time-invariant parameters. In such systems, it is assumed that; at a particular temperature, the chemical properties remain constant or vary slightly which enables us to neglect that variation. This paper introduces and studies the nonautonomous Belousov–Zhabotinsky (B–Z) reaction at which the parameters are allowed to be time-varying. Simulations have shown that this generalized system is still able to oscillate and to create limit cycles. Furthermore, we derive conditions that make the concentrations of reactants; as functions of time, are globally defined on [ t 0 , ∞) and vanish over time. In addition to the aforementioned origin attractivity, we investigate the rate-dependent and rate-independent hysteresis behaviors exhibited by one of the concentrations and derive a mathematical expression for the so-called "hysteresis loop". [ABSTRACT FROM AUTHOR]

This paper studies the existence, uniqueness, asymptotic and S p -globally exponential stability of Stepanov-like pseudo almost automorphic solution to Lotka–Volterra recurrent neural networks (LVRNNs) with time-varying delays on time scales by applying D-matrix theory, Banach fixed point theorem, constructing a suitable Lyapunov functional and the theory of time scales calculations. An example and simulations are given to prove the effectiveness of main theoretical results. [ABSTRACT FROM AUTHOR]

HIV (human immunodeficiency virus) is a dangerous virus that constantly diminishes an individual's immune system by explicitly targeting CD4 cells, which are the body's key protectors against disease by obstructing them to make duplicates of themselves. If left untreated, it can lead to AIDS (acquired immunodeficiency syndrome). The Treatment involves antiretroviral therapy which maintains the immunity to a specific level and thus helps in suppressing the virus replication. This paper emphasizes on the development of the model involving healthy and infected population, virus population, antibodies and CTL cells. The investigation encapsulates the local stability based on thresholds followed by the local bifurcation analysis based on β 1 and R 0 . The global stability analysis is done the using Graph- theoretic approach. Further the optimal control problem is discussed using Linear feedback control method which aims to reduce the viral load by keeping antibodies to a certain level. Numerical discussion includes surface plots of the thresholds based on various parameters, graphs showing the comparison between without control and with control especially for the virus population, infected population and antibodies which are our target. Finally, we have also shown the curve-fitting for our data using optimized Nedlar-Mean algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a disease transmission model coupled virus infection in host with incubation delay and environmental effects is studied. For the virus infection model in host with immune, latent delay and environmental virus invading, the threshold criteria on the global stability of antibody-free and antibody response infection equilibria are established. For the disease transmission model with incubation delay and immune response in host, basic reproduction number R 0 is defined, and the local stability of equilibria are established, i.e., the disease-free equilibrium is locally asymptotically stable if R 0 < 1 , and the endemic equilibrium is locally asymptotically stable if R 0 > 1 . Furthermore, the uniform persistence of positive solutions is studied while there is not the direct transmission of disease by the infected individuals. Finally, the numerical examples are presented to verify the main results. [ABSTRACT FROM AUTHOR]

In this paper, an attempt has been made to study and investigate a non-linear, non-integer SIR epidemic model for COVID-19 by incorporating Beddington–De Angelis incidence rate and Holling type II saturated cure rate. Beddington–De Angelis incidence rate has been chosen to observe the effects of measure of inhibition taken by both: susceptible and infective. This includes measure of inhibition taken by susceptibles as wearing proper mask, personal hygiene and maintaining social distance and the measure of inhibition taken by infectives may be quarantine or any other available treatment facility. Holling type II treatment rate has been considered for the present model for its ability to capture the effects of available limited treatment facilities in case of Covid 19. To include the neglected effect of memory property in integer order system, Caputo form of non-integer derivative has been considered, which exists in most biological systems. It has been observed that the model is well posed i.e., the solution with a positive initial value is reviewed for non-negativity and boundedness. Basic reproduction number R 0 is determined by next generation matrix method. Routh Hurwitz criteria has been used to determine the presence and stability of equilibrium points and then stability analyses have been conducted. It has been observed that the disease-free equilibrium Q d is stable for R 0 < 1 i.e., there will be no infection in the population and the system tends towards the disease-free equilibrium Q d and for R 0 > 1 , it becomes unstable, and the system will tend towards endemic equilibrium Q e . Further, global stability analysis is carried out for both the equilibria using R 0 . Lastly numerical simulations to assess the effects of various parameters on the dynamics of disease has been performed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of periodic solutions for feedback control coupled systems on networks (FCCSNs) by a novel approach, which is made up of the continuation theorem of coincidence degree theory, graph theory, Lyapunov method, and some novel analysis skills. As an application of our approach, the existence and global asymptotic stability of periodic solutions for feedback control coupled oscillators on networks are investigated. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of our results. [ABSTRACT FROM AUTHOR]

In this paper, the actual background of the susceptible population being directly patients after inhaling a certain amount of PM 2.5 is taken into account. The concentration response function of PM 2.5 is introduced, and the SISP respiratory disease model is proposed. Qualitative theoretical analysis proves that the existence, local stability and global stability of the equilibria are all related to the daily emission P 0 of PM 2.5 and PM 2.5 pathogenic threshold K. Based on the sensitivity factor analysis and time-varying sensitivity analysis of parameters on the number of patients, it is found that the conversion rate β and the inhalation rate η has the largest positive correlation. The cure rate γ of infected persons has the greatest negative correlation on the number of patients. The control strategy formulated by the analysis results of optimal control theory is as follows: The first step is to improve the clearance rate of PM 2.5 by reducing the PM 2.5 emissions and increasing the intensity of dust removal. Moreover, such removal work must be maintained for a long time. The second step is to improve the cure rate of patients by being treated in time. After that, people should be reminded to wear masks and go out less so as to reduce the conversion rate of susceptible people becoming patients. [ABSTRACT FROM AUTHOR]

In this paper, we study the periodic and stable dynamics of an interactive wild and sterile mosquito population model with density-dependent survival probability. We find a release amount upper bound G ∗ , depending on the release waiting period T, such that the model has exactly two periodic solutions, with one stable and another unstable, provided that the release amount does not exceed G ∗ . A numerical example is also given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept of input-to-state practical h-stability (h-ISpS) and integral input-to-state practical h-stability (h-iISpS) for nonlinear time-varying systems. Necessary and sufficient conditions for h-ISpS and h-iISpS are given based on indefinite Lyapunov functions. The practical h-stability analysis is accomplished with the help of scalar practical h-stable functions. Our main result provides conditions for h-ISpS of perturbed, cascaded and interconnected systems. Furthermore, a feedback control law is provided for a class of nonlinear control systems by which the closed-loop system is h-iISpS with respect to disturbances acting in the input. Some examples are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

Although novel coronavirus pneumonia (COVID-19) was widely spread in mainland China in early 2020, it was soon controlled. To study the impact of government interventions on the spread of disease during epidemics, a differential equation system is established to simulate the process of virus propagation in this paper. We first analyze its basic properties, basic reproduction number R 0 and existence of equilibria. Then we prove that the disease-free equilibrium (DFE) is Globally Asymptotically Stable when R 0 is less than 1. Through the analysis of the daily epidemic data from January 10, 2020 to March 11, 2020, combined with the implementation of the national epidemic policy, we divide the whole process into three stages: the first stage (natural state), the second stage (isolation state), the third stage (isolation, detection and treatment). By using the weighted nonlinear least square method to fit the data of three stages, the parameters are obtained, and three basic reproduction numbers are calculated, which are: R 01 = 2.6735 , R 02 = 0.85077 , R 03 = 0.18249 . Sensitivity analysis of threshold parameters and corresponding graphical results were also performed to examine the relative importance of various model parameters to the spread and prevalence of COVID-19. Finally, we simulate the trend of three stages and verify the theory of Global Asymptotic Stability of DFE. The conclusion of this paper proves theoretically that the Chinese government's epidemic prevention measures are effective in the fight against the spread of COVID-19. This study can not only provide a reference for research methods to simulate COVID-19 transmission in other countries or regions, but also provide recommendations on COVID-19 prevention measures for them. [ABSTRACT FROM AUTHOR]

We study the local and global asymptotic stability of the two steady-states, disease-free and endemic, of hybrid differential–difference SIR and SIS epidemic models with a nonlinear force of infection and a temporary phase of protection against the disease, e.g. by vaccination or medication. The initial model is an age-structured system that is reduced using the method of characteristic lines to a hybrid system, coupled between differential equations and a time continuous difference equation. We first prove that the solutions of the original system can be obtained from the reduced one. We then focus on the reduced system to obtain new results on the asymptotic stability of the two steady-states. We determine the local asymptotic stability of the two steady-states by studying the associated characteristic equation. We then discuss their global asymptotic stability in various situations (SIR, SIS, mass action, nonlinear force of infection), by constructing appropriate Lyapunov functions. [ABSTRACT FROM AUTHOR]

The Wolbachia-induced incompatible insect technique is a promising strategy for controlling wild mosquito populations. However, recent experimental studies have shown that mosquito migration into target areas dilutes the strategy’s effectiveness. In this work, we formulate a delay differential equation model to assess the impact of migration on mosquito population suppression. We identify that mosquito migration into an idealized target area makes it impossible to eliminate the target population completely. Our analysis identifies a lower bound of the suppression rate γ ∗ for a given migration number, which reveals the possible maximum reduction of wild population size in the peak season. For a given suppression rate target γ 0 > γ ∗ , we identify the permitted maximum migration number D (γ 0) , above which is impossible to reduce the field mosquito density up to (1 - γ 0) × 100 % in peak season. To reduce more than 95 % of Aedes albopictus population during its peak season in Guangzhou within six weeks, the required minimum release number of Wolbachia-infected males climbs steeply as the migration number increases to D(0.05). [ABSTRACT FROM AUTHOR]

Intraguild predation, the most fundamental mechanism in food webs with three species, is a mix of competition and predation in which two species that are participating in a predator–prey relationship are also competing for a common resource. We investigate an intraguild predation model by considering three population, namely shared resource, IG-prey and IG-predator by using a coupled system of ordinary differential equations and use Holling type II functional response between IG-prey and IG-predator. The dynamic properties of the proposed model are analyzed, including positivity, boundedness, uniform persistent, the existence and stability of the equilibria and Hopf bifurcation. We derive the sufficient conditions for the persistence and extinction of all feasible scenarios for the proposed model by providing a comprehensive view of their global stability. Our results reveal that the attacking rate and decay rate of the intraguild-predator can promote the formation of the stability of the model by transforming it from an unstable state to a stable state. The region of stability around interior equilibrium and around IG-predator free equilibrium has been obtained in terms of the attacking rate and decay rate of the intraguild-predator. The parameters interval for the coexistence of the three species has been determined. Our theoretical analysis and numerical illustrations demonstrate that intraguild predation model is prone to have coexistence of all the three populations. [ABSTRACT FROM AUTHOR]

Due to the role of cytoplasmic incompatibility (CI), releasing Wolbachia-infected male mosquitoes into the wild becomes a very promising strategy to suppress the wild mosquito population. When developing a mosquito suppression strategy, our main concerns are how often, and in what amount, should Wolbachia-infected mosquitoes be released under different CI intensity conditions, so that the suppression is most effective and cost efficient. In this paper, we propose a mosquito population suppression model that incorporates suppression and self-recovery under different CI intensity conditions. We adopt the new modeling idea that only sexually active Wolbachia-infected male mosquitoes are considered in the model and assume the releases of Wolbachia-infected male mosquitoes are impulsive and periodic with period T. We particularly study the case where the release period is greater than the sexual lifespan of the Wolbachia-infected male mosquitoes. We define the CI intensity threshold, mosquito release thresholds, and the release period threshold to characterize the model dynamics. The global and local asymptotic stability of the origin and the existence and stability of T-periodic solutions are investigated. Our findings provide useful guidance in designing practical release strategies to control wild mosquitoes. [ABSTRACT FROM AUTHOR]

Recently, propagation models of worms in the mobile environment are drawing extensive attention, particularly in the Wi-Fi scenario. Considering that worm-free equilibrium is exponential convergent means that the propagation time and control time of worms are much shorter than for other asymptotic convergence. Besides, the global asymptotic stability of the endemic equilibrium is more important than the local asymptotic stability, which reflects the more global qualitative behavior of the worm propagation. In this paper, we discuss the global dynamics of SEIQR worm propagation model in mobile internet proposed by Xiao et al. [X. Xiao, P. Fu, C. Dou, Q. Li, G. Hu, and S. Xia, "Design and analysis of SEIQR worm propagation model in mobile internet," Commun. Nonlinear Sci. Numer. Simulat., vol. 43, pp. 341–350, 2017] to improve and complement the related results. Through a series of mathematical derivations, sufficient conditions are derived to ensure the global exponentially stability of worm-free equilibrium, and the exponential convergent rate can be unveiled. Then, by using the classical geometric approach, it is shown that the endemic equilibrium is globally asymptotically stable and the system is persistent when R0 > 1. Moreover, numerical simulations are given to demonstrate our theoretical results. [ABSTRACT FROM AUTHOR]

In general, bifurcation delay occurs near a transcritical bifurcation point of the critical curve in two-dimensional singular perturbation systems. However, if the transcritical bifurcation point is exactly an equilibrium of the model under certain parameter values, what happens near such “degenerate transcritical bifurcation point”? In this paper, by combining geometric singular perturbation theory, center manifold reduction and blow-up technique we show that a degenerate transcritical bifurcation point can be a global attractor via a concrete example—a slow-fast modified Leslie-Gower model. That is, bifurcation delay cannot occur near degenerate transcritical bifurcation point in this model. Numerical simulations verify the theoretical predictions. [ABSTRACT FROM AUTHOR]

The commonly defined fractional derivatives, like Riemann-Liouville and Caputo ones, are non-local operators which have the long-term memory characteristic, since they are in connection with all historical data. Because of this special property, they may be invalid for modeling some processes and materials with short-term memory phenomena. Motivated by this observation and in order to enlarge the applicability of fractional calculus theories, a fractional derivative with the short-term memory property is defined in this paper. It can be viewed as an extension of the Caputo fractional derivative. Several properties of this short memory fractional derivative are given and proved. Meanwhile, the stability problem for fractional differential equations with such a derivative is studied. By applying fractional Lyapunov direct methods, the stability conditions applicable to the local case and the global case are established respectively. Finally, three numerical examples are provided to demonstrate the correctness and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic behavior of a class of switched systems with internally forced switching (IFS) is investigated. By introducing the definitions of continuous dependence and differentiability, the continuous dependence and differentiability of the solution relative to the control function are obtained. In the past studies, the optimal control problem given by IFS mainly focused on a special class of controlled systems (the piece affine system). Our results lay a good foundation for studying the more general internally forced switching problem. [ABSTRACT FROM AUTHOR]

In this paper, we consider a two-predator–one-prey population model that incorporates both the inter-specific competition between two predator populations and the intra-specific competition within each predator population. We investigate the dynamics of this model by addressing the existence, local and global stability of equilibria, uniform persistence as well as saddle-node and Hopf bifurcations. Numerical simulations are presented to explore the joint impacts of inter-specific and intra-specific competition on competition outcomes. Though inter-specific competition along does not admit a stable coexistence equilibrium, with intra-specific competition, the coexistence of the two competing predator species becomes possible and the two coexisting predator species may maintain at two different equilibrium populations. [ABSTRACT FROM AUTHOR]

A detailed survey of existing works on fractional-order nonlinear systems reveals the fact that practically no results exist on stability or any performance analysis of Markovian jumping fractional-order systems (FOSs) in general. The main reason is the theory of infinitesimal generator used to estimate the derivative of Lyapunov–Krasovskii Functional (LKF) is not well-developed in the fractional domain. This shortage, in theory, is focussed in this manuscript. In this work, we provide a lemma that aids in analyzing the stability of fractional-order delayed systems via integer-order derivative of LKF. Using this lemma, by constructing a new suitable LKF and employing known integral inequalities, linear matrix inequality (LMI)-based sufficient conditions that ensure stability along with H∞/passive performance of the proposed fractional-order neural networks (FONNs) with Markovian jumping parameters are derived for the first time. Unlike the existing works, the results derived in the present study depend on the fractional order (FO) of the NNs. The importance of such order-dependent criteria is highlighted in numerical examples. Finally, the simulation results are given to show the reliability of the derived conditions. [ABSTRACT FROM AUTHOR]

In the spread of infectious diseases, media reports have played a positive role. However, in the process of game communication, there are not only positive but also negative media reports. Therefore, in this paper, we establish a model with positive and negative media reports to analyze the role of media reports in the process of game communication. First, we study its positivity and boundedness, and calculate the basic reproduction number R 0 under three different incidence rates. The existence and stability of the equilibria are proved. Secondly, the optimal control problem is studied by adding two dynamic variables of media reports. Finally, in the simulation we simulate the stability of the equilibria, so as to verify the correctness of the theory. Then the influence of media parameters on R 0 is analyzed. The numerical results of optimal control are simulated by forward and backward sweep method. By comparing the results of the optimal control and without control, the media coverage should be controlled according to the optimal control measures shown in this paper. The serious situation of game addiction will be greatly alleviated, which can reduce the infection rate by at least 90%. [ABSTRACT FROM AUTHOR]

In this paper, we propose a mosquito population suppression model which is composed of two sub-models switching each other. We assume that the releases of sterile mosquitoes are periodic and impulsive, only sexually active sterile mosquitoes play a role in the mosquito population suppression process, and the survival probability is density-dependent. For the release waiting period T and the release amount c, we find three thresholds denoted by T ∗ , g ∗ , and c ∗ with c ∗ > g ∗ . We show that the origin is a globally or locally asymptotically stable equilibrium when c ≥ c ∗ and T ≤ T ∗ , or c ∈ (g ∗ , c ∗) and T < T ∗ . We prove that the model generates a unique globally asymptotically stable T-periodic solution when either c ∈ (g ∗ , c ∗) and T = T ∗ , or c > g ∗ and T > T ∗ . Two numerical examples are provided to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we inspect the global asymptotic stability (GAS) of Ebola–epidemic using a modified Susceptible-Infected-Deceased-Pathogen (SIDP) model with perturbation. The feasible region is obtained, and we determine the basic reproduction number using the next-generation matrix method. The GAS of the disease-free and endemic equilibria are discuss and provide parameter conditions for which the stability exists. We show theoretically that the contaminated environmental Ebola human–deceased transmission model is GAS with and without probability. Numerical simulation to support our theoretical findings are presented. [ABSTRACT FROM AUTHOR]