scholarly journals Bi-stable dynamics of a host-pathogen model

BIOMATH ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 1901029 ◽  
Author(s):  
Roumen Anguelov ◽  
Rebecca Bekker ◽  
Yves Dumont
Keyword(s):  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Traveling Wave Solution ◽  
Host Pathogen Interaction ◽  
Temporal System ◽  
Host Pathogen ◽  
Temporal Model ◽  
Long Term Behavior ◽  
Monotone Dynamical Systems

Crop host-pathogen interaction have been a main issue for decades, in particular for food security. In this paper, we focus on the modeling and long term behavior of soil-borne pathogens. We first develop a new compartmental temporal model, which exhibits bi-stable asymptotical dynamics. To investigate the long term behavior, we use LaSalle Invariance Principle to derive sufficient conditions for global asymptotic stability of the pathogen free equilibrium and monotone dynamical systems theory to provide sufficient conditions for permanence of the system. Finally, we develop a partially degenerate reaction diffusion system, providing a numerical exploration based on the results obtained for the temporal system. We show that a traveling wave solution may exist where the speed of the wave follows a power law.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system

2020 ◽  
Vol 21 (7-8) ◽  
pp. 749-759
Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linearization Method ◽  
Direct Lyapunov Method ◽  
Fractional Systems ◽  
Reaction Diffusion Model ◽  
Theoretical Results

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.

Credibility Trap: Japan today and China tomorrow

2006 ◽  
Vol 25 (1) ◽  
pp. 31-50
Author(s):  
Kensei Hiwaki ◽  
Junie Tong
Keyword(s):  
Human Development ◽  
Present Article ◽  
Socioeconomic Development ◽  
Sufficient Conditions ◽  
Theoretical Framework ◽  
Normative Framework ◽  
Specific Culture ◽  
Prevention And Cure ◽  
Necessary And Sufficient

This article provides a theoretical framework for a long-term socioeconomic lethargy (Credibility Trap) that results from the liquidation of holistic society-specific culture. As for example, it deals with the cases of Japan today and China tomorrow, elaborating on the slight of their respective society-specific cultures in a century-long process of “modernization”. The present theoretical framework primarily consists of three pivotal concepts, viz., Credibility Trap, society-specific cultures (Cultures) and market fundamentalism (Market), which facilitates a clear, concise and effective argument that the liquidation of their respective holistic Cultures may intimately relate to their actual and potential socioeconomic lethargy. Also, the present article concentrates on the elaboration of some promising avenues for prevention and cure of Credibility Trap. Such avenues comprise the necessary and sufficient conditions for a balanced socioeconomic development; a theoretical framework for a perpetual “virtuous” circle among cultural enrichment, comprehensive human development and balanced socioeconomic development; and a normative framework of multi-faceted value enhancement for vitality augmentation and cultural enrichment within a society.

scholarly journals The Role of Macrophages in the Host’s Defense against Sporothrix schenckii

Pathogens ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 905
Author(s):  
Estela Ruiz-Baca ◽  
Armando Pérez-Torres ◽  
Yolanda Romo-Lozano ◽  
Daniel Cervantes-García ◽  
Carlos A. Alba-Fierro ◽  
...  
Keyword(s):  
Immune Responses ◽  
Macrophage Polarization ◽  
Sporothrix Schenckii ◽  
Macrophage Cell ◽  
Cell Recruitment ◽  
Host Pathogen Interaction ◽  
Interaction Processes ◽  
Host Pathogen ◽  
Molecular Patterns

The role of immune cells associated with sporotrichosis caused by Sporothrix schenckii is not yet fully clarified. Macrophages through pattern recognition receptors (PRRs) can recognize pathogen-associated molecular patterns (PAMPs) of Sporothrix, engulf it, activate respiratory burst, and secrete pro-inflammatory or anti-inflammatory biological mediators to control infection. It is important to consider that the characteristics associated with S. schenckii and/or the host may influence macrophage polarization (M1/M2), cell recruitment, and the type of immune response (1, 2, and 17). Currently, with the use of new monocyte-macrophage cell lines, it is possible to evaluate different host–pathogen interaction processes, which allows for the proposal of new mechanisms in human sporotrichosis. Therefore, in order to contribute to the understanding of these host–pathogen interactions, the aim of this review is to summarize and discuss the immune responses induced by macrophage-S. schenckii interactions, as well as the PRRs and PAMPs involved during the recognition of S. schenckii that favor the immune evasion by the fungus.

Effects of acute seizures on cell proliferation, synaptic plasticity and long-term behavior in adult zebrafish

2021 ◽  
Vol 1756 ◽  
pp. 147334
Author(s):  
Charles Budaszewski Pinto ◽  
Natividade de Sá Couto-Pereira ◽  
Felipe Kawa Odorcyk ◽  
Kamila Cagliari Zenki ◽  
Carla Dalmaz ◽  
...  
Keyword(s):  
Cell Proliferation ◽  
Synaptic Plasticity ◽  
Adult Zebrafish ◽  
Acute Seizures ◽  
Long Term Behavior

Using Generalized Cell Mapping to Approximate Invariant Measures on Compact Manifolds

1997 ◽  
Vol 07 (11) ◽  
pp. 2487-2499 ◽  
Author(s):  
Rabbijah Guder ◽  
Edwin Kreuzer
Keyword(s):  
Dynamical Systems ◽  
Invariant Measures ◽  
Nonlinear Dynamical Systems ◽  
Powerful Method ◽  
Cell Mapping ◽  
Generalized Cell Mapping ◽  
Nonlinear Dynamical ◽  
Long Term Behavior ◽  
Mapping Theory

In order to predict the long term behavior of nonlinear dynamical systems the generalized cell mapping is an efficient and powerful method for numerical analysis. For this reason it is of interest to know under what circumstances dynamical quantities of the generalized cell mapping (like persistent groups, stationary densities, …) reflect the dynamics of the system (attractors, invariant measures, …). In this article we develop such connections between the generalized cell mapping theory and the theory of nonlinear dynamical systems. We prove that the generalized cell mapping is a discretization of the Frobenius–Perron operator. By applying the results obtained for the Frobenius–Perron operator to the generalized cell mapping we outline for some classes of transformations that the stationary densities of the generalized cell mapping converges to an invariant measure of the system. Furthermore, we discuss what kind of measures and attractors can be approximated by this method.

Sign in / Sign up

Export Citation Format

Share Document