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Mathematical Biosciences and... Jan 2023In this paper, an SIR model with a strong Allee effect and density-dependent transmission is proposed, and its characteristic dynamics are investigated. The elementary...
In this paper, an SIR model with a strong Allee effect and density-dependent transmission is proposed, and its characteristic dynamics are investigated. The elementary mathematical characteristic of the model is studied, including positivity, boundedness and the existence of equilibrium. The local asymptotic stability of the equilibrium points is analyzed using linear stability analysis. Our results indicate that the asymptotic dynamics of the model are not only determined using the basic reproduction number ${R_0}$. If ${R_0} < 1$, there are three disease-free equilibrium points, and a disease-free equilibrium is always stable. At the same time, the conditions for other disease-free equilibrium points to be bistable were determined. If ${R_0} > 1$ and in certain conditions, either an endemic equilibrium emerges and is locally asymptotically stable, or the endemic equilibrium becomes unstable. What must be emphasized is that there is a locally asymptotically stable limit cycle when the latter happens. The Hopf bifurcation of the model is also discussed using topological normal forms. The stable limit cycle can be interpreted in a biological significance as a recurrence of the disease. Numerical simulations are used to verify the theoretical analysis. Taking into account both density-dependent transmission of infectious diseases and the Allee effect, the dynamic behavior becomes more interesting than when considering only one of them in the model. The Allee effect makes the SIR epidemic model bistable, which also makes the disappearance of diseases possible, since the disease-free equilibrium in the model is locally asymptotically stable. At the same time, persistent oscillations due to the synergistic effect of density-dependent transmission and the Allee effect may explain the recurrence and disappearance of disease.
Topics: Humans; Epidemiological Models; Models, Biological; Communicable Diseases; Basic Reproduction Number; Epidemics
PubMed: 36899556
DOI: 10.3934/mbe.2023129 -
Computational and Mathematical Methods... 2022In recent years, there are many new definitions that were proposed related to fractional derivatives, and with the help of these definitions, mathematical models were...
In recent years, there are many new definitions that were proposed related to fractional derivatives, and with the help of these definitions, mathematical models were established to overcome the various real-life problems. The true purpose of the current work is to develop and analyze Atangana-Baleanu (AB) with Mittag-Leffler kernel and Atangana-Toufik method (ATM) of fractional derivative model for the Smoking epidemic. Qualitative analysis has been made to `verify the steady state. Stability analysis has been made using self-mapping and Banach space as well as fractional system is analyzed locally and globally by using first derivative of Lyapunov. Also derive a unique solution for fractional-order model which is a new approach for such type of biological models. A few numerical simulations are done by using the given method of fractional order to explain and support the theoretical results.
Topics: Computer Simulation; Epidemics; Humans; Models, Biological; Models, Theoretical; Smoking
PubMed: 35633925
DOI: 10.1155/2022/9683187 -
Mathematical Biosciences and... Jan 2022In this paper we introduce and analyze a non-standard discretized SIS epidemic model for a homogeneous population. The presented model is a discrete version of the...
In this paper we introduce and analyze a non-standard discretized SIS epidemic model for a homogeneous population. The presented model is a discrete version of the continuous model known from literature and used by us for building a model for a heterogeneous population. Firstly, we discuss basic properties of the discrete system. In particular, boundedness of variables and positivity of solutions of the system are investigated. Then we focus on stability of stationary states. Results for the disease-free stationary state are depicted with the use of a basic reproduction number computed for the system. For this state we also manage to prove its global stability for a given condition. It transpires that the behavior of the disease-free state is the same as its behavior in the analogous continuous system. In case of the endemic stationary state, however, the results are presented with respect to a step size of discretization. Local stability of this state is guaranteed for a sufficiently small critical value of the step size. We also conduct numerical simulations confirming theoretical results about boundedness of variables and global stability of the disease-free state of the analyzed system. Furthermore, the simulations ascertain a possibility of appearance of Neimark-Sacker bifurcation for the endemic state. As a bifurcation parameter the step size of discretization is chosen. The simulations suggest the appearance of a supercritical bifurcation.
Topics: Basic Reproduction Number; Epidemics; Epidemiological Models; Models, Biological
PubMed: 34902983
DOI: 10.3934/mbe.2022006 -
BMC Bioinformatics Sep 2021The desire to understand genomic functions and the behavior of complex gene regulatory networks has recently been a major research focus in systems biology. As a result,...
BACKGROUND
The desire to understand genomic functions and the behavior of complex gene regulatory networks has recently been a major research focus in systems biology. As a result, a plethora of computational and modeling tools have been proposed to identify and infer interactions among biological entities. Here, we consider the general question of the effect of perturbation on the global dynamical network behavior as well as error propagation in biological networks to incite research pertaining to intervention strategies.
RESULTS
This paper introduces a computational framework that combines the formulation of Boolean networks and factor graphs to explore the global dynamical features of biological systems. A message-passing algorithm is proposed for this formalism to evolve network states as messages in the graph. In addition, the mathematical formulation allows us to describe the dynamics and behavior of error propagation in gene regulatory networks by conducting a density evolution (DE) analysis. The model is applied to assess the network state progression and the impact of gene deletion in the budding yeast cell cycle. Simulation results show that our model predictions match published experimental data. Also, our findings reveal that the sample yeast cell-cycle network is not only robust but also consistent with real high-throughput expression data. Finally, our DE analysis serves as a tool to find the optimal values of network parameters for resilience against perturbations, especially in the inference of genetic graphs.
CONCLUSION
Our computational framework provides a useful graphical model and analytical tools to study biological networks. It can be a powerful tool to predict the consequences of gene deletions before conducting wet bench experiments because it proves to be a quick route to predicting biologically relevant dynamic properties without tunable kinetic parameters.
Topics: Algorithms; Cell Cycle; Gene Regulatory Networks; Models, Biological; Models, Genetic; Saccharomyces cerevisiae; Systems Biology
PubMed: 34535069
DOI: 10.1186/s12859-021-04361-8 -
Trends in Pharmacological Sciences Aug 2020Hormesis is a generalizable dose-response relationship characterized by low-dose stimulation and high-dose inhibition. Despite debate over this biphasic dose-response... (Review)
Review
Hormesis is a generalizable dose-response relationship characterized by low-dose stimulation and high-dose inhibition. Despite debate over this biphasic dose-response curve, hormesis is challenging central beliefs in the evaluation of chemicals or drugs and has influenced biological model selection, concentration range, study design, and hypothesis testing. We integrate the traditional Chinese philosophy - Yin/Yang doctrine - into the representation of the Western hormetic dose-response relationship and review the Yin/Yang historical philosophy contained in the hormesis concept, aiming to promote general acceptance and wider applications of hormesis. We suggest that the Yin/Yang doctrine embodies the hormetic dose-response, including the relationship between the opposing components, curve shape, and time-dependence, and may afford insights that clarify the hormetic dose-response relationship in toxicology and pharmacology.
Topics: Dose-Response Relationship, Drug; Hormesis; Humans; Models, Biological
PubMed: 32564900
DOI: 10.1016/j.tips.2020.05.004 -
Bulletin of Mathematical Biology Mar 2022We show that under the assumption of weak frequency-dependent selection a wide class of population dynamical models can be analysed using perturbation theory. The inner...
We show that under the assumption of weak frequency-dependent selection a wide class of population dynamical models can be analysed using perturbation theory. The inner solution corresponds to the ecological dynamics, where to zeroth order, the genotype frequencies remain constant. The outer solution provides the evolutionary dynamics and corresponds, to zeroth order, to a generalisation of the replicator equation. We apply this method to a model of public goods dynamics and construct, using matched asymptotic expansions, a composite solution valid for all times. We also analyse a Lotka-Volterra model of predator competition and show that to zeroth order the fraction of wild-type predators follows a replicator equation with a constant selection coefficient given by the predator death rate. For both models, we investigate how the error between approximate solutions and the solution to the full model depend on the order of the approximation and show using numerical comparison, for [Formula: see text] and 2, that the error scales according to [Formula: see text], where [Formula: see text] is the strength of selection and k is the order of the approximation.
Topics: Biological Evolution; Mathematical Concepts; Models, Biological; Population Dynamics
PubMed: 35305188
DOI: 10.1007/s11538-022-01009-3 -
The Biochemical Journal Jun 2022In living cells, chemical reactions are connected by sharing their products and substrates, and form complex systems, i.e. chemical reaction network. One of the largest... (Review)
Review
In living cells, chemical reactions are connected by sharing their products and substrates, and form complex systems, i.e. chemical reaction network. One of the largest missions in modern biology is to understand behaviors of such systems logically based on information of network structures. However, there are series of obstacles to study dynamical behaviors of complex network systems in biology. For example, network structure does not provide sufficient information to determine details of the dynamical behaviors. In this review, I will introduce a novel mathematical theory, structural sensitivity analysis, by which the responses of reaction systems upon the changes in enzyme activities/amounts are determined from network structure alone. The patterns of responses exhibit characteristic features, localization and hierarchy, depending on the topology of the network. The theory also shows that ranges of enzymatic regulations are governed by a mathematical law characterized by local topology of substructures. These findings imply that the network topology is one of the origins of biological robustness.
Topics: Models, Biological
PubMed: 35713414
DOI: 10.1042/BCJ20210545 -
Journal of Neurochemistry Jul 2007Neurotrophin stimulation of tropomyosin-related kinase (Trk) and p75 receptors influences cellular processes such as proliferation, growth, differentiation, and other... (Review)
Review
Neurotrophin stimulation of tropomyosin-related kinase (Trk) and p75 receptors influences cellular processes such as proliferation, growth, differentiation, and other cell-specific functions, as well as regeneration. In contrast to Trk receptors, which have a well-defined trophic role, p75 has activities ranging from trophism to apoptosis. Continued neurotrophin stimulation of differentiating neurons transforms the initially trophic character of p75 signaling into negative growth control and overstimulation leads to apoptosis. This function shift reflects the signaling effects of ceramide that is generated upon stimulation of p75. The use of ceramide signaling by p75 may provide a key to understanding the cell-biological role of p75. The review presents arguments that the control of cell shape formation and cell selection can serve as an organizing principle of p75 signaling. Concurrent stimulation by neurotrophins of p75 and Trk receptors constitutes a dual growth control with antagonistic and synergistic elements aimed at optimal morphological and functional integration of cells and cell populations into their context.
Topics: Animals; Apoptosis; Cell Shape; Ceramides; GTP Phosphohydrolases; Humans; Membrane Lipids; Models, Biological; Nerve Growth Factors; Neurites; Receptor, Nerve Growth Factor; Signal Transduction
PubMed: 17437539
DOI: 10.1111/j.1471-4159.2007.04496.x -
Journal of Theoretical Biology Apr 2019Bifurcation theory provides a powerful framework to analyze the dynamics of differential systems as a function of specific parameters. Abou-Jaoudé et al. (2009)...
Bifurcation theory provides a powerful framework to analyze the dynamics of differential systems as a function of specific parameters. Abou-Jaoudé et al. (2009) introduced the concept of logical bifurcation diagrams, an analog of bifurcation diagrams for the logical modeling framework. In this work, we propose a formal definition of this concept. Since logical models are inherently discrete, we use the piecewise differential (PWLD) framework to introduce the underlying bifurcation parameters. Given a regulatory graph, a set of PWLD models is mapped to a set of logical models consistent with this graph, thereby linking continuous changes of bifurcation parameters to sequences of valuations of logical parameters. A logical bifurcation diagram corresponds then to a sequence of valuations of the logical parameters (with their associated set of attractors) consistent with at least one bifurcation diagram of the set of PWLD models. Necessary conditions on logical bifurcation diagrams in the general case, as well as a characterization of these diagrams in the Boolean case, exploiting a partial order between the logical parameters, are provided. We also propose a procedure to determine a logical bifurcation diagram of maximum length, starting from an initial valuation of the logical parameters, in the Boolean case. Finally, we apply our methodology to the analysis of a biological model of the p53-Mdm2 network.
Topics: Algorithms; Computer Simulation; Models, Genetic
PubMed: 30658053
DOI: 10.1016/j.jtbi.2019.01.008 -
Bio Systems Mar 2023Robert Rosen defines organisms as natural systems closed to efficient causation, and proposes the (M, R) system as a model for them. He argues that the study of this...
Robert Rosen defines organisms as natural systems closed to efficient causation, and proposes the (M, R) system as a model for them. He argues that the study of this formal system provides an understanding of living beings that cannot be obtained from conventional biology. However, he recognizes that answering specific questions about specific organisms requires identifying his relational concepts with specific characteristics of individual biological systems. Therefore, to apply the proposed model to biological research, it is necessary to recover the material systems through a process of realization of the formal system. The description of the cell as a realization of the (M, R) system has been notoriously problematic to date. This article posits a cell model based on the functional organization of cellular biochemical processes, and on Rosen's construction of the replication function. Then, based on the proposed model, the meaning of the replication function is discussed and the (M, R) system is analyzed as a theory of life.
Topics: Cells; Models, Biological
PubMed: 36775022
DOI: 10.1016/j.biosystems.2023.104846