Analysis of a class of fractal hybrid fractional differential equation with application to a biological model.

Recently, the area devoted to fractional calculus has given much attention by researchers. The reason behind such huge attention is the significant applications of the mentioned area in various disciplines. Different problems of real world processes have been investigated by using the concepts of fractional calculus and important and applicable outcomes were obtained. Because, there has been a lot of interest in fractional differential equations. It is brought on by both the extensive development of fractional calculus theory and its applications. The use of linear and quadratic perturbations of nonlinear differential equations in mathematical models of a variety of real-world problems has received a lot of interest. Therefore, motivated by the mentioned importance, this research work is devoted to analyze in detailed, a class of fractal hybrid fractional differential equation under Atangana- Baleanu- Caputo ABC derivative. The qualitative theory of the problem is examined by using tools of non-linear functional analysis. The Ulam-Hyer's (U-H) type stability criteria is also applied to the consider problem. Further, the numerical solution of the model is developed by using powerful numerical technique. Lastly, the Wazewska-Czyzewska and Lasota Model, a well-known biological model, verifies the results. Several graphical representations by using different fractals fractional orders values are presented. The detailed discussion and explanations are given at the end.

Wavelet Collocation Method for HIV-1/HTLV-I Co-Infection Model Using Hermite Polynomial.

In this study, the dynamic behavior of fractional order co-infection model with human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLV-I) is analyzed using operational matrix of Hermite wavelet collocation method. Also, the uniqueness and existence of solutions are calculated based on the fixed point hypothesis. For the fractional order co-infection model, its positivity and boundedness are demonstrated. Furthermore, different types of Ulam-Hyres stability are also discussed. The numerical solution of the model are obtained by using the operational matrix of the Hermite wavelet approach. This scheme is used to solve the system of nonlinear equations that are very fruitful and easy to implement. Additionally, the stability analysis of the numerical scheme is explained. The mathematical model taken in this work incorporates the biological characteristics of both HIV-1 and HTLV-I. After that all the equilibrium points of the fractional order co-infection model are found and their existence conditions are explored with the help of the Caputo derivative. The global stability of all equilibrium points of this model are determined with the help of Lyapunov functions and the LaSalle invariance principle. Convergence analysis is also discussed. Hermite wavelet operational matrix methods are more accurate and convergent than other numerical methods. Lastly, variations in model dynamics are found when examining different fractional order values. These findings will be valuable to biologists in the treatment of HIV-1/HTLV-I.

On quasi-linear reaction diffusion systems arising from compartmental SEIR models.

The global existence and boundedness of solutions to quasi-linear reaction-diffusion systems are investigated. The system arises from compartmental models describing the spread of infectious diseases proposed in Viguerie et al. (Appl Math Lett 111:106617, 2021); Viguerie et al. (Comput Mech 66(5):1131-1152, 2020), where the diffusion rate is assumed to depend on the total population, leading to quasilinear diffusion with possible degeneracy. The mathematical analysis of this model has been addressed recently in Auricchio et al. (Math Methods Appl Sci 46:12529-12548, 2023) where it was essentially assumed that all sub-populations diffuse at the same rate, which yields a positive lower bound of the total population, thus removing the degeneracy. In this work, we remove this assumption completely and show the global existence and boundedness of solutions by exploiting a recently developed L p -energy method. Our approach is applicable to a larger class of systems and is sufficiently robust to allow model variants and different boundary conditions.

Exploring the dynamics of nonlocal coupled systems of fractional q -integro-differential equations with infinite delay.

In this study, we explore a coupled system of fractional integro-differential equations with infinite delay and nonlocal conditions. This system encompasses classical derivatives of different orders and the fractional derivative of Caputo-Fabrizio type, as well as the fractional integral of the q -Riemann-Liouville operator. We introduce a novel definition of the Caputo and Fabrizio differential operators, enhancing the mathematical formulation. Our main focus is to investigate the system's fundamental properties, including existence, uniqueness, and continuous dependence. Through rigorous mathematical analysis, we establish the existence and uniqueness of solutions and examine how small perturbations in initial conditions or parameters impact the solutions. For the numerical aspect, we use the finite-trapezoidal approach, a reliable method for solving fractional integro-differential equations. We provide a concise explanation of the approach and demonstrate its effectiveness through two numerical examples. Overall, this comprehensive study contributes to the understanding of coupled systems with fractional derivatives and infinite delays, with implications for various scientific and engineering fields.

Intersubjectivity as an analytical concept to study human-animal interaction in historical context: street dogs in Late Ottoman period.

Human knowledge pertaining to human-animal interaction is constructed by the human author, albeit the presence of animal subjects. Such a human lens is pronounced when studying human-animal interactions across history, whose nonhuman animal subjects are not only absent, and therefore eliminating the possibility of conducting empirical studies in situ, but also their experiences are filtered by the interpretative lens of human authors of extant historical accounts as well as contemporary human analysts who interpret these accounts. This article draws upon such epistemological limitations of understanding nonhuman animal presence in historical accounts and offers human-animal intersubjectivity as an analytical concept, involving generative iterability and indistinctive boundaries that emphasise intersubjective openness and relationality, to trace and disclose the continuity of human-animal co-existence. The article's historical scope is the Late Ottoman period characterised by a sense of temporal and spatial disorientation and reorientation for humans as well as street dogs during its modernisation processes.

Spatiotemporal Variations in Co-Occurrence Patterns of Planktonic Prokaryotic Microorganisms along the Yangtze River.

Bacteria and archaea are foundational life forms on Earth and play crucial roles in the development of our planet's biological hierarchy. Their interactions influence various aspects of life, including eukaryotic cell biology, molecular biology, and ecological dynamics. However, the coexistence network patterns of these microorganisms within natural river ecosystems, vital for nutrient cycling and environmental health, are not well understood. To address this knowledge gap, we systematically explored the non-random coexistence patterns of planktonic bacteria and archaea in the 6000-km stretch of the Yangtze River by using high-throughput sequencing technology. By analyzing the O/R ratio, representing the divergence between observed (O%) and random (R%) co-existence incidences, and the module composition, we found a preference of both bacteria and archaea for intradomain associations over interdomain associations. Seasons notably influenced the co-existence of bacteria and archaea, and archaea played a more crucial role in spring as evidenced by their predominant presence of interphyla co-existence and more species as keystone ones. The autumn network was characterized by a higher node or edge number, greater graph density, node degree, degree centralization, and nearest neighbor degree, indicating a more complex and interconnected structure. Landforms markedly affected microbial associations, with more complex networks and more core species found in plain and non-source areas. Distance-decay analysis suggested the importance of geographical distance in shaping bacteria and archaea co-existence patterns (more pronounced in spring). Natural, nutrient, and metal factors, including water temperature, NH4+-N, Fe, Al, and Ni were identified as crucial determinants shaping the co-occurrence patterns. Overall, these findings revealed the dynamics of prokaryotic taxa coexistence patterns in response to varying environmental conditions and further contributed to a broader understanding of microbial ecology in freshwater biogeochemical cycling.

Stability analysis and solutions of fractional boundary value problem on the cyclopentasilane graph.

The study is being applied to a model involving silane and on cyclopentasilane graph. We consider a graph with labeled vertices by 0 or 1 inspired by the molecular structure of cyclopentasilane. In this paper, we first study the existence of solutions to fractional conformable boundary value problem on the cyclopentasilane graph by applying Scheafer and Krasnoselskii fixed point theorems. Furthermore, we investigate different kinds of Ulam stability such as Ulam-Hyers stable, generalized Ulam-Hyers stable, Ulam-Hyers-Rassias stable and generalized Ulam-Hyers-Rassias stable for the given problem. Finally, we give an example to support our important results.

Enhanced degradation of polylactic acid microplastics in acidic soils: Does the application of biochar matter?

Biodegradable plastics, as an alternative to petroleum plastics, are fiercely increasing, but their incomplete degradation under natural conditions may lead to the breakdown into microplastics (MPs). Here, we explored the impacts of chicken manure-derived (MBC) and wood waste-derived biochar (WBC) on the degradation of polylactic acid microplastics (PLA-MPs) during soil incubation for one year. Both biochars induced more pronounced degradation characteristics in PLA-MPs, including enhanced surface roughness, the proportion of MPs < 100 µm by 12.89 %-25.67 %, oxygen loading and O/C ratio to 71.74 %-75.87 % and 1.70-1.76, as well as accelerated carbon loss and the cleavage of ester group and C-C bond. Also, biochar increased soil pH, depleted inorganic nitrogen and available phosphorus, and changed enzymic activity in PLA-MP-polluted soils. We proposed that both biochars accelerated the PLA-MP degradation by inducing alkaline, aminolysis/ammonolysis, oxidative, and microbial degradation. Among these, MBC induced aminolysis/ammonolysis by NH4+ via Fe2+-driven NO3-/NO2- reduction and microbial nitrogen fixation, and oxidative degradation by radicals generated through Fenton/Fenton-like reaction. WBC caused aminolysis/ammonolysis and oxidative degradation mainly through dissimilatory nitrate reduction to ammonium and surface free radicals on biochar. These findings indicate that biochar has the potential to accelerate PLA-MP degradation, and its regulatory mechanism depends on the type of biochar.

Infection spreading in tissue as a reaction-diffusion wave.

Viral infection develops in the organism due to virus replication inside infected cells and its transmission from infected to uninfected cells through the extracellular matrix or cell junctions. In this work, we model infection spreading in tissue with a delay reaction-diffusion system of equations for the concentrations of uninfected cells, infected cells and virus. We prove the wave existence, determine its speed of propagation and introduce a simplified one-equation model obtained from the complete model using a quasi-stationary approximation.

Dataset on Sasirangan existence as learning sources of biology.

The patterns, dyes, and meanings/ values of Sasirangan in Banjarmasin contribute significantly to biology education at all levels. However, no data regarding the attitudes, knowledge, and understanding of students regarding the existence of Sasirangan have been found to date. This study aimed to examine attitudes, knowledge, and understanding of high school students in Banjarmasin regarding the existence of Sasirangan. This study employed a survey involving 256 high school students in Banjarmasin, Indonesia. The instrument has two aspects: the knowledge and understanding aspect has nine items, while the attitude aspect has eight. The data were analyzed using percentage-based descriptive statistics. There were 100% of the students that were aware of the existence of Sasirangan, but they did not have a clear understanding of its pattern, coloring, or value. Moreover, high school students in the city of Banjarmasin expressed pride in the existence of Sasirangan as a superior product of South Kalimantan, and the majority stated that Sasirangan must be preserved.

Time-dependent interference of surfactants and CeO2/Fe2O3 nanoparticles co-occurrence on the volatile fatty acids biosynthesis during semi-continuous sludge fermentation.

Various exogenous contaminants typically coexist in waste activated sludge (WAS), and the long-term impacts of these co-occurring contaminants on WAS anaerobic fermentation and associated mechanisms remain largely unknown. This study reveals that the co-occurrence of surfactants and nanoparticles (NPs, i.e., Fe2O3 and CeO2, frequently detected in sludge) exhibited time-dependent impacts on the volatile fatty acids (VFAs) biosynthesis. Surfactants triggered WAS decomposition and enhanced NPs dispersion, leading to increased exposure of functional anaerobes to NPs toxicity, negatively affecting them. Consequently, key fermentation processes, acidogenic bacterial abundance, and metabolic functions were inhibited in co-occurrence reactors compared to those containing only surfactants in the early stage (before 56 d). Surprisingly, the fermentation systems containing surfactants collapsed subsequently, with VFAs yield at 72 d decreasing by 48.59-71.27 % compared to 56 d. The keystone microbes (i.e., Acidobacteria (16 d) vs Patescibacteria (56 d)) were reshaped, and metabolic traits (i.e., proB involved in intracellular metabolism) were downregulated by 0.05-78.02 % due to reduced microbial adaptive capacity (i.e., quorum sensing (QS)). Partial least squares path modeling (PLS-PM) analysis suggests that the microbial community was the predominant factor influencing VFAs generation. This study provides new insights into the long-term effects of co-contaminants on the biological treatment of WAS.

A room of their own: White lesbian coming outs and second wave feminism.

While the concept of "coming out" is relatively well-critiqued, few of these critiques trouble the way a near exclusive focus on disclosure positions sexuality as an essential identity. Based on life history interviews with 18 lesbian, pansexual, and queer women elders (ages 65+), I find coming out did not describe disclosing or even acknowledging same-gender desire, but, rather, choosing to act on it. For participants, coming out is the process of forming desire into a coherent identity (lesbian woman), a process that required continued interactions with lesbian existence; contrary to essentialist understandings, desire alone did not enable participants to become lesbians. In this article, I describe the two paths participants followed while becoming lesbians and consider how the historical context in which participants came out, specifically the second wave feminist movement, uniquely facilitated coming out for white women. Ultimately, I argue lesbian sexuality is a richly constructed social identity formed in community and defined by resistance to compulsory heterosexuality. By viewing sexual identity as based on shared political commitments formed in community, this article both corrects an essentializing tendency in the coming out literature and offers a potential point of repair between older and younger generations of lesbians.

Chronic pulmonary aspergillosis incidence in newly detected pulmonary tuberculosis cases during follow-up.

BACKGROUND: Chronic pulmonary aspergillosis (CPA) is known to complicate patients with post-tubercular lung disease. However, some evidence suggests that CPA might co-exist in patients with newly-diagnosed pulmonary tuberculosis (P.TB) at diagnosis and also develop during therapy. The objective of this study was to confirm the presence of CPA in newly diagnosed P.TB at baseline and at the end-of-TB-therapy. MATERIALS AND METHODS: This prospective longitudinal study included newly diagnosed P.TB patients, followed up at third month and end-of-TB-therapy with symptom assessment, anti-Aspergillus IgG antibody and imaging of chest for diagnosing CPA. RESULTS: We recruited 255 patients at baseline out of which 158 (62%) completed their follow-up. Anti-Aspergillus IgG was positive in 11.1% at baseline and 27.8% at end-of-TB-therapy. Overall, proven CPA was diagnosed in 7% at baseline and 14.5% at the end-of-TB-therapy. Around 6% patients had evidence of aspergilloma in CT chest at the end-of-TB-therapy. CONCLUSIONS: CPA can be present in newly diagnosed P.TB patients at diagnosis and also develop during anti-tubercular treatment. Patients with persistent symptoms or developing new symptoms during treatment for P.TB should be evaluated for CPA. Whether patients with concomitant P.TB and CPA, while receiving antitubercular therapy, need additional antifungal therapy, needs to be evaluated in future studies.

Fractal fractional model for tuberculosis: existence and numerical solutions.

This paper deals with the mathematical analysis of Tuberculosis by using fractal fractional operator. Mycobacterium TB is the bacteria that causes tuberculosis. This airborne illness mostly impacts the lungs but may extend to other body organs. When the infected individual coughs, sneezes or speaks, the bacterium gets released into the air and travels from one person to another. Five classes have been formulated to study the dynamics of this disease: susceptible class, infected of DS, infected of MDR, isolated class, and recovered class. To study the suggested fractal fractional model's wellposedness associated with existence results, and boundedness of solutions. Further, the invariant region of the considered model, positive solutions, equilibrium point, and reproduction number. One would typically employ a fractional calculus approach to obtain numerical solutions for the fractional order Tuberculosis model using the Adams-Bashforth-Moulton method. The fractional order derivatives in the model can be approximated using appropriate numerical schemes designed for fractional order differential equations.

Analysis of a fractional-order model for dengue transmission dynamics with quarantine and vaccination measures.

A comprehensive mathematical model is proposed to study two strains of dengue virus with saturated incidence rates and quarantine measures. Imperfect dengue vaccination is also assumed in the model. Existence, uniqueness and stability of the proposed model are proved using the results from fixed point and degree theory. Additionally, well constructed Lyapunov function candidates are also applied to prove the global stability of infection-free equilibria. It is also demonstrated that the model is generalized Ulam-Hyers stable under some appropriate conditions. The model is fitted to the real data of dengue epidemic taken from the city of Espirito Santo in Brazil. For the approximate solution of the model, a non-standard finite difference(NSFD) approach is applied. Sensitivity analysis is also carried out to show the influence of different parameters involved in the model. The behaviour of the NSFD is also assessed under different denominator functions and it is observed that the choice of the denominator function could influence the solution trajectories. Different scenario analysis are also assessed when the reproduction number is below or above one. Furthermore, simulations are also presented to assess the epidemiological impact of dengue vaccination and quarantine measures for infected individuals.

Clinical laboratory characteristics and gene mutation spectrum of Ph-negative MPN patients with atypical variants of JAK2, MPL, or CALR.

OBJECTIVE: To evaluate the incidence, clinical laboratory characteristics, and gene mutation spectrum of Ph-negative MPN patients with atypical variants of JAK2, MPL, or CALR. METHODS: We collected a total of 359 Ph-negative MPN patients with classical mutations in driver genes JAK2, MPL, or CALR, and divided them into two groups based on whether they had additional atypical variants of driver genes JAK2, MPL, or CALR: 304 patients without atypical variants of driver genes and 55 patients with atypical variants of driver genes. We analyzed the relevant characteristics of these patients. RESULTS: This study included 359 patients with Ph-negative MPNs with JAK2, MPL, or CALR classical mutations and found that 55 (15%) patients had atypical variants of JAK2, MPL, or CALR. Among them, 28 cases (51%) were male, and 27 (49%) were female, with a median age of 64 years (range, 21-83). The age of ET patients with atypical variants was higher than that of ET patients without atypical variants [70 (28-80) vs. 61 (19-82), p = 0.03]. The incidence of classical MPL mutations in ET patients with atypical variants was higher than in ET patients without atypical variants [13.3% (2/15) vs. 0% (0/95), p = 0.02]. The number of gene mutations in patients with atypical variants of driver genes PV, ET, and Overt-PMF is more than in patients without atypical variants of PV, ET, and Overt-PMF [PV: 3 (2-6) vs. 2 (1-7), p < 0.001; ET: 4 (2-8) vs. 2 (1-7), p < 0.05; Overt-PMF: 5 (2-9) vs. 3 (1-8), p < 0.001]. The incidence of SH2B3 and ASXL1 mutations were higher in MPN patients with atypical variants than in those without atypical variants (SH2B3: 16% vs. 6%, p < 0.01; ASXL1: 24% vs. 13%, p < 0.05). CONCLUSION: These data indicate that classical mutations of JAK2, MPL, and CALR may not be completely mutually exclusive with atypical variants of JAK2, MPL, and CALR. In this study, 30 different atypical variants of JAK2, MPL, and CALR were identified, JAK2 G127D being the most common (42%, 23/55). Interestingly, JAK2 G127D only co-occurred with JAK2V617F mutation. The incidence of atypical variants of JAK2 in Ph-negative MPNs was much higher than that of the atypical variants of MPL and CALR. The significance of these atypical variants will be further studied in the future.

Fractional epidemic model of coronavirus disease with vaccination and crowding effects.

Most of the countries in the world are affected by the coronavirus epidemic that put people in danger, with many infected cases and deaths. The crowding factor plays a significant role in the transmission of coronavirus disease. On the other hand, the vaccines of the covid-19 played a decisive role in the control of coronavirus infection. In this paper, a fractional order epidemic model (SIVR) of coronavirus disease is proposed by considering the effects of crowding and vaccination because the transmission of this infection is highly influenced by these two factors. The nonlinear incidence rate with the inclusion of these effects is a better approach to understand and analyse the dynamics of the model. The positivity and boundedness of the fractional order model is ensured by applying some standard results of Mittag Leffler function and Laplace transformation. The equilibrium points are described analytically. The existence and uniqueness of the non-integer order model is also confirmed by using results of the fixed-point theory. Stability analysis is carried out for the system at both the steady states by using Jacobian matrix theory, Routh-Hurwitz criterion and Volterra-type Lyapunov functions. Basic reproductive number is calculated by using next generation matrix. It is verified that disease-free equilibrium is locally asymptotically stable if R 0 < 1 and endemic equilibrium is locally asymptotically stable if R 0 > 1 . Moreover, the disease-free equilibrium is globally asymptotically stable if R 0 < 1 and endemic equilibrium is globally asymptotically stable if R 0 > 1 . The non-standard finite difference (NSFD) scheme is developed to approximate the solutions of the system. The simulated graphs are presented to show the key features of the NSFD approach. It is proved that non-standard finite difference approach preserves the positivity and boundedness properties of model. The simulated graphs show that the implementation of control strategies reduced the infected population and increase the recovered population. The impact of fractional order parameter α is described by the graphical templates. The future trends of the virus transmission are predicted under some control measures. The current work will be a value addition in the literature. The article is closed by some useful concluding remarks.

New results on bifurcation for fractional-order octonion-valued neural networks involving delays.

This work chiefly explores fractional-order octonion-valued neural networks involving delays. We decompose the considered fractional-order delayed octonion-valued neural networks into equivalent real-valued systems via Cayley-Dickson construction. By virtue of Lipschitz condition, we prove that the solution of the considered fractional-order delayed octonion-valued neural networks exists and is unique. By constructing a fairish function, we confirm that the solution of the involved fractional-order delayed octonion-valued neural networks is bounded. Applying the stability theory and basic bifurcation knowledge of fractional order differential equations, we set up a sufficient condition remaining the stability behaviour and the appearance of Hopf bifurcation for the addressed fractional-order delayed octonion-valued neural networks. To illustrate the justifiability of the derived theoretical results clearly, we give the related simulation results to support these facts. Simultaneously, the bifurcation plots are also displayed. The established theoretical results in this work have important guiding significance in devising and improving neural networks.

A nonautonomous model for the interaction between a size-structured consumer and an unstructured resource.

In this paper, we propose and analyze a nonautonomous model that describes the dynamics of a size-structured consumer interacting with an unstructured resource. We prove the existence and uniqueness of the solution of the model using the monotone method based on a comparison principle. We derive conditions on the model parameters that result in persistence and extinction of the population via the upper-lower solution technique. We verify and complement the theoretical results through numerical simulations.

Global dynamics and computational modeling approach for analyzing and controlling of alcohol addiction using a novel fractional and fractal-fractional modeling approach.

In recent years, alcohol addiction has become a major public health concern and a global threat due to its potential negative health and social impacts. Beyond the health consequences, the detrimental consumption of alcohol results in substantial social and economic burdens on both individuals and society as a whole. Therefore, a proper understanding and effective control of the spread of alcohol addictive behavior has become an appealing global issue to be solved. In this study, we develop a new mathematical model of alcohol addiction with treatment class. We analyze the dynamics of the alcohol addiction model for the first time using advanced operators known as fractal-fractional operators, which incorporate two distinct fractal and fractional orders with the well-known Caputo derivative based on power law kernels. The existence and uniqueness of the newly developed fractal-fractional alcohol addiction model are shown using the Picard-Lindelöf and fixed point theories. Initially, a comprehensive qualitative analysis of the alcohol addiction fractional model is presented. The possible equilibria of the model and the threshold parameter called the reproduction number are evaluated theoretically and numerically. The boundedness and biologically feasible region for the model are derived. To assess the stability of the proposed model, the Ulam-Hyers coupled with the Ulam-Hyers-Rassias stability criteria are employed. Moreover, utilizing effecting numerical schemes, the models are solved numerically and a detailed simulation and discussion are presented. The model global dynamics are shown graphically for various values of fractional and fractal dimensions. The present study aims to provide valuable insights for the understanding the dynamics and control of alcohol addiction within a community.