Stability of non-monotone critical waves in a population dynamics model with spatio-temporal delay

Zhou, Yonghui; Yang, Yun-Xia; Zhang, Hongjuan

doi:10.22436/mns.02.01.02

Cited by 5 publications

(6 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, the bistability of the positive equilibrium and the semi-trivial periodic solution indicate that the outcomes under this state-dependent control strategy depend on the initial conditions of the susceptible population and the infected population, hence a personalized strategy is recommended. Our model does not cover spatio-temporal delay, thus considering the effect of spatio-temporal delay [ 7 ] could be a valuable issue for future research.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Since the outbreak of COVID-19 at the end of 2019, it has spread to over 200 countries with 163,212,543 confirmed cases and 3,383,979 deaths globally till May 18, 2021 [ 3 ]. Therefore, it is crucial to conduct an early prediction and give warning of the epidemics for guiding the development of control interventions [ 4 ] and to evaluate the efficacy of different strategies of control interventions in successfully controlling the spread of the disease [ 5 – 7 ].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics and bifurcation analysis of a state-dependent impulsive SIS model

Wang

2021

Adv Differ Equ

View full text Add to dashboard Cite

Recently, considering the susceptible population size-guided implementations of control measures, several modelling studies investigated the global dynamics and bifurcation phenomena of the state-dependent impulsive SIR models. In this study, we propose a state-dependent impulsive model based on the SIS model. We firstly recall the complicated dynamics of the ODE system with saturated treatment. Based on the dynamics of the ODE system, we firstly discuss the existence and the stability of the semi-trivial periodic solution. Then, based on the definition of the Poincaré map and its properties, we systematically investigate the bifurcations near the semi-trivial periodic solution with all the key control parameters; consequently, we prove the existence and stability of the positive periodic solutions.

show abstract

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics and bifurcation analysis of a state-dependent impulsive SIS model

Wang

2021

Adv Differ Equ

View full text Add to dashboard Cite

show abstract

“…A study of a fractional-order model of HIV is given in [ 24 ]. The authors in [ 25 ] proposed a research on the dynamics of a population model. In [ 26 ], a COVID-19 model along with necessary awareness programs has been explored.…”

Section: Introductionmentioning

confidence: 99%

A case study of 2019-nCOV cases in Argentina with the real data based on daily cases from March 03, 2020 to March 29, 2021 using classical and fractional derivatives

et al. 2021

View full text Add to dashboard Cite

In this study, our aim is to explore the dynamics of COVID-19 or 2019-nCOV in Argentina considering the parameter values based on the real data of this virus from March 03, 2020 to March 29, 2021 which is a data range of more than one complete year. We propose a Atangana–Baleanu type fractional-order model and simulate it by using predictor–corrector (P-C) method. First we introduce the biological nature of this virus in theoretical way and then formulate a mathematical model to define its dynamics. We use a well-known effective optimization scheme based on the renowned trust-region-reflective (TRR) method to perform the model calibration. We have plotted the real cases of COVID-19 and compared our integer-order model with the simulated data along with the calculation of basic reproductive number. Concerning fractional-order simulations, first we prove the existence and uniqueness of solution and then write the solution along with the stability of the given P-C method. A number of graphs at various fractional-order values are simulated to predict the future dynamics of the virus in Argentina which is the main contribution of this paper.

show abstract

“…The focus of their research was to depict the transport of Covid-19 spread through wind with high speed. The stability of nonmonotone critical waves by antiweighted method for a kind of nonmonotone timedelayed reaction-diffusion equations, including Nicholson's blowflies equation, which describes the population dynamics of a single species with age structure, was studied in [45]. In [6], homotopy transform methods, namely, homotopy analysis transform method and homotopy perturbation Sumudu transform method, were implemented to examine the fractional model for HIV infection of CD4 + T lymphocyte cells.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis and optimal control interventions for sex structured syphilis model with three stages of infection and loss of immunity

et al. 2021

View full text Add to dashboard Cite

In this study, we develop a nonlinear ordinary differential equation to study the dynamics of syphilis transmission incorporating controls, namely prevention and treatment of the infected males and females. We obtain syphilis-free equilibrium (SFE) and syphilis-present equilibrium (SPE). We obtain the basic reproduction number, which can be used to control the transmission of the disease, and thus establish the conditions for local and global stability of the syphilis-free equilibrium. The stability results show that the model is locally asymptotically stable if the Routh–Hurwitz criteria are satisfied and globally asymptotically stable. The bifurcation analysis result reveals that the model exhibits backward bifurcation. We adopted Pontryagin’s maximum principle to determine the optimality system for the syphilis model, which was solved numerically to show that syphilis transmission can be optimally best control using a combination of condoms usage and treatment in the primary stage of infection in both infected male and female populations.

show abstract

Stability of non-monotone critical waves in a population dynamics model with spatio-temporal delay

Abstract: This paper, we show the stability of non-monotone critical waves by a anti-weighted method for a kind of non-monotone time-delayed reaction-diffusion equations including Nicholson's blowflies equation which describes the population dynamics of a single species with age structure.

Cited by 5 publications

References 12 publications

Dynamics and bifurcation analysis of a state-dependent impulsive SIS model

Dynamics and bifurcation analysis of a state-dependent impulsive SIS model

A case study of 2019-nCOV cases in Argentina with the real data based on daily cases from March 03, 2020 to March 29, 2021 using classical and fractional derivatives

Mathematical analysis and optimal control interventions for sex structured syphilis model with three stages of infection and loss of immunity

Contact Info

Product

Resources

About