Permanence and positive periodic solution for the single-species nonautonomous delay diffusive models

We investigate general HIV infection models with three types of infected cells: latently infected cells, long-lived productively infected cells, and short-lived productively infected cells. We incorporate three discrete or distributed time delays into the models. Moreover, we consider the effect of humoral immunity on the dynamical behavior of the HIV. The HIV-target incidence rate, production/proliferation, and removal rates of the cells and HIV are represented by general nonlinear functions. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive two threshold parameters which fully determine the existence and stability of the three steady states of the model. Using Lyapunov functionals, we establish the global stability of the steady states of the model. The theoretical results are confirmed by numerical simulations.MSC: 34D20; 34D23; 37N25; 92B05

show abstract

“…Using Lemma 2 in [40], the solutions of system (12)- (17) with the initial states (18) satisfy X(t) ∈ R . Let…”

Section: Preliminariesmentioning

confidence: 99%

Effect of cellular reservoirs and delays on the global dynamics of HIV

2018

View full text Add to dashboard Cite

show abstract

“…In the case of positive economic interest, it is easy to compute that 0 < v < 0.0202 based on (21). v = 0.0005 is utilized in the following numerical simulations, which is arbitrarily selected within the interval (0, 0.0202) and is enough to merit the theoretical analysis.…”

Section: Numerical Simulationmentioning

confidence: 99%

Modeling and analysis in a prey–predator system with commercial harvesting and double time delays

Liu¹,

Lü²,

Zhang³

et al. 2016

Applied Mathematics and Computation

View full text Add to dashboard Cite

“…Due to Lemma 2 in Yang et al, [39], any solution of (1.2) with positive initial conditions exist uniquely and each component of X remains in the interval [0,b) for someb > 0. Furthermore, ifb < +∞ then lim sup t→+∞ [S(t) + I(t) + P (t)] = +∞.…”

Section: Positivity and Boundedness Of Solutionsmentioning

confidence: 99%

Stability and Hopf Bifurcation of a Delay Eco‐epidemiological Model With Nonlinear Incidence Rate

Zhou

Cui

2010

Mathematical Modelling and Analysis

View full text Add to dashboard Cite

Abstract. In this paper, a three-dimensional eco-epidemiological model with delay is considered. The stability of the two equilibria, the existence of Hopf bifurcation and the permanence are investigated. It is found that Hopf bifurcation occurs when the delay τ passes a sequence of critical values. Moreover, by applying Nyquist criterion, the length of delay is estimated for which the stability continues to hold. Numerical simulation with a hypothetical set of data has been done to support the analytical results.

show abstract

Permanence and positive periodic solution for the single-species nonautonomous delay diffusive models

Cited by 250 publications

References 3 publications

Effect of cellular reservoirs and delays on the global dynamics of HIV

Effect of cellular reservoirs and delays on the global dynamics of HIV

Modeling and analysis in a prey–predator system with commercial harvesting and double time delays

Stability and Hopf Bifurcation of a Delay Eco‐epidemiological Model With Nonlinear Incidence Rate

Contact Info

Product

Resources

About