A diffusive epidemic model with two delays subjecting to Neumann boundary conditions is considered. First we obtain the existence and the stability of the positive constant steady state. Then we investigate the existence of Hopf bifurcations by analyzing the distribution of the eigenvalues. Furthermore, we derive the normal form on the center manifold near the Hopf bifurcation singularity. Finally, some numerical simulations are carried out to illustrate the theoretical results.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.3934/mbe.2020229 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Electrically Driven Liquid Crystal Elastomer Self-Oscillators via Rheostat Feedback Mechanism.
Polymers (Basel)
February 2025
School of Mechanical and Electrical Engineering, Anhui Jianzhu University, Hefei 230601, China.
The reliance of feedback mechanisms in conventional light-fueled self-oscillating systems on spatially distributed light and intricately designed structures impedes their application and development in micro-robots, miniature actuators, and other small-scale devices. This paper presents a straightforward rheostat feedback mechanism to create an electrically driven liquid crystal elastomer (LCE) self-oscillator which comprises an LCE fiber, a rheostat, a spring, and a mass. Based on the electrothermally responsive LCE model, we first derive the governing equation for the system's dynamics and subsequently formulate the asymptotic equation.
View Article and Find Full Text PDFEffects of vector preferential settling in the dynamics of a plant virus model with latent periods.
Heliyon
February 2025
Department of Mathematics and Computer Science, University of the Philippines Baguio, Governor Pack Road, Baguio City, Philippines.
Insect vectors transmit many plant viruses of agricultural importance. In most cases, these viruses manipulate their vectors' behavior and movement leading to vector settling and feeding preferences that influence virus spread. The latent period within the insect vector is also crucial in virus transmission during vector feeding, however is assumed to be negligible in previous studies.
View Article and Find Full Text PDFWidespread neuronal chaos induced by slow oscillating currents.
Chaos
March 2025
Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, 100 Piedmont Ave., Atlanta, Georgia 30303, USA.
This paper investigates the origin and onset of chaos in a mathematical model of an individual neuron, arising from the intricate interaction between 3D fast and 2D slow dynamics governing its intrinsic currents. Central to the chaotic dynamics are multiple homoclinic connections and bifurcations of saddle equilibria and periodic orbits. This neural model reveals a rich array of codimension-2 bifurcations, including Shilnikov-Hopf, Belyakov, Bautin, and Bogdanov-Takens points, which play a pivotal role in organizing the complex bifurcation structure of the parameter space.
View Article and Find Full Text PDFThe origin of localized patterns with a spatiotemporal oscillatory background state.
Chaos
March 2025
School of Computer and Information Technology, Shanxi University, Taiyuan 030006, China.
The localized patterns observed with a spatiotemporal oscillatory background in the experiment are believed to emerge due to the bistability of supercritical Turing-Hopf modes. However, the branching origin of these patterns remains unclear. In this paper, we explore the formation of local patterns near the subcritical Turing-Hopf bifurcation point using the Gray-Scott model as an example.
View Article and Find Full Text PDFEvaluating the long-term effects of combination antiretroviral therapy of HIV infection: a modeling study.
J Math Biol
March 2025
School of Public Health, Nanjing Medical University, 101 Longmian Road, Nanjing, 211166, Jiangsu, China.
Current HIV/AIDS treatments effectively reduce viral loads to undetectable levels as measured by conventional clinical assays, but immune recovery remains highly variable among patients. To assess the long-term treatment efficacy, we propose a mathematical model that incorporates latently infected CD4 T cells and the homeostatic proliferation of CD4 T cells. We investigate the dynamics of this model both theoretically and numerically, demonstrating that homeostatic proliferation can induce bistability, which implies that steady-state CD4 T cell count is sensitively affected by initial conditions.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!