In this paper, we propose a class of discrete SIR epidemic models which are derived from with distributed delays by using variation the backward Euler method. Applying Lyapunov functional technique, it is shown that global dynamics each model fully determined single threshold parameter and effect time harmless for stability endemic equilibrium model.

We investigate the dynamics of a prey–predator model with cooperative hunting among specialist predators and maturation delay in predator growth. First, we consider without explore effect time on coexistence their prey. When is long enough cooperation rate weak, prey species tend to coexist. Furthermore, observe occurrences series bifurcations that depend time. Second, introduce for growth analyse its impact system's dynamics. find as becomes larger, become more likely go extinct, hinders...

In this paper, by applying a variation of the backward Euler method, we propose discrete-time SIR epidemic model whose discretization scheme preserves global asymptotic stability equilibria for class corresponding continuous-time models. Using analogue Lyapunov functionals, is fully determined basic reproduction number , when infection incidence rate has suitable monotone property.

We propose a delayed SIRS computer virus propagation model. Applying monotone iterative techniques and Lyapunov functional techniques, we establish sufficient conditions for the global asymptotic stability of both virus-free equilibria

In this paper, we establish the global asymptotic stability of equilibria for an SIR model infectious diseases with distributed time delays governed by a wide class nonlinear incidence rates. We obtain properties proving permanence and constructing suitable Lyapunov functional. Under some assumptions on term in rate, dynamics is completely determined basic reproduction number $R_0$ do not influence model.

Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead several difficulties understanding evolution of history, especially when population sizes reach carrying capacity. r/K selection theory explains what types strategies evolve presence differences. However, relationship between schedules individuals size is still unclear, even if can classify appropriately. To address this issue, we propose a few...

SIRS type epidemiological model has a fundamental form to study the role of temporal immunity recovered individuals in disease transmission dynamics and several variant models have been considered last century, but up now dynamical aspects are not fully elucidated. We here look over previous studies concerning qualitative analysis for family models. To this aim we construct general delay equation, coupled system renewal equation differential equations, structuring infected population by...

In this paper, we propose a discrete-time SIS epidemic model which is derived from continuous-time models with immigration of infectives by the backward Euler method. For discretized model, applying new Lyapunov function techniques, establish global asymptotic stability disease-free equilibrium for and endemic , where R 0 basic reproduction number model. This just discrete analogue continuous infectives.

We analyze local asymptotic stability of an SIRS epidemic model with a distributed delay. The incidence rate is given by general saturated function the number infective individuals.Our first aim to find class nonmonotone rates such that unique endemic equilibrium always asymptotically stable.We establish characterization for rate, which shows nonmonotonicity delay in necessary destabilization equilibrium. further elaborate analysis specific rate. Here we improve condition obtained [Y. Yang...

In this paper, we consider the global dynamics of S(E)IS model with delays denoting an incubation time. By constructing a Lyapunov functional, prove stability disease‐free equilibrium E 0 under condition different from that in recent paper. Then claim R ≤1 is necessary and sufficient which globally asymptotically stable. We also propose discrete preserving positivity same equilibria as continuous distributed delays, by means analogs functional.

In this paper, we investigate the global stability of a delayed multi-group SIRS epidemic model which includes not only nonlinear incidence rates but also immunity loss and relapse infection. The analysis can be regarded as an extension to in [Muroya, Li Kuniya, Complete with graded cure rate incomplete recovery rate, J. Math. Anal. Appl. 410 (2014) 719-732] is studied. Applying Lyapunov functional approach, prove that disease-free equilibrium model, globally asymptotically stable, if...

Abstract In this paper, we show dynamical consistency between the continuous SEIS epidemic model and its discrete-time analogue, that is, both global dynamics of a ‘without delays’ positive solutions corresponding backward Euler discretization with mesh width are fully determined by same single-threshold parameter which is basic reproduction number model. To prove this, first obtain lower bounds for permanence analogue then apply discrete version Lyapunov function technique in paper [12]....