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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]

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, almost sure exponential stability and pth moment exponential stability of stochastic cellular neural networks with mixed delays are investigated. Employing the methods of stochastic analysis, the Lyapunov’s method, and useful inequality techniques, a sufficient condition ensuring the almost sure exponential stability and pth moment exponential stability is obtained. Two examples are given to illustrate this sufficient condition. [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]

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]

This paper studies the global dynamics of piecewise smooth differential equations defined in the two-dimensional torus and sphere in the case when the switching manifold breaks the manifold into two connected components. Over the switching manifold, we consider the Filippov's convention for discontinuous differential equations. The study of piecewise smooth dynamical systems over torus and sphere is common for maps and up to where we know this is the first characterization for piecewise smooth flows arising from solutions of differential equations. We provide conditions under generic families of piecewise smooth equations to get periodic and dense trajectories. Considering these generic families of piecewise differential equations, we prove that a non-deterministic chaotic behaviour appears. Global bifurcations are also classified. [ABSTRACT FROM AUTHOR]

In this paper, the delay-interval-dependent robust stability is studied for a class of neutral stochastic neural networks with time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the upper bound is known and the lower bound is not restricted to zero. For the neural networks under study, the uncertainty includes polytopic uncertainty and linear fractional norm-bounded uncertainty. Sufficient conditions for the stability of the addressed neutral stochastic neural networks with time-varying delays are established by employing the proper Lyapunov-Krasovskii functional, a combination of the stochastic analysis theory, some inequality techniques and new linear matrix inequality (LMI). Finally, three numerical examples are provided to demonstrate less conservatism and effectiveness of the proposed LMI conditions. [ABSTRACT FROM AUTHOR]

In this paper, we consider a multi-group viral infection model with age structure and general incidence. We first give the positivity and boundedness of the solutions. Then, we study the local stability of the equilibria and uniform persistence of this model. Moreover, we establish the global results by constructing Lyapunov functionals. Finally, two special cases are presented to verify the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a deterministic model characterizing the within-host infection of Hepatitis C virus (HCV) in intrahepatic and extrahepatic tissues is presented. In addition, the model also includes the effect of the cytotoxic T lymphocyte (CTL) immunity described by a linear activation rate by infected cells. Firstly, the non-negativity and boundedness of solutions of the model are established. Secondly, the basic reproduction number R 01 and immune reproduction number R 02 are calculated, respectively. Three equilibria, namely, infection-free, CTL immune response-free and infected equilibrium with CTL immune response are discussed in terms of these two thresholds. Thirdly, the stability of these three equilibria is investigated theoretically as well as numerically. The results show that when R 01 < 1 , the virus will be cleared out eventually and the CTL immune response will also disappear; when R 02 < 1 < R 01 , the virus persists within the host, but the CTL immune response disappears eventually; when R 02 > 1 , both of the virus and the CTL immune response persist within the host. Finally, a brief discussion will be given. [ABSTRACT FROM AUTHOR]

In this paper, we consider a diffusive epidemic model with latent period and vaccination strategy. The well-posedness of solutions is first investigated for such a system. Then, in terms of the basic reproduction number and the critical wave speed, we establish a complete threshold result which reveals the existence and nonexistence of the strong traveling waves connecting the disease-free equilibrium to the endemic steady state. Finally, some numerical simulations are performed to illustrate our theoretical analysis. Our results implies that (i) the diffusion ability of the infected individuals can accelerate the minimal wave speed; and (ii) the latent period and vaccination strategy would slow down the spread of the disease. [ABSTRACT FROM AUTHOR]

This paper studies the globally asymptotic stability of neutral-type impulsive neural networks with discrete and bounded continuously distributed delays. By using the Lyapunov functional method, quadratic convex combination approach, a novel Gu's Lemma, Jensen integral inequality and linear convex combination technique, several novel sufficient conditions are derived to ensure the globally asymptotic stability of the equilibrium point of the networks. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a class model for neutral-type bidirectional associative memory (BAM) neural networks (NNS) with infinite distributed delay. The model extends and improves some recent works for BAM-NNS. Based on the Lyapunov–Krasovskii functional (LKF) theory, the linear matrix inequality (LMI) method and some analysis techniques, the novel stability criteria for such model are obtained. Four numerical examples prove the validity and less conservativeness of the proposed criteria. The developed results are helpful to design of an actual system. [ABSTRACT FROM AUTHOR]

Scarlet fever is an acute respiratory infectious disease and the incidence rate is increasing from 2011 throughout the world. In this paper, the mathematical models are proposed, which incorporate both direct transmissions and indirect transmissions of scarlet fever. The threshold conditions for disease invasion are obtained in terms of the basic reproduction number. The peak value, final size and epidemic time in a seasonal prevalence are investigated numerically. Furthermore, the effects of seasonal fluctuations on disease outbreak are also studied on the basis of real data in China. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonautonomous predator-prey system with Beddington-DeAngelis functional response and explore the global stability of boundary solution. Based on the dynamics of logistic equation, some new sufficient conditions on the global asymptotic stability of boundary solution are presented for general time-dependence case. Our main results indicate that (i) the long-term ineffective predation behaviour or high mortality of predator species will lead the predator species to extinction, even if the intraspecies competition of predator species is weak or no intraspecies competition; (ii) the long-term intense intraspecific competition may lead the predator species to extinction, even though the long-term accumulative predation benefit is higher than the death lose. When all parameters are periodic functions with common period, a necessary and sufficient condition on the global stability of boundary periodic solution is obtained. In addition, some numerical simulations are performed to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on the stabilization problem for a class of fractional-order bidirectional associative memory neural networks with mixed time delays (discrete delay and finite-time distributed delay). Based on adaptive control and delay feedback control, two kinds of adaptive control schemes are proposed to realize the global stabilization of systems. Different from those in earlier works, our method mainly depends on two fractional inequalities and a new fractional-order Barbalat lemma. Finally, some numerical simulations are provided to illustrate the feasibility and effectiveness of the proposed adaptive control schemes. [ABSTRACT FROM AUTHOR]

This paper discusses the issue of dissipativity and passivity analysis for a class of impulsive neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are modelled as a continuous-time discrete-state Markov chain. Based on a multiple integral inequality technique, a novel delay-dependent dissipativity criterion is established via a suitable Lyapunov functional involving the multiple integral terms. The proposed dissipativity and passivity conditions for the impulsive neural networks are represented by means of linear matrix inequalities. Finally, three numerical examples are given to show the effectiveness of the proposed criteria. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the synchronization problem for an array of linearly coupled neural networks with simultaneous presence of both the discrete and unbounded distributed time-delays. By utilizing a novel Lyapunov-Krasovskii functional and the Kronecker product, it is shown that the addressed synchronization problem is solvable if several linear matrix inequalities (LMIs) are feasible. Hence, different from the commonly used matrix norm theories (such as the M-matrix method), a unified LMI approach is developed to establish sufficient conditions for the coupled neural networks to be globally synchronized, where the LMIs can be easily solved by using the Matlab LMI toolbox and no tuning of parameters is required. It is also shown that the synchronization of coupled neural networks with bounded distributed delays is just a special case of our main results. A numerical example is provided to show the usefulness of the proposed global synchronization condition. [ABSTRACT FROM AUTHOR]

This paper studies the global stability of discrete-time viral infection models with humoural immunity. We consider both latently and actively infected cells. We study also a model with general production and clearance rates of all compartments as well as general incidence rate of infection. We use nonstandard finite difference method to discretize the continuous-time models. The positivity and boundedness of solutions of the discrete models are established. We establish by using Lyapunov method, the global stability of equilibria in terms of the basic reproduction number R 0 and the humoural immune response activation number R 1 . The results signify that the infection dies out if R 0 ≤ 1. Moreover, the infection persists with inactive immune response if R 1 ≤ 1 < R 0 and with active immune response if R 1 > 1. We illustrate our theoretical results by using numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate four non-autonomous chemostat models with non-monotonic consumption function, where wall growth and nutrient recycling are also taken into account. In each case, we prove the existence and uniqueness of non-negative global solution that generates a non-autonomous dynamical system. In addition, we also prove the existence of a unique (global) pullback attractor whose internal structure provides detailed information about the long-time behaviour of the state variables, for instance, conditions to ensure the extinction and the persistence of the species. We also display numerical simulations to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the global stability of a discrete-time pathogen infection model with humoral immunity. The incidence rate of infection as well as the production and clearance rates of the cells, pathogens and antibodies are modelled by general functions. We use nonstandard finite difference method to discretize the continuous-time model. Two threshold parameters are derived, the basic reproduction number R 0 and the humoral immune response activation number R 1 . The basic and global properties of the model are established. A global stability analysis of the equilibria is performed using the Lyapunov method. Theoretical results are illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we have formulated an e-epidemic energy efficient susceptible-infected--terminally infected-recovered (SITR) model to analyse the attacking behaviour of worms in wireless sensor network (WSN) using cyrtoid type functional response. In this model, once a sensor node has been attacked by the worms, the terminally infected node spreads the worms to its neighbouring nodes using normal communications, which further spread it to their neighbouring nodes and the process continues. To tackle this issue, we proposed an SITR model by considering the sleep mode concept of WSN in which the operational capabilities and power consumption of the motes decreases. Boundedness, existence of equilibrium points, stability and bifurcation analysis are analysed for the proposed model system. Stability and direction of Hopf-bifurcation are also obtained for endemic equilibrium point using center manifold theorem. Finally, numerical simulations are carried out that supports the analytical findings. The impact of the control parameters like transmission rate (β), inter-nodes interference coefficient (θ1) and intrinsic growth rate (r1) on the dynamics of the model system are investigated. [ABSTRACT FROM AUTHOR]

Novel passivity criteria are presented for the passivity of a class of cellular neural networks with discrete and unbounded distributed time-varying delays. Two types of uncertainty are considered: one is time-varying structured uncertainty while the other is interval uncertainty. The Gu's discretized Lyapunov–Krasovskii functional method is integrated with the technique of introducing the free-weighting matrix between the terms of the Leibniz–Newton formula. The integrated method leads to the establishment of new delay-dependent sufficient conditions in form of linear matrix inequalities for passivity of delayed neural networks. A numerical simulation study is conducted to demonstrate the obtained theoretical results, which shows their less conservatism than the existing passivity criteria. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct a non-standard finite difference (NSFD) scheme that can be used to calculate numerical solutions for an epidemic model with vaccination. Here, the NSFD method is employed to derive a set of difference equations for the epidemic model with vaccination. We show that when, the discretized model preserves positivity and global dynamics of the continuous model. Numerical simulation illustrates the effectiveness of our results. [ABSTRACT FROM PUBLISHER]

In this paper, we study the effects of Beddington-DeAngelis interference and squabbling, respectively, on the minimal rate of predator release required to drive a pest population to zero. A two-dimensional system of coupled ordinary differential equations is considered, augmented by an impulsive component depicting the periodic release of predators into the system. This periodic release takes place independently of the detection of the pests in the field. We establish the existence of a pest-free solution driven by the periodic releases, and express the global stability conditions for this solution in terms of the minimal predator rate required to bring an outbreak of pests to nil. In particular, we show that with the interference effects, the minimal rate will only guarantee eradication if the releases are carried out frequently enough. When Beddington-DeAngelis behaviour is considered, an additional constraint for the existence itself of a successful release rate is that the pest growth rate should be less than the predation pressure, the latter explicitly formulated in terms of the predation function and the interference parameters. [ABSTRACT FROM AUTHOR]

This paper is intended to investigate the effect of network topology on the spread of computer viruses in the presence of removable storage media. For that purpose, a novel network-based computer virus spreading model is proposed. Both theoretically and experimentally, it is shown that, under proper conditions, viruses on a scale-free network would tend to extinction. Experimental results show that either smaller maximum node degree or larger power-law exponent is conducive to the containment of virus spreading. To our knowledge, this is the first time the effect of network topology on virus spreading is investigated in this context. [ABSTRACT FROM AUTHOR]

HIV can infect cells via virus-to-cell infection or cell-to-cell viral transmission. These two infection modes may occur in a synergistic way and facilitate viral spread within an infected individual. In this paper, we developed an HIV latent infection model including both modes of transmission and time delays between viral entry and integration or viral production. We analysed the model by defining the basic reproductive number, showing the existence, positivity and boundedness of the solution, and proving the local and global stability of the infection-free and infected steady states. Numerical simulations have been performed to illustrate the theoretical results and evaluate the effects of time delays and fractions of infection leading to latency on the virus dynamics. The estimates of the relative contributions to the HIV latent reservoir and the virus population from the two modes of transmission have also been provided. [ABSTRACT FROM PUBLISHER]

Time delays can affect the dynamics of HIV infection predicted by mathematical models. In this paper, we studied two mathematical models each with two time delays. In the first model with HIV latency, one delay is the time between viral entry into a cell and the establishment of HIV latency, and the other delay is the time between cell infection and viral production. We defined the basic reproductive number and showed the local and global stability of the steady states. Numerical simulations were performed to evaluate the influence of time delays on the dynamics. In the second model with HIV immune response, one delay is the time between cell infection and viral production, and the other delay is the time needed for the adaptive immune response to emerge to control viral replication. With two positive delays, we obtained the stability crossing curves for the model, which were shown to be a series of open-ended curves. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyse a virus dynamics model with humoral immune response including latently infected cells. The incidence rate is given by Beddington–DeAngelis functional response. We have derived two threshold parameters, the basic infection reproduction numberand the humoral immune response activation numberwhich completely determined the basic and global properties of the virus dynamics model. By constructing suitable Lyapunov functions and applying LaSalle's invariance principle we have proven that if, then the infection-free equilibrium is globally asymptotically stable (GAS), if, then the chronic-infection equilibrium without humoral immune response is GAS, and if, then the chronic-infection equilibrium with humoral immune response is globally asymptotically stable. These results are further illustrated by numerical simulations. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce a nonresident computer virus model and prove the existence of at least one positive periodic solution. The proposed model is based on a biological approach and is obtained by considering that all rates (rates that the computers are disconnected from the internet, the rate that the computers are cured, etc.) are time dependent real functions. Assuming that the initial condition is a positive vector and the coefficients are positive ω−periodic and applying the topological degree arguments we deduce that generalized nonresident computer virus model has at least one positive ω−periodic solution. The proof consists of two big parts. Firstly, an appropriate change of variable which conserves the periodicity property and implies the positive behavior. Secondly, a reformulation of transformed system as an operator equation which is analyzed by applying the continuation theorem of the coincidence degree theory. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the notation and properties of-weighted pseudo almost automorphy for stochastic processes. And then, we apply the results obtained to consider the existence and uniqueness of-weighted pseudo almost automorphic solutions to some stochastic differential equations in a real separable Hilbert space under global Lipschitz conditions. Moreover, we also investigate asymptotic behavior of solutions to a stochastic differential equation under-weighted pseudo almost automorphic coefficients without global Lipschitz conditions. Our main results extend some known ones in the sense of square-mean weighted pseudo almost automorphy or-pseudo almost automorphy for stochastic processes. [ABSTRACT FROM AUTHOR]

This paper is concerned with travelling wave solutions for a class of monostable delayed reaction–diffusion equations on higher dimensional lattices. We first show that, for any fixed unit vector, there is a minimal wave speedsuch that a travelling front exists if and only if its speed is above this minimal speed. The exact asymptotic behaviour of the wave profiles at infinity is then established. Finally, we show that any travelling wave solution is strictly monotone and unique (up to a translation), including even the minimal wave. Of particular interest is the effects of the delay, spatial dimension and direction of wave on the minimal wave speed and we obtain some interesting phenomena for the delayed lattice dynamical system which are different from the case when the spatial variable is continuous. [ABSTRACT FROM PUBLISHER]

In this paper, we consider spatial predator-prey models with diffusion and prey-taxis. We investigate necessary conditions for pattern formation using a variety of non-linear functional responses, linear and non-linear predator death terms, linear and non-linear prey-taxis sensitivities, and logistic growth or growth with an Allee effect for the prey. We identify combinations of the above non-linearities that lead to spatial pattern formation and we give numerical examples. It turns out that prey-taxis stabilizes the system and for large prey-taxis sensitivity we do not observe pattern formation. We also study and find necessary conditions for global stability for a type I functional response, logistic growth for the prey, non-linear predator death terms, and non-linear prey-taxis sensitivity. [ABSTRACT FROM AUTHOR]

Consider the fluctuation of environmental noise and the incubation period of virus, a stochastic vector-host model with incubation delay is proposed to describe the transmission of Dengue fever virus (DFVs) between humans and mosquitoes. By constructing suitable stochastic Lyapunov functional, the existence and uniqueness of global positive solutions of this model are proved. Furthermore, some sufficient conditions are obtained for the asymptotic pathwise estimation of solutions. In addition, we also consider the asymptotic pathwise estimation of solutions, the existence and uniqueness of stationary distribution of this model without delay, which imply that disease is stochastic persistent. Finally, numerical simulations explain the theoretical results and discuss the effects of stochastic perturbations and delays on DFVs transmission. Our results imply that the spread of DFVs presents many unpredictability under the influence of stochastic perturbation, and the reproduction number can no longer be used as a threshold condition for the extinction or persistence of disease. Moreover, ignoring the incubation delay will not only overestimate the risk of disease outbreaks but also underestimate the duration of diseases. Rational application of stochastic perturbations on disease transmission and incubation periods will play a very important role in vector-borne disease control. [ABSTRACT FROM AUTHOR]

A mathematical model is formulated for the transmission and spread of cholera in a heterogeneous host population that consists of several patches of homogeneous host populations sharing a common water source. The basic reproduction number ℛ0is derived and shown to determine whether or not cholera dies out. Explicit formulas are derived for target/type reproduction numbers that measure the control strategies required to eradicate cholera from all patches. [ABSTRACT FROM AUTHOR]

A novel strategy for controlling mosquito-borne diseases, such as dengue, malaria and Zika, involves releases of Wolbachia-infected mosquitoes as Wolbachia cause early embryo death when an infected male mates with an uninfected female. In this work, we introduce a delay differential equation model with mating inhomogeneity to discuss mosquito population suppression based on Wolbachia. Our analyses show that the wild mosquitoes could be eliminated if either the adult mortality rate exceeds the threshold δ A ∗ or the release amount exceeds the threshold r ∗ uniformly. We also present the nonlinear dependence of δ A ∗ and r ∗ on the parameters, respectively, as well as the effect of pesticide spraying on wild mosquitoes. Our simulations suggest that the releasing should be started at least 5 weeks before the peak dengue season, taking into account both the release amount and the suppression speed. [ABSTRACT FROM AUTHOR]

We analysed a epidemiological model with varying populations of susceptible, carriers, infectious and recovered (SCIR) and a general non-linear incidence rate of the form f (S) [ g (C) + h (I) ]. We show that this model exhibits two positive equilibriums: the disease-free and disease equilibrium. We proved using the Lyapunov direct method that these two equilibriums are globally asymptotically stable under some sufficient conditions over the functions f, g, h. [ABSTRACT FROM AUTHOR]

A class of autonomous Kolmogorov systems that are dissipative and competitive with the origin as a repellor are considered when each nullcline surface is either concave or convex. Geometric method is developed by using the relative positions of the upper and lower planes of the nullcline surfaces for global asymptotic stability of an interior or a boundary equilibrium point. Criteria are also established for global repulsion of an interior or a boundary equilibrium point on the carrying simplex. This method and the theorems can be viewed as a natural extension of those results for Lotka-Volterra systems in the literature. [ABSTRACT FROM AUTHOR]

We formulate a deterministic mathematical model for the dynamical transmission of Neisseria meningitidis serogroup A (NmA) within a community. The model incorporates the key epidemiological and biological features ofNmAsuch as the vaccine efficacy and the waning of both vaccine-induced and recovery-induced immunity . We provide a theoretical study of the model. We compute the disease-free equilibrium (DFE) and derive the basic reproduction numberthat determines the extinction and the persistence of the disease. We compute equilibria and study their stability. More precisely, we show that there exists a threshold parameterξsuch that when, the DFE is globally asymptotically stable while when, the model exhibits the phenomenon of backward bifurcation on a feasible region. We also investigate the impact of imperfect mass vaccination with waning immunity within a community. The theory is supported by numerical simulations, which further suggest that the control of the epidemic ofNmApass through a combination of a large coverage vaccination of young susceptible individuals and the production of a vaccine with a high level of efficacy. Sensitivity analysis of the model has been performed in order to determine the impact of related parameters on meningitis outbreak. [ABSTRACT FROM PUBLISHER]

We investigate a system of two nonlinear age-structured partial differential equations describing the dynamics of proliferating and quiescent hematopoietic stem cell (HSC) populations. The method of characteristics reduces the age-structured model to a system of coupled delay differential and renewal difference equations with continuous time and distributed delay. By constructing a Lyapunov–Krasovskii functional, we give a necessary and sufficient condition for the global asymptotic stability of the trivial steady state, which describes the population dying out. We also give sufficient conditions for the existence of unbounded solutions, which describe the uncontrolled proliferation of HSC population. This study may be helpful in understanding the behavior of hematopoietic cells in some hematological disorders. [ABSTRACT FROM AUTHOR]

Human African Trypanosomiasis (HAT) and Nagana in cattle, commonly called sleeping sickness, is caused by trypanosome protozoa transmitted by bites of infected tsetse flies. We present a deterministic model for the transmission of HAT caused by Trypanosoma brucei gambiense between human hosts, cattle hosts and tsetse flies. The model takes into account the growth of the tsetse fly, from its larval stage to the adult stage. Disease in the tsetse fly population is modeled by three compartments, and both the human and cattle populations are modeled by four compartments incorporating the two stages of HAT. We provide a rigorous derivation of the basic reproduction number R0. For R0 < 1, the disease free equilibrium is globally asymptotically stable, thus HAT dies out; whereas (assuming no return to susceptibility) for R0 > 1, HAT persists. Elasticity indices for R0 with respect to different parameters are calculated with baseline parameter values appropriate for HAT in West Africa; indicating parameters that are important for control strategies to bring R0 below 1. Numerical simulations with R0 > 1 show values for the infected populations at the endemic equilibrium, and indicate that with certain parameter values, HAT could not persist in the human population in the absence of cattle. [ABSTRACT FROM AUTHOR]

This work deals with the relationship between a dengue disease transmission model and numerical methods for its computer simulations, viewed as discrete dynamical systems. Dynamic consistency is defined with respect to particular properties of a system and generally these properties will vary from one system to another. Here, this concept means that discretization scheme preserves correct number and stability of the equilibria, the positivity and the boundedness of the solutions for the corresponding continuous-time model. Using discrete-time analogue of Lyapunov functions, the global asymptotic stability of the equilibria is fully determined by the basic reproduction numberindependent of the time step sizeh, which is consistent with the corresponding continuous system. Finally, numerical simulations are presented to illustrate our theoretical results. [ABSTRACT FROM PUBLISHER]

We examine a mathematical model for the transmission of Streptococcus Pneumoniae amongst young children when the carriage transmission coefficient depends on the serotype. Carriage means pneumococcal colonization. There are two sequence types (STs) spreading in a population each of which can be expressed as one of two serotypes. We derive the differential equation model for the carriage spread and perform an equilibrium and global stability analysis on it. A key parameter is the effective reproduction number R e. For R e ≤ 1,  there is only the carriage-free equilibrium (CFE) and the carriage will die out whatever be the starting values. For R e > 1, unless the effective reproduction numbers of the two STs are equal, in addition to the CFE there are two carriage equilibria, one for each ST. If the ST with the largest effective reproduction number is initially present, then in the long-term the carriage will tend to the corresponding equilibrium. [ABSTRACT FROM PUBLISHER]

We analyse a selection-mutation size-structured model with n ecotypes competing for common resources. Uniform persistence and robust uniform persistence are established, when the selection-mutation matrix Γ is irreducible, i.e. individuals of one ecotype may contribute directly or indirectly to individuals of other ecotypes. Similar results are also presented for a particular reducible form of Γ. In the case of pure selection in which the offspring of one ecotype belong to the same ecotype, i.e. Γ=I, the identity matrix, we prove that the boundary equilibrium that describes competitive exclusion, with the fittest being the winner ecotype, is globally asymptotically stable. We show that small perturbations of the pure selection matrix lead to the existence of globally asymptotically stable interior equilibria. For the case when the selection-mutation matrix is reducible, we present and discuss the outcome of a series of numerical simulations. [ABSTRACT FROM AUTHOR]

We consider a four-compartment tuberculosis model including exogenous reinfection. We derive sufficient conditions, in terms of the parameters of the system, which guarantee the occurrence of backward bifurcation. We also discuss the global stability of the endemic state by using a generalization of the Poincare-Bendixson criterion. An application is given for the case of Internally Displaced People's Camps in North Uganda. The study suggests how important it is to provide qualitative indications on the threshold value of the population density in the area occupied by the camps, in order to possibly eradicate the disease. [ABSTRACT FROM AUTHOR]

A class of generalized Lienard differential equations determined by prescribed bilateral bounds for the nonlinear terms is considered. Necessary and sufficient conditions for exponential stability of the system expressed in the indicated bounds are found. The results are compared with known sufficient stability conditions obtained via the Lyapunov function method. [ABSTRACT FROM AUTHOR]

The lethargic crab disease (LCD) is an emergent infirmity that has decimated native populations of the mangrove land crab (Ucides cordatus, Decapoda: Ocypodidae) along the Brazilian coast. Several potential etiological agents have been linked with LCD, but only in 2005 was it proved that it is caused by an ascomycete fungus. This is the first attempt to develop a mathematical model to describe the epidemiological dynamics of LCD. The model presents four possible scenarios, namely, the trivial equilibrium, the disease-free equilibrium, endemic equilibrium, and limit cycles arising from a Hopf bifurcation. The threshold values depend on the basic reproductive number of crabs and fungi, and on the infection rate. These scenarios depend on both the biological assumptions and the temporal evolution of the disease. Numerical simulations corroborate the analytical results and illustrate the different temporal dynamics of the crab and fungus populations. [ABSTRACT FROM AUTHOR]

The classical MacArthur Rosenzweig predator-prey system has a stable coexistence point or, if either the prey capacity is large or the predator mortality is low, a stable limit cycle. The question here is how the stability properties of the coexistence point change when the prey or the predator or both can go quiescent. It can be shown that a stable equilibrium stays stable, but an unstable equilibrium may become stable. The exact stability domain is determined. In general, increasing the duration of the quiescent phase of the prey or of the predator widens the stability window. Numerical studies show that limit cycles shrink when quiescent phases are introduced. [ABSTRACT FROM AUTHOR]

We establish the basic theory of almost periodic sequences on +. Dichotomy techniques are then utilized to find sufficient conditions for the existence of a globally attracting almost periodic solution of a semilinear system of difference equations. These existence results are, subsequently, applied to discretely reproducing populations with and without overlapping generations. Furthermore, we access evidence for attenuance and resonance in almost periodically forced population models. [ABSTRACT FROM AUTHOR]