Theory in Biosciences最新文献

The dynamics of DNA molecules play a crucial role in understanding genetic information storage, replication, and transmission. This study investigates the nonlinear dynamics of double-chain DNA systems using fractional-order differential equations, addressing the need for accurate mathematical models to capture the complex, non-local interactions inherent in biological systems. Traditional integer-order models often fail to account for memory effects and anomalous diffusion observed in DNA behavior. By employing fractional calculus, we develop a more realistic framework to model longitudinal and transverse displacements in DNA strands. The Laplace Residual Power Series Method (L-RPSM) is utilized to derive analytical solutions for (2+1)- and (3+1)-dimensional fractional DNA models, validated through numerical and graphical comparisons with exact solutions. Numerical experiments demonstrate that the method achieves absolute errors up to ${10}^{-18}$ compared with exact solutions. Our results demonstrate the efficacy of fractional calculus in capturing the nuanced dynamics of DNA, offering insights into soliton propagation and structural analysis, which are vital for applications in biophysics and genetic engineering.

This study advances the understanding of genetic transmission by exploring the dynamic behavior of double-chain deoxyribonucleic acid (DNA) through a newly established dynamic model using the Galilean transformation. Using planar dynamical systems theory, we apply bifurcation techniques to reveal the model's sensitivity to initial conditions and assess its stability, supported by numerical simulations via the Runge-Kutta method. To explore chaotic dynamics, we introduce perturbations and perform a detailed analysis using two-phase portraiture, two-dimensional phase diagrams, and Lyapunov exponents. Furthermore, we derive novel soliton solutions using the improved generalized Riccati method and the double expansion technique. Graphical results generated in MATLAB illustrate key features such as bifurcation points, conditions for chaos, and the influence of perturbations, providing deeper insights into DNA dynamics. Overall, this research enhances theoretical understanding while bridging applied mathematics and experimental biology, offering valuable perspectives on the complex behavior of DNA.

Smart's model (SM) describing the geometry of avian eggs is, uniquely, based on physiological characteristics of eggs formation in oviduct walls transforming a sphere to an ellipsoid, to an ovoid. The purpose of this study was to revisit and perform a more in-depth examination of SM, providing a possible improvement in terms of reducing the number of initial parameters and compliance with geometric principles fundamental for bodies of revolution. SM requires measuring five egg parameters: length (L), maximum breadth (B), displacement of the central axis to the level of maximum breadth (w), and two radii of the egg at a point shifted by ¼L from the pointed (r) and blunt (R) ends, respectively. A practical test for the reproduction degree of three egg shape varieties using five-parameter model confirmed its maximum accuracy compared to all others. Modifications using four parameters (L, B, w and r or B₀, which is egg diameter at ½L) were also relatively accurate, and only slightly inferior. Using three parameters (L, B and w) was clearly insufficient; however, one of our three-parameter models met the requirements of the "Main Axiom of the mathematical formula of the bird's egg". In our opinion, two of Smart's postulates, the point of applying an oviduct force to provide the appropriate egg shape and the equality of L and the length of original ellipsoid, were used as fixed initial premises, which allowed to exclude many other possible options and to derive a mathematical model. Such an assumption arose according to the theoretical studies presented herein. Nevertheless, Smart's formula derivation based on physiology of egg formation is a pioneering approach to the development of egg-shape models.

A mathematical analysis of influenza virus transmission is undertaken, combining rigorous theoretical development with numerical simulations informed by real-world data. The terms in the equations introduce parameters which are determined by fitting the model for matching clinical data sets using nonlinear least-square method. Wave patterns, critical illness factors, and forecasts of influenza transmission at national levels in Mexico, Italy, and South Africa are examined, alongside evaluations of the effectiveness of existing control measures and proposals for alternative policy interventions. Data for 120 weeks from October 2021 to March 2023 are used to fit the model. Numerical simulations and sensitivity analysis reveal the effectiveness of various prevention strategies. We performed data fitting using Latin hypercube sampling, sensitivity indices, Partial Rank Correlation Coefficient (PRCC), and p values to estimate the basic reproduction number $R_0$ and validate the model with data from these countries. Leveraging this validation, we identify optimal control strategies involving antiviral treatment protocols to suppress viral spread, reduce new infections, and minimize systemic costs. The existence and uniqueness of the optimal control pair are rigorously established, with the derived optimality system solved numerically. Additionally, we investigated the qualitative behavior of the threshold quantity, which determines whether the disease dies out or persists in the population. Finally, numerical experiments illustrate the impact of key parameters on transmission dynamics, corroborating theoretical predictions.

In this paper, we investigate traveling wave solutions for a delayed reaction-diffusion epidemic model incorporating both local and nonlocal diffusion mechanisms. The model describes the dynamics of susceptible, infected, and recovered populations, with infection spreading influenced by delayed interactions. The susceptible and recovered populations follow a nonlocal diffusion process, while the infected population undergoes local diffusion. We derive comprehensive results regarding the existence and nonexistence of traveling wave solutions. Specifically, we demonstrate that if the basic reproduction number $R_0$ satisfies $R_0<1$ , the system does not admit any traveling wave solutions. Conversely, when $R_0>1$ we identify a critical wave speed ${\rho }^{\ast }>0$ , such that for any $\rho \ge {\rho }^{\ast }$ , the system admits a non-critical bounded traveling wave solution. For $\rho <{\rho }^{\ast }$ , however, the model does not admit bounded, non-negative traveling wave solutions. Numerical simulations are performed to validate these theoretical results, highlighting the influence of both diffusion and delay mechanisms on wave propagation in the SIR model.

This article proposes a reaction-diffusion SIQR epidemiological model with the inclusion of the Laplacian operator and by considering two diffusion coefficients. Our primary focus is to investigate the influence of quarantine measures on disease transmission dynamics within a specific spatiotemporal context. We prove the existence, uniqueness, positivity, and boundedness of the solution to the proposed model by using $C_0$ semigroup theory. Furthermore, an investigation of the stability properties, both locally and globally, of the disease-free equilibrium and the endemic equilibrium is conducted through an examination of their respective characteristic equations. To obtain numerical solutions for the state system, we develop a discrete iterative scheme based on the finite difference method. Through extensive numerical simulations, the effectiveness of the proposed control strategy is thoroughly demonstrated. The obtained results underscore the remarkable significance of the suggested quarantine control approach, emphasizing its pivotal role in attaining highly meaningful outcomes. Those outcomes also show that the evolution of the epidemics depend heavily on the place where the disease originates.

The Price equation provides a formal account of selection building on a right-total mapping between two classes of individuals, which is usually interpreted as a parent-offspring relation. This paper presents a new formulation of the Price equation in terms of fuzzy set-mappings to account for structures where the targets of selection may vary in the degree to which they belong to the classes of "parents" and "offspring," and in the degree to which these two classes of individuals are related. The fuzzy set formulation widens the scope of the Price equation such that it equally applies to natural selection, cultural selection, operant selection, and selection in physical systems.

In this study, we conduct a mathematical and numerical investigation of a density-dependent model for the anaerobic digestion process, described by a system of four nonlinear ordinary differential equations, featuring an indirect feedback loop. Our analysis focuses on the acetogenesis and hydrogenotrophic methanogenesis phases. The model incorporates two microbial populations, acetogenic bacteria and hydrogenotrophic methanogens, and two substrates, volatile fatty acids (VFA) and hydrogen, with a specific emphasis on the inhibition of acetogen growth by methanogens. Using a broad class of nonmonotonic growth functions, we establish the necessary and sufficient conditions for the existence and stability of the system's steady states through rigorous mathematical analysis. Operating diagrams are constructed as functions of inlet substrate concentrations and the dilution rate. Numerical simulations further reveal the range of dynamic behaviors, highlighting the impact of methanogen-induced inhibition on acetogen dynamics. Contrary to the findings of Di and Yang in (JRSI 16:20180859, 2019), we demonstrate that when inhibition is sufficiently strong and VFA concentrations are high, the microbial community exhibits damped oscillations that converge to a positive steady state. These results illustrate the system's ability to stabilize at a coexistence equilibrium, even under the influence of an indirect feedback loop.

Due to predicted global climate change, there have been significant alterations in agricultural production patterns, which had a negative impact on ecosystems as well as the commercial and export prospects for the production of grapevines. The natural biochemistry of grapevines, including their chlorophyll content, net photosynthetic rate, Fv/Fm ratio, photorespiration, reduced yield, and quality is also anticipated to be negatively impacted by the various effects of light, temperature, and carbon dioxide at elevated scales. Grapevine phenology, physiology, and quality are impacted by the inactivation of photosystems (I and II), the Rubisco enzyme system, pigments, chloroplast integrity, and light intensity by temperature and increasing CO₂ levels. Grape phenological events are considerably altered by climatic conditions; in particular, berries mature earlier, increasing the sugar-to-acid ratio. In enology, the sugar-to-acid ratio is crucial since it determines the wine's final alcohol concentration and flavour. As light intensity and CO₂ levels rise, the biosynthesis of anthocyanins and tannins declines. As the temperature rises, the production of antioxidants diminishes, affecting the quality of raisins. Table grapes are more sensitive to temperature because of physiological problems like pink berries and a higher sugar-to-acidity ratio. Therefore, the systemic impact of light intensity, temperature, and increasing CO₂ levels on grapevine physiology, phenology, photosystems, photosynthesis enzyme system, and adaptive strategies for grape producers and researchers are highlighted in this article.

Various types of symmetry of polynucleotide sequences and methods of their algebraic description are considered. Among the methods of description, the main attention is paid to the application of semigroup theory (in particular, group theory). For convenience, all symmetry is divided into types. Combinatorial symmetry, first of all, it is associated with the explicit and hidden periodicity of the arrangement of identical nucleotides in subsequences. The above is generalized to the case of color symmetry, when different types of nucleotides or their associations can transform into each other upon shift. Fractal symmetry can also be added to this. Biofunctional symmetry means the presence of sequence factors of different nature (and size), which can be interchanged (swap places) solely due to their biological equivalence in the strand. A number of issues that are indirectly related to symmetry are also touched upon, for example, the presence of closed loops in polynucleotide (or polypeptide) chains and some physicochemical aspects.