Fundamental Number Research Articles

Initial Steps of XY Sex Chromosome Differentiation in the Armored Catfish Hypostomus albopunctatus (Siluriformes: Loricariidae) Revealed by Heterochromatin Accumulation.

In fish species, heterochromatinization is one process that could trigger sex chromosome differentiation. The present article describes a nascent XX/XY sex chromosome system evidenced by heterochromatin accumulation and microsatellite (GATA)8 in Hypostomus albopunctatus from two populations of the Paraná River basin. The specimens of H. albopunctatus from the Campo and Bossi Rivers share the same karyotype. The species exhibits 74 chromosomes (8m+14sm +16st +36a, fundamental number = 112). The C-banding technique suggests male heterogamety in H. albopunctatus, where the Y-chromosome is morphologically like the X-chromosome but differs from it for having long arms that are entirely heterochromatic. Double fluorescence in situ hybridization (FISH) with 18S and 5S rDNA probes confirmed the Ag-nucleolus organizer region sites in a single pair for both populations, and minor rDNA clusters showed interpopulational variation. FISH with the microsatellite (GATA)8 probe showed a dispersed pattern in the karyotype, accumulating these sequences of sex chromosomes of both populations. FISH with microsatellite (CGC)10 probe showed interpopulational variation. The absence of differentiated sex chromosomes in H. albopunctatus is described previously, and a new variant is documented herein where XY chromosomes can be seen in an early stage of differentiation.

Fractional Optimal Control Model and Bifurcation Analysis of Human Syncytial Respiratory Virus Transmission Dynamics

In this paper, the Caputo-based fractional derivative optimal control model is looked at to learn more about how the human respiratory syncytial virus (RSV) spreads. Model solution properties such as boundedness and non-negativity are checked and found to be true. The fundamental reproduction number is calculated by using the next-generation matrix’s spectral radius. The fractional optimal control model includes the control functions of vaccination and treatment to illustrate the impact of these interventions on the dynamics of virus transmission. In addition, the order of the derivative in the fractional optimal control problem indicates that encouraging vaccination and treatment early on can slow the spread of RSV. The overall analysis and the simulated behavior of the fractional optimum control model are in good agreement, and this is due in large part to the use of the MATLAB platform.

Modeling and Analysis of an Age-Structured Malaria Model in the Sense of Atangana–Baleanu Fractional Operators

In this paper, integer- and fractional-order models are discussed to investigate the dynamics of malaria in a human host with a varied age distribution. A system of differential equation model with five human state variables and two mosquito state variables was examined. Preschool-age (0–5) and young-age individuals make up our model’s division of the human population. We investigated the existence of an area in which the model is both mathematically and epidemiologically well posed. According to the findings of our mathematical research, the disease-free equilibrium exists whenever the fundamental reproduction number R0 is smaller than one and is asymptotically stable. The disease-free equilibrium point is unstable when R0>1. We showed that the endemic equilibrium point is unique for R0>1. Also, the most influential control parameters of the spread of malaria were identified. Numerical simulations of both classical and fractional order were conducted, and we used ODE (45) for classical part and numerical technique developed by Toufik and Atangana for fractional order. The infected population will grow because of the high biting frequency of the mosquito and the high likelihood of transmission from the infected mosquito to the susceptible human. R=1.622, which is more than one, indicating that the mosquito vector keeps on growing. This supports the stability of the endemic equilibrium point theorem, which states that the disease becomes endemic when R=1. The susceptible human population will decrease because of the presence of the infective mosquito, which has a high biting frequency for the first couple of days. Since the infective mosquito bit the susceptible human, the susceptible human became infected and went to the infected human compartments. Then, the susceptible population will decrease and the infested human population will increase. After a certain amount of time, it becomes zero due to the growth of protected classes. In this case, a disease-free equilibrium point exists and is stable. This condition exists because R0=2.827×10−5 is less than 1. This supports the theorem that the stability of the disease-free equilibrium point is obtained when R0<1. Depending on equation, we have shown that the possibility of some endemic equilibria exists when R0<1, that is, it undergoes backward bifurcation, even when the disease-free equilibrium is locally stable, and the result means that the society may misunderstand the level of malaria prevalence in the community.

A MATHEMATICAL MODEL FOR NIPAH VIRUS DISEASE BY USING PIECEWISE FRACTIONAL ORDER CAPUTO DERIVATIVE

In the Caputo sense, the goal of this paper is to develop a thorough analysis for the Nipah virus sickness under piecewise equations with fractional order derivative. Here, we take into account a SIRD-type model with classes for susceptible, infected, recovered, and dead individuals. We evaluate the solution’s viability using the notion of fractional order derivative. The fundamental reproduction number is also calculated. Here, we offer sufficient requirements for the Ulam–Hyers (UH) stability and the existence theory of the solution. We also give some numerical simulations for several compartments using the RK4 approach. In order to deepen our investigation, we therefore investigate the aforementioned disease’s transmission process using some novel fractional calculus notions.

Mathematical modeling and dynamics of immunological exhaustion caused by measles transmissibility interaction with HIV host.

This paper mainly addressed the study of the transmission dynamics of infectious diseases and analysed the effect of two different types of viruses simultaneously that cause immunodeficiency in the host. The two infectious diseases that often spread in the populace are HIV and measles. The interaction between measles and HIV can cause severe illness and even fatal patient cases. The effects of the measles virus on the host with HIV infection are studied using a mathematical model and their dynamics. Analysing the dynamics of infectious diseases in communities requires the use of mathematical models. Decisions about public health policy are influenced by mathematical modeling, which sheds light on the efficacy of various control measures, immunization plans, and interventions. We build a mathematical model for disease spread through vertical and horizontal human population transmission, including six coupled nonlinear differential equations with logistic growth. The fundamental reproduction number is examined, which serves as a cutoff point for determining the degree to which a disease will persist or die. We look at the various disease equilibrium points and investigate the regional stability of the disease-free and endemic equilibrium points in the feasible region of the epidemic model. Concurrently, the global stability of the equilibrium points is investigated using the Lyapunov functional approach. Finally, the Runge-Kutta method is utilised for numerical simulation, and graphic illustrations are used to evaluate the impact of different factors on the spread of the illness. Critical factors that effect the dynamics of disease transmission and greatly affect the rate and range of the disease's spread in the population have been determined through a thorough analysis. These factors are crucial in determining the expansion of the disease.

A study of periodic solutions of several types of nonlinear models in biomathematics

Abstract Biomathematics is a cross-discipline formed by the interpenetration of mathematics with life sciences, biology, and other disciplines, and biomathematical models provide an effective tool for solving problems in the above application areas. Our aim in this paper is to combine mathematical analytical tools and numerical simulation methods to investigate the existence and steady state of periodic solutions in different nonlinear models. Time lags with both discrete and distributed characteristics are introduced into the Lotka-Volterra predator-feeder system, and based on the discussion of the central manifold theorem and canonical type theory, it is proved that the branching periodic solution exists when the discrete time lag parameter τ > τ 0. In the SEIRS infectious disease model with nonlinear incidence term and vertical transmission, the global stability of the disease-free equilibrium point and the local asymptotic stability of the endemic equilibrium point are analyzed through the computation and discussion of the fundamental regeneration number R 0 (p, q). A class of convergence-growth models with nonlinear sensitivity functions is studied, and the global boundedness of classical solutions and their conditions are demonstrated based on global dynamics. A mathematical generalization of the muscular vascular model is made by introducing a centralized parameter, the relationship between periodic solutions and chaotic phenomena is explored utilizing a systematic equivalence transformation, and the equation of the homoscedastic orbitals is deduced to be z 2 = x 2 ( A - 1 2 x 2 ) {z^2} = {x^2}\left( {A - {1 \over 2}{x^2}} \right) .

Citogenética comparativa em felídeos (Carnivora: Felidae): Leopardus wiedii, Panthera onca, Puma concolor e Felis catus

ABSTRACT This study aims to conduct a cytogenetic analysis on four South American feline species: the jaguar (Panthera onca), the puma (Puma concolor), the ocelot (Leopardus wiedii), and the domestic cat (Felis catus). We discovered that the jaguar and the puma mainly differ in their fundamental number of chromosomes. Furthermore, we observed a morphological difference in a pair of chromosomes between the jaguar and the domestic cat. This suggests that, over the course of evolution, there was a pericentric inversion in a pair of B4 group chromosomes, leading them to become part of the A group in the jaguar. When analyzing the puma, we noticed the presence of a fourth pair of chromosomes in the E group, along with a deletion in the F group. Additionally, we observed the presence of an additional pair of chromosomes in the C group in the ocelot. Another interesting aspect of the study was the location of nucleolar organizer regions (NORs) on the chromosomes. To elucidate the origin of other chromosome pairs, we employed chromosomal banding techniques, allowing us to better understand the evolution of the C3 pair in the Leopardus genus and the E4 pair in the Puma genus.

MATHEMATICAL MODELS OF DENGUE TRANSMISSION DYNAMICS WITH VACCINATION AND WOLBACHIA PARAMETERS AND SEASONAL ASPECTS

The Aedes aegypti mosquito is the main carrier of dengue virus transmission to humans. In this study, a mathematical model for the transmission of the dengue virus is constructed using vaccination and Wolbachia parameters in an attempt to control the virus's spread. Furthermore, the fundamental reproduction number is set as a parameter of the infection threshold. Based on the stability of the equilibrium point analysis, it is found that the disease-free equilibrium point is locally asymptotically stable if . Then, a mathematical model of dengue was created by examining the seasonal aspect and adding a periodic term to the mosquito birth rate. Dengue virus transmission in mosquito populations is controlled by air temperature in addition to seasonal variables. In this study, three weather scenarios were simulated: scenario 1 for cold weather (air temperature 14 °C), scenario 2 for hot weather (air temperature 26 °C), and scenario 3 for moderate weather (air temperature between 14 and 26 °C).

Analysis of a discrete time fractional-order Vallis system

Vallis system is a model describing nonlinear interactions of the atmosphere and temperature fluctuations with a strong influence in the equatorial part of the Pacific Ocean. As the model approaches the fractional order from the integer order, numerical simulations for different situations arise. To see the behavior of the simulations, several cases involving integer analysis with different non-integer values of the Vallis systems were applied. In this work, a fractional mathematical model is constructed using the Caputo derivative. The local asymptotic stability of the equilibrium points of the fractional-order model is obtained from the fundamental production number. The chaotic behavior of this system is studied using the Caputo derivative and Lyapunov stability theory. Hopf bifurcation is used to vary the oscillation of the system in steady and unsteady states. In order to perform these numerical simulations, we apply Grünwald–Letnikov tactics with Binomial coefficients to obtain the effects on the non-integer fractional degree and discrete time vallis system and plot the phase diagrams and phase portraits with the help of MATLAB and MAPLE packages.

Mathematical Model for COVID-19 pandemic with implementation of intervention strategies and Cost-Effectiveness Analysis

In this study, a novel mathematical model for the dissemination dynamics of COVID-19 is developed. The main objective is to analyze the effectiveness of pharmaceutical interventions in lowering the COVID-19 contagions. We first demonstrate the positivity and boundedness of the solutions of the model and then compute the fundamental reproduction number. The stability analysis of contagion-free equilibrium is performed. The model is fitted to the COVID-19 reported data for a period of twelve months in India and estimate three parameters. The sensitivity analysis is conducted to identify the significant factors which impact the COVID-19 disease prevalence. We then define an optimum control problem using pharmaceutical interventions vaccination and treatment as the control functions to minimize the dissemination of COVID-19 contagions and disease-related mortality. Cost-effectiveness analysis is employed to determine the most effective and least costly strategy. The results are determined that the combination of vaccination and treatment is the most effective and least costly strategy in mitigating the spread of COVID-19 contagions. Furthermore, the impact of different levels of vaccine efficacy on contagion trajectories is examined, and it is shown that COVID-19 contagions and disease related fatalities would decrease as vaccination efficacy increases. The outcomes would assist administrators in developing efficient strategies to reduce the scope of the COVID-19 pandemic.

Techniques and advances in mammalian chromosome identification

Cytogenetics, through the study of the karyotype, with its characteristics such as diploid number (2n), chromosomal morphology of autosomes (fundamental number – FN), and sexual system, constitutes an important tool that can help clarify the phylogenetic relationships and taxonomic status of several taxa, receiving the name cytotaxonomy. In addition to conventional staining, there are several classical techniques of chromosomal bandings, such as GTG, CBG, and Ag-NORs bandings, which help in species comparisons to search for homologies and understand chromosome structure, function, and behavior. Systematic and taxonomic problems, as well as chromosome structure and behavior, have been elucidated in some groups of mammals with these banding techniques. In this study, we present the procedures for direct chromosomal preparations from bone marrow and peripheral blood used in the field and laboratory to obtain suspended mitotic metaphase cells. We also describe the main techniques of conventional staining and chromosomal banding for analyzing karyotypes in mammals.

Chromosome Banding Properties of Neogobius fluviatilis (Pallas, 1814) (Perciformes, Gobiidae)

The monkey goby, Neogobius fluviatilis (Pallas, 1814) that distributed in Türkiye was studied cytogenetically for the first time. In this context, diploid chromosome number, chromosome morphology and also chromosomal banding properties (C-banding and Ag-NOR staining) of N. fluviatilis were revealed out. Chromosome slides were prepared from head kidney cells according to the air-drying technique. Chromosome slides were observed under the microscope and metaphases were photographed. The chromosomes were measured by digital caliper and karyotype was arranged manually. The diploid chromosome number was found as 46. Karyotype was composed with all uniarmed chromosomes. Fundamental arm number was calculated as 46 too. No heteromorphic sex chromosomes were determined in the karyotype. C-bands were detected on the pericentromeres of almost all chromosomes. Otherwise, two Ag-NORs were found in the silver-stained metaphases. This study revealed out chromosomal properties of N. fluviatilis from Türkiye with conventional cytogenetic techniques. This report may improve the cytogenetic data of the genus Neogobius.

Effect of Flow Rate Modulation on Alginate Emulsification in Multistage Microfluidics.

The encapsulation of stem cells into alginate microspheres is an important aspect of tissue engineering or bioprinting which ensures cell growth and development. We previously demonstrated the encapsulation of stem cells using the hanging drop method. However, this conventional process takes a relatively long time and only produces a small-volume droplet. Here, an experimental approach for alginate emulsification in multistage microfluidics is reported. By using the microfluidic method, the emulsification of alginate in oil can be manipulated by tuning the flow rate for both phases. Two-step droplet emulsification is conducted in a series of polycarbonate and polydimethylsiloxane microfluidic chips. Multistage emulsification of alginate for stem cell encapsulation has been successfully reported in this study under certain flow rates. Fundamental non-dimensional numbers such as Reynolds and capillary are used to evaluate the effect of flow rate on the emulsification process. Reynolds numbers of around 0.5-2.5 for alginate/water and 0.05-0.2 for oil phases were generated in the current study. The capillary number had a maximum value of 0.018 to ensure the formation of plug flow. By using the multistage emulsification system, the flow rates of each process can be tuned independently, offering a wider range of droplet sizes that can be produced. A final droplet size of 500-1000 µm can be produced using flow rates of 0.1-0.5 mL/h and 0.7-2.4 mL/h for the first stage and second stage, respectively.

Cytogenetic Study of Five Varieties of Callisia repens (Jacq.) L. (Commelinaceae) from Laos

Cytogenetical studies were carried out on five varieties of Callisia repens, i.e., turtle vine, green, pink lady, gold, and Bianca. The morphological characteristics of all five varieties differed in leaf shape and color of the plant. All five varieties have the same chromosome number, 2n = 12, and the fundamental number (NF) = 24. The number of metacentric (m), submetacentric (sm), and subtelocentric (st) chromosomes was related to the discrepancies between the various karyotypes that were found. The formula for each of the karyotypes was 2m + 2sm + 8st (turtle vine), 2m + 10st (green), 8m + 4st 14 (pink lady), 2m + 4sm + 6st (gold), and 2m + 2sm + 8st (Bianca). Therefore, all five strains had asymmetrical karyotypes. The chromosome number of C. repens has been reported previously, but this is the first report of karyotype variation among the varieties. Furthermore, principal component analysis (PCA) of the karyotype formula was able to distinguish C. repens ‘pink lady’, C. repens ‘green’, and C. repens ‘gold’, but it was unable to differentiate between C. repens ‘Bianca’ and C. repens ‘turtle vine’. Additionally, PCA conducted on the centromeric index (CI) and the leaf colors of the five varieties of C. repens successfully separated all of them. Therefore, the prominent morphological traits and karyotype information of the five varieties of C. repens from Laos can be used to distinguish between them.

A Susceptible Vaccinated Exposed Infected Hospitalized and Removed/Recovered (SVEIHR) Model Framework for COVID-19

In reaction to the severe socio-economic effects and upheavals that the Covid-19 sickness had on the world within the first few weeks of its introduction, everyone involved had to act quickly to look for possible solutions for preventing the ensuing epidemics. A prompt response is more critical given Nigeria's subpar social, economic, and healthcare infrastructure. Investigated was the efficacy of various pharmacological, non-pharmaceutical, or a combination of both therapies in flattening the Covid-19 incidence curve. In order to investigate the impact of these interventions, a deterministic SVEIHR model was created and applied. The Nigerian Center for Disease Control (NCDC) portal's Covid-19 data were used to parametrize the model. For simulations using a system dynamic simulation, estimated parameters were employed. The fundamental reproduction number, R0, was used to evaluate the success of our suggested intervention in effectively managing COVID-19 transmission. The simulation results demonstrated that the use of only non-pharmaceutical interventions, such as the use of face masks, a light lockdown, and hand washing at baseline or high levels, is insufficient, with the R0 varying from vaccination at the vaccination rate of 0.5% with non-pharmaceutical interventions at any level of compliance, and a combination of vaccination at 0.05% and high hygiene level were effective in flattening the Covid-19 disease incidence curve in Nigeria, returning a R0 less than 1. Furthermore, maintaining a high level of cleanliness, which includes hand washing and the use of a face mask, would be sufficient to stop the spread of Covid-19 disease and eventually flatten Covid-19 disease incidence curve in Nigeria, given a low turnout of 0.05% for vaccination and the easing of lockdown.

Exploring the effectiveness of control measures and long-term behavior in Hepatitis B: An analysis of an endemic model with horizontal and vertical transmission

This study presents an optimal control and stability analysis of a mathematical model for the spread of Hepatitis B with a harmonic mean type incidence rate, providing insights into the effectiveness of control measures and the long-term behavior of the disease dynamics. The hepatitis B virus causes hepatitis B infection. It is one of the most serious viral infections out there, as well as a global health issue. Various stages, such as chronic and acute carrier stages, serve an essential role in the transition of hepatitis B infection. Chronic disease is characterized by the presence of individuals who do not show any symptoms but are nevertheless able to spread the illness. In this study, we focused on the infectiousness of hepatitis B at different stages of illness and created an endemic model by means of a nonlinear occurrence rate. To accomplish so, we start by dividing the infectious group into two further sub-classes: i.e., acute infected and chronic carriers, both of which can transmit horizontally and vertically. The suggested model’s basic characteristics are provided. The method of the next-generation matrix is utilized to compute the basic reproduction number. The biological significance of the threshold state is thoroughly researched and addressed. We also discover the criteria for investigating all of the model’s potential equilibria in terms of the fundamental reproduction number. Finally, to supplement our analytical work, we do the numerical estimation.

Novel insights for a nonlinear deterministic-stochastic class of fractional-order Lassa fever model with varying kernels

Lassa fever is a hemorrhagic virus infection that is usually spread by rodents. It is a fatal infection that is prevalent in certain West African countries. We created an analytical deterministic-stochastic framework for the epidemics of Lassa fever employing a collection of ordinary differential equations with nonlinear solutions to identify the influence of propagation processes on infected development in individuals and rodents, which include channels that are commonly overlooked, such as ecological emergent and aerosol pathways. The findings shed light on the role of both immediate and subsequent infectiousness via the power law, exponential decay and generalized Mittag-Leffler kernels. The scenario involves the presence of a steady state and an endemic equilibrium regardless of the fundamental reproduction number, Re _{0}<1, making Lassa fever influence challenging and dependent on the severity of the initial sub-populations. Meanwhile, we demonstrate that the stochastic structure has an exclusive global positive solution via a positive starting point. The stochastic Lyapunov candidate approach is subsequently employed to determine sufficient requirements for the existence and uniqueness of an ergodic stationary distribution of non-negative stochastic simulation approaches. We acquire the particular configuration of the random perturbation associated with the model’s equilibrium Re _{0}^{s}<1 according to identical environments as the presence of a stationary distribution. Ultimately, modeling techniques are used to verify the mathematical conclusions. Our fractional and stochastic findings exhibit that when all modes of transmission are included, the impact of Lassa fever disease increases. The majority of single dissemination pathways are less detrimental with fractional findings; however, when combined with additional spread pathways, they boost the Lassa fever stress.

Mathematical study of fractal-fractional leptospirosis disease in human and rodent populations dynamical transmission

In both industrialized and developing nations, leptospirosis is one of the most underdiagnosed and under-reported diseases. It is known that people are more likely to contract a disease depending on their employment habits and the environment they live in, which varies from community to community. The absence of global data for morbidity and mortality has contributed to leptospirosis' neglected disease status even though it is a life-threatening illness and is widely acknowledged as a significant cause of pulmonary hemorrhage syndrome. This study aims to examine the impact of rodent-borne leptospirosis on the human population by constructing and evaluating a compartmental mathematical model using fractional-order differential equations. The model considers both the presence of disease-causing agents in the environment and the rate of human infection resulting from interactions with infected rodents and the environment. Through this approach, the research investigates the dynamics and implications of leptospirosis transmission in the context of human-rodent interactions and environmental factors. We create a fractal-fractional model using the mittag-leffler kernel. The positivity and boundedness of solutions are first discussed. The model equilibria and fundamental reproduction number are then presented. With the use of the Lyapunov function method, the solutions are subjected to global stability analysis. The fixed-point theory is used to derive the fractional-order model's existence and uniqueness. Solutions are produced using a two-step Lagrange polynomial in the generalized form of the Mittag-Leffler kernel to explore the effect of the fractional operator with numerical simulations, which shows the influence of the sickness due to the effect of different parameters involved. Such a study will aid in the development of control strategies to combat the disease in the community and an understanding of the behavior of the Leptospira virus.

Morphological Differentiation and Karyotypic Studies of the African Common Toad Sclerophrys (Bufo) Regularis (Reuss, 1833)

The study analyzed the morphological differentiation and karyotype among populations of the common toad, Sclerophrys (Bufo) regularis from six Local Government Areas in Ondo state. Variations in fifteen morphometric and qualitative characters in one hundred and seventy-one animals from six population samples were analyzed using univariate and multivariate statistics. Descriptives of sexes and correlation between morphological characters was also analyzed. Female toads had larger mean values of most of the morphological characters studied with weight contributing the largest variance. The chromosomes of twenty-four specimens of the toad were also studied using standard bone marrow smear techniques. A chromosome complement of 2n=20 was observed for this species. The chromosomes consists of nine pairs of metacentric and one pair of submetacentric chromosomes. The chromosomes based on centromeric position could be grouped into two - metacentric and submetacentric - and based on size, into three metacentric chromosomes; 1-4 which were large, metacentric chromosomes; 5-6 medium sized metacentric chromosomes, while 7-9 were small sized, and the last pair (10), submetacentric chromosomes were small. The fundamental number of this species is 40 and with no sex chromosomes or satellites reported, while bi-armed chromosomes were observed. Findings also showed that female individuals of the species weighed more than the male.

Chromosomal analysis of Sander lucioperca (L., 1758) (Perciformes: Percidae) from Turkey

Sander lucioperca (pikeperch) is a percid fish species of high commercial value and potential for being aquaculture in Turkey. However, karyological studies are deficient for population of Turkey. So, the aim of this study is to carry out diploid chromosome number, karyotype formula, fundamental arm number and chromosomal banding properties (with C-banding and Ag-NOR staining) of S. lucioperca. Specimens of S. lucioperca were captured from Konya, Turkey and alive specimens carried to the laboratory. Chromosome obtaining was provided by using air-drying technique from the head kidney. Chromosome slides were prepared and banding procedures were applied. Result of the analysis, diploid chromosome number was found as 48 and karyotype of the pikeperch consist of 32 biarmed and 16 uniarmed chromosomes. Constitutive heterochromatin regions were observed on the pericentromeres of some of the chromosomes. Ag-NORs were determined on one pair of submetacentric chromosome. This report is the first that determines chromosomal properties of S. lucioperca from Turkey. This study may contribute the cytogenetic information of this species.