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Abstract Infectious diseases have long been a shaping force in human history, necessitating a comprehensive understanding of their dynamics. This study introduces a co-evolution model that integrates both epidemiological and evolutionary dynamics. Utilizing a system of differential equations, the model represents the interactions among susceptible, infected, and recovered populations for both ancestral and evolved viral strains. Methodologically rigorous, the model’s existence and uniqueness have been verified, and it accommodates both deterministic and stochastic cases. A myriad of graphical techniques have been employed to elucidate the model’s dynamics. Beyond its theoretical contributions, this model serves as a critical instrument for public health strategy, particularly predicting future outbreaks in scenarios where viral mutations compromise existing interventions.

Norovirus is a leading global cause of viral gastroenteritis, significantly affecting mortality, morbidity, and healthcare costs. This paper develops and analyzes a stochastic SEIQR epidemic model for norovirus dynamics, incorporating temporal immunity and a generalized incidence rate. The model is proven to have a unique positive global solution, with extinction conditions explored. Using Khasminskii’s method, the model’s ergodicity and equilibrium distribution are investigated, demonstrating a unique ergodic stationary distribution when R^s>1. Extinction occurs when R0E<1. Computer simulations confirm that noise level significantly influences epidemic spread.

In this study, we develop a comprehensive mathematical model to analyze the dynamics of epidemic cholera, characterized by acute diarrhea due to pathogen overabundance in the human body. The model is first developed from a deterministic point of view, and then it is modified to include the randomness by stochastic differential equations. The study selected Lévy noise above other well-known types of noise, emphasizing its importance in epidemic modeling. Besides presenting a biological justification for the stochastic system, we demonstrate that the equivalent deterministic model exhibits possible equilibria. The introduction is followed by theoretical analysis of the model. Through rigorous analysis, we establish that the stochastic model ensures a unique global solution. Lyapunov function theory is applied to construct necessary conditions, which on average, guarantee the model’s stability for R0s>1. Our findings suggest the likelihood of eradicating the disease when Rs is below one, a significant insight supported by graphical simulations of the model. Graphical illustrations were generated from simulating the model in order to increase the analytical results’ robustness. This work provides a strong theoretical framework for a thorough comprehension of a range of such diseases. This research not only provides a deeper understanding of cholera dynamics but also offers a robust theoretical framework applicable to a range of similar diseases, alongside a novel approach for constructing Lyapunov functions for nonlinear models with random disturbances.

DNA, as the storage medium in organisms, can address the shortcomings of existing electromagnetic storage media, such as low information density, high maintenance power consumption, and short storage time. Current research on DNA storage mainly focuses on designing corresponding encoders to convert binary data into DNA base data that meets biological constraints. We have created a new Chinese character code table that enables exceptionally high information storage density for storing Chinese characters (compared to traditional UTF-8 encoding). To meet biological constraints, we have devised a DNA shift coding scheme with low algorithmic complexity, which can encode any strand of DNA even has excessively long homopolymer. The designed DNA sequence will be stored in a double-stranded plasmid of 744bp, ensuring high reliability during storage. Additionally, the plasmid‘s resistance to environmental interference ensuring long-term stable information storage. Moreover, it can be replicated at a lower cost.

Abstract Background Influenza B virus can cause epidemics with high pathogenicity, so it poses a serious threat to public health. A feature representation algorithm is proposed in this paper to identify the pathogenicity phenotype of influenza B virus. Methods The dataset included all 11 influenza virus proteins encoded in eight genome segments of 1724 strains. Two types of features were hierarchically used to build the prediction model. Amino acid features were directly delivered from 67 feature descriptors and input into the random forest classifier to output informative features about the class label and probabilistic prediction. The sequential forward search strategy was used to optimize the informative features. The final features for each strain had low dimensions and included knowledge from different perspectives, which were used to build the machine learning model for pathogenicity identification. Results The 40 signature positions were achieved by entropy screening. Mutations at position 135 of the hemagglutinin protein had the highest entropy value (1.06). After the informative features were directly generated from the 67 random forest models, the dimensions for class and probabilistic features were optimized as 4 and 3, respectively. The optimal class features had a maximum accuracy of 94.2% and a maximum Matthews correlation coefficient of 88.4%, while the optimal probabilistic features had a maximum accuracy of 94.1% and a maximum Matthews correlation coefficient of 88.2%. The optimized features outperformed the original informative features and amino acid features from individual descriptors. The sequential forward search strategy had better performance than the classical ensemble method. Conclusions The optimized informative features had the best performance and were used to build a predictive model so as to identify the phenotype of influenza B virus with high pathogenicity and provide early risk warning for disease control. Graphical Abstract

In the present study, we introduce some new separation axioms for binary topological spaces. This new idea gives the notion of generalized binary (T0, T1, T2, T3, and T4 spaces) and binary generalized semi (T0, T1, T2, T3, and T4 spaces) using generalized binary open sets and binary generalized semi open sets to investigate their properties. We also provide adequate examples to assist and understand abstract concepts. In the similar manner, we begin researching the b-sg-T0, b-sg-T1, b-sg-T2, b-sg-T3, and b-sg-T4 spaces in binary topological spaces. The study on the axioms is done over binary-T0, binary-T1, binary-T2, binary-T3, and binary-T4 spaces, motivated to do the analysis of the spaces gb(b-gs)-T0, gb(b-gs)-T1, gb(b-gs)-T2, gb(b-gs)-T3, and gb(b-gs)-T4 as well.

Unsteady magneto-hydrodynamic double-diffusive convection flows between two infinite vertical parallel plates have been investigated in the presence of the inclined magnetic field, heat generation or absorption, and chemical reaction. The dimensionless form of governing equations for momentum, energy and concentration has been solved using the integral transforms (Laplace and finite sine-Fourier transforms). The exact solutions for the velocity, temperature and concentration are obtained without any constraints. Semi analytical solutions of these problems are also established by using the Laplace inversion numerical algorithms Stehfest’s and Tzou’s. Further, we compare our obtained analytical and numerical results in graphical and tabular forms. Finally, the influence of pertinent parameters on the fluid velocity, temperature and concentration have been disused in detailed through graphs.

Abstract The aim of this paper is to establish new generalized fractional versions of the Hadamard and the Fejér–Hadamard integral inequalities for harmonically convex functions. Fractional integral operators involving an extended generalized Mittag-Leffler function which are further generalized via a monotone increasing function are utilized to get these generalized fractional versions. The results of this paper give several consequent fractional inequalities for harmonically convex functions for known fractional integral operators deducible from utilized generalized fractional integral operators.

Abstract In this paper we have derived the fractional integral inequalities by defining exponentially ( s , m ) $(s,m)$ -convex functions. These inequalities provide upper bounds, boundedness, continuity, and Hadamard type inequality for fractional integrals containing an extended Mittag-Leffler function. The results about fractional integral operators for s-convex, m-convex, ( s , m ) $(s,m)$ -convex, exponentially convex, exponentially s-convex, and convex functions are direct consequences of presented results.

Brain tumor research has been stapled for human health while brain network research is crucial for us to understand brain activity. Here the structural controllability theory is applied to study three human brain-specific gene regulatory networks, including forebrain gene regulatory network, hindbrain gene regulatory network and neuron associated cells cancer related gene regulatory network, whose nodes are neural genes and the edges represent the gene expression regulation among the genes. The nodes are classified into two classes: critical nodes and ordinary nodes, based on the change of the number of driver nodes upon its removal. Eight topological properties (out-degree DO, in-degree DI, degree D, betweenness B, closeness CA, in-closeness CI, out-closeness CO and clustering coefficient CC) are calculated in this paper and the results prove that the critical genes have higher score of topological properties than the ordinary genes. Then two bioinformatic analysis are used to explore the biologic significance of the critical genes. On the one hand, the enrichment scores in several kinds of gene databases are calculated and reveal that the critical nodes are richer in essential genes, cancer genes and the neuron related disease genes than the ordinary nodes, which indicates that the critical nodes may be the biomarker in brain-specific gene regulatory network. On the other hand, GO analysis and KEGG pathway analysis are applied on them and the results show that the critical genes mainly take part in 14 KEGG pathways that are transcriptional misregulation in cancer, pathways in cancer and so on, which indicates that the critical genes are related to the brain tumor. Finally, by deleting the edges or routines in the network, the robustness analysis of node classification is realized, and the robustness of node classification is proved. The comparison of neuron associated cells cancer related GRN (Gene Regulatory Network) and normal brain-specific GRNs (including forebrain and hindbrain GRN) shows that the neuron-related cell cancer-related gene regulatory network is more robust than other types.

In this paper, we define the concept of level graphs on interval-valued fuzzy graphs (IVFGs) and introduce the notions of α,β−α,β− homomorphism, isomorphism, weak isomorphism, and co-weak isomorphism of IVFGs by α,β− homomorphism. Also, an application of homomorphism of IVFGs has been presented by using coloring-FG.

Covering, matching, and domination are the basic concepts in graphs that play a decisive role in the properties of graphs. Calculating these parameters is one of the difficulties in fuzzy graphs when it is not possible to accurately determine the values of the vertices of a graph. The interval-valued intuitionistic fuzzy graph (IVIFG) is one of the fuzzy graphs which can play an important role in solving uncertain problems in different sciences such as psychology, biological sciences, medicine, and social networks. The necessity of using a range of value instead of one number caused them to help researchers in optimizing and saving time and cost. In this study, we introduce some of the specific concepts such as covering, matching, and paired domination using strong arc or effective edges by giving appropriate examples. In addition, we have calculated strong node covering number, strong independent number, and other parameters of complete bipartite IVIFGs with several examples. Finally, we have presented an application of IVIFG in social networks.

Abstract Background Avian influenza virus can directly cross species barriers and infect humans with high fatality. As antigen novelty for human host, the public health is being challenged seriously. The pandemic risk of avian influenza viruses should be analyzed and a prediction model should be constructed for virology applications. Results The 178 signature positions in 11 viral proteins were firstly screened as features by the scores of five amino acid factors and their random forest rankings. The Supporting Vector Machine algorithm achieved well performance. The most important amino acid factor (Factor 5) and the minimal range of signature positions (63 amino acid residues) were also explored. Moreover, human-origin avian influenza viruses with three or four genome segments from human virus had pandemic risk with high probability. Conclusion Using machine learning methods, the present paper scores the amino acid mutations and predicts pandemic risk with well performance. Although long evolution distances between avian and human viruses suggest that avian influenza virus in nature still need time to fix among human host, it should be notable that there are high pandemic risks for H7N9 and H9N2 avian viruses.

Considering all physical, biological, and social systems, fuzzy graph (FG) models serve the elemental processes of all natural and artificial structures. As the indeterminate information is an essential real-life problem, which is mostly uncertain, modeling the problems based on FGs is highly demanding for an expert. Vague graphs (VGs) can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems, in which FGs possibly will not succeed in bringing about satisfactory results. In addition, VGs are a very useful tool to examine many issues such as networking, social systems, geometry, biology, clustering, medical science, and traffic plan. The previous definition restrictions in FGs have made us present new definitions in VGs. A wide range of applications has been attributed to the domination in graph theory for several fields such as facility location problems, school bus routing, modeling biological networks, and coding theory. Concepts from domination also exist in problems involving finding the set of representatives, in monitoring communication and electrical networks, and in land surveying (e.g., minimizing the number of places a surveyor must stand in order to take the height measurement for an entire region). Hence, in this article, we introduce different concepts of dominating, equitable dominating, total equitable dominating, weak (strong) equitable dominating, equitable independent, and perfect dominating sets in VGs and also investigate their properties by some examples. Finally, we present an application in medical sciences to show the importance of domination in VGs.

The graph entropy was proposed by Körner in the year 1973 when he was studying the problem of coding in information theory. The foundation of graph entropy is in information theory, but it was demonstrated to be firmly identified with some established and often examined graph-theoretic ideas. For instance, it gives an equal definition to a graph to be flawless, and it can likewise be connected to acquire lower bounds in graph covering problems. The objective of this study is to solve the open problem suggested by Kwun et al. in 2018. In this paper, we study the weighted graph entropy by taking augmented Zagreb edge weight and give bounds of it for regular, connected, bipartite, chemical, unicyclic, etc., graphs. Moreover, we compute the weighted graph entropy of certain nanotubes and plot our results to see dependence of weighted entropy on involved parameters.

Laplace transform is a powerful tool for solving differential and integrodifferential equations in engineering sciences. The use of Laplace transform for the solution of differential or integrodifferential equations sometimes leads to the solutions in the Laplace domain that cannot be inverted to the real domain by analytic methods. Therefore, we need numerical methods to invert the solution to the real domain. In this work, we construct numerical schemes based on Laplace transform for the solution of fractional-order Volterra integrodifferential equations in the sense of the Atangana-Baleanu Caputo derivative. We propose two numerical methods for approximating the solution of fractional-order linear and nonlinear Volterra integrodifferential equations. In our scheme, the inverse Laplace transform is approximated using a contour integration method and Stehfest method. Some numerical experiments are performed to check the accuracy and efficiency of the methods. The results obtained using these methods are compared.

Graph theory and its wide applications in natural sciences and social sciences open a new era of research. Making the graph of computer networks and analyzing it with aid of graph theory are extensively studied and researched in the literature. An important discussion is based on distance between two nodes in a network which may include closeness of objects, centrality of objects, average path length between objects, and vertex eccentricity. For example, (1) disease transmission networks: closeness and centrality of objects are used to measure vulnerability to particular disease and its infectivity; (2) routing networks: eccentricity of objects is used to find vertices which form the periphery objects of the network. In this manuscript, we have discussed distance measurements including center, periphery, and average eccentricity for the Cartesian product of two cycles. The results are obtained using the definitions of eccentricity, radius, and diameter of a graph, and all possible cases (for different parity of length of cycles) have been proved.

The biggest bottleneck in DNA computing is exponential explosion, in which the DNA molecules used as data in information processing grow exponentially with an increase of problem size. To overcome this bottleneck and improve the processing speed, we propose a DNA computing model to solve the graph vertex coloring problem. The main points of the model are as follows: ① The exponential explosion problem is solved by dividing subgraphs, reducing the vertex colors without losing the solutions, and ordering the vertices in subgraphs; and ② the bio-operation times are reduced considerably by a designed parallel polymerase chain reaction (PCR) technology that dramatically improves the processing speed. In this article, a 3-colorable graph with 61 vertices is used to illustrate the capability of the DNA computing model. The experiment showed that not only are all the solutions of the graph found, but also more than 99% of false solutions are deleted when the initial solution space is constructed. The powerful computational capability of the model was based on specific reactions among the large number of nanoscale oligonucleotide strands. All these tiny strands are operated by DNA self-assembly and parallel PCR. After thousands of accurate PCR operations, the solutions were found by recognizing, splicing, and assembling. We also prove that the searching capability of this model is up to O(359). By means of an exhaustive search, it would take more than 896 000 years for an electronic computer (5 × 1014 s−1) to achieve this enormous task. This searching capability is the largest among both the electronic and non-electronic computers that have been developed since the DNA computing model was proposed by Adleman’s research group in 2002 (with a searching capability of O(220)). Keywords: DNA computing, Graph vertex coloring problem, Polymerase chain reaction

In this work, we study the notion of w-pseudo-order on an ordered (semi)hyperring and give some explicit examples. In addition, we give some examples to compare weak pseudo-order relations with pseudo-order relations. Finally, we construct ordered (semi)hyperrings using regular relations.

For a graph G with no isolated vertex, let γpr(G) and sdγpr(G) denote the paired-domination and paired-domination subdivision numbers, respectively. In this note, we show that if T is a tree of order n≥4 different from a healthy spider (subdivided star), then sdγpr(T)≤min{γpr(T)2+1,n2}, improving the (n−1)-upper bound that was recently proven.

As one of the well-studied RNA methylation modifications, N6-methyladenosine (m6A) plays important roles in various biological progresses, such as RNA splicing and degradation, etc. Identification of m6A sites is fundamentally important for better understanding of their functional mechanisms. Recently, machine learning based prediction methods have emerged as an effective approach for fast and accurate identification of m6A sites. In this paper, we proposed “M6AMRFS”, a new machine learning based predictor for the identification of m6A sites. In this predictor, we exploited a new feature representation algorithm to encode RNA sequences with two feature descriptors (dinucleotide binary encoding and Local position-specific dinucleotide frequency), and used the F-score algorithm combined with SFS (Sequential Forward Search) to enhance the feature representation ability. To predict m6A sites, we employed the eXtreme Gradient Boosting (XGBoost) algorithm to build a predictive model. Benchmarking results showed that the proposed predictor is competitive with the state-of-the art predictors. Importantly, robust predictions for multiple species by our predictor demonstrate that our predictive models have strong generalization ability. To the best of our knowledge, M6AMRFS is the first tool that can be used for the identification of m6A sites in multiple species. To facilitate the use of our predictor, we have established a user-friendly webserver with the implementation of M6AMRFS, which is currently available in http://server.malab.cn/M6AMRFS/. We anticipate that it will be a useful tool for the relevant research of m6A sites.

Avian influenza virus (AIV) can directly cross species barriers and infect humans with high fatality. Using machine learning methods, the present paper scores the amino acid mutations and predicts interspecies transmission. Initially, 183 signature positions in 11 viral proteins were screened by the scores of five amino acid factors and their random forest rankings. The most important amino acid factor (Factor 3) and the minimal range of signature positions (50 amino acid residues) were explored by a supporting vector machine (the highest-performing classifier among four tested classifiers). Based on these results, the avian-to-human transmission of AIVs was analyzed and a prediction model was constructed for virology applications. The distributions of human-origin AIVs suggested that three molecular patterns of interspecies transmission emerge in nature. The novel findings of this paper provide important clues for future epidemic surveillance.

Fuzzy graphs (FGs) are efficient mathematical models for analyzing many problems of daily life. Various problems in the fields of physics, telecommunication science, psychology and genetics can be modeled and solved with the help of fuzzy graph theory. One of the most widely used types of FG is vague graph (VG). VGs play an important role in various fields such as computer science, psychology, medicine, and political sciences and are used to find effective people in an organization or social institution. Today, connectivity indices are used in computer networks and economics to find the most suitable place for construction. These indices also have many applications in medical sciences, including ultrasound and radiology. Hence, in this research, we introduce connectivity index (CI), average connectivity index (ACI), and randic index (RI) in VGs with some examples. Likewise, some new vertices such as enhancing vertex (EV), reducing vertex (RV), and neutral vertex (NV) are described. Finally, an application of CI in the selecting town for building a school is given. [ABSTRACT FROM AUTHOR]

COVID-19 has caused severe health complications and produced a substantial adverse economic impact around the world. Forecasting the trend of COVID-19 infections could help in executing policies to effectively reduce the number of new cases. In this study, we apply the decomposition and ensemble model to forecast COVID-19 confirmed cases, deaths, and recoveries in Pakistan for the upcoming month until the end of July. For the decomposition of data, the Ensemble Empirical Mode Decomposition (EEMD) technique is applied. EEMD decomposes the data into small components, called Intrinsic Mode Functions (IMFs). For individual IMFs modelling, we use the Autoregressive IntegratedMoving Average (ARIMA) model. The data used in this study is obtained from the official website of Pakistan that is publicly available and designated for COVID-19 outbreak with daily updates. Our analyses reveal that the number of recoveries, new cases, and deaths are increasing in Pakistan exponentially. Based on the selected EEMD-ARIMA model, the new confirmed cases are expected to rise from 213,470 to 311,454 by 31 July 2020, which is an increase of almost 1.46 times with a 95% prediction interval of 246,529 to 376,379. The 95% prediction interval for recovery is 162,414 to 224,579, with an increase of almost two times in total from 100802 to 193495 by 31 July 2020. On the other hand, the deaths are expected to increase from 4395 to 6751, which is almost 1.54 times, with a 95% prediction interval of 5617 to 7885. Thus, the COVID-19 forecasting results of Pakistan are alarming for the next month until 31 July 2020. They also confirm that the EEMD-ARIMA model is useful for the short-termforecasting of COVID-19, and that it is capable of keeping track of the real COVID-19 data in nearly all scenarios. The decomposition and ensemble strategy can be useful to help decision-makers in developing short-term strategies about the current number of disease occurrences until an appropriate vaccine is developed. [ABSTRACT FROM AUTHOR]