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The Nipah virus (NiV) is one of the most lethal viruses which can infect humans and lead to fatal encephalitis. The recent significant awareness of NiV is due to its elevated death rate and effective transmission capabilities among humans. With its recurrent outbreaks and exceptionally high mortality rate, the NiV infections have emerged as one of the most concerning hazards to public health. The exploration of NiV and its characteristics revealed that NiV has two distinct strains, namely, the Malaysia (NiVM) strain and the Bangladesh (NiVB) strain. In this paper, we propose a novel Caputo fractional order mathematical model to simulate the dynamics of the two strains NiV. The positivity and boundedness of the model’s solutions are investigated. The existence and asymptotic stability of the equilibrium points of the model are examined. The analysis of basic reproduction number is presented to determine whether the infection will die out or persist. The effects of key parameters of the model on its dynamical behaviors are also explored. Finally, efficient numerical technique is used to confirm the analytical results through detailed numerical simulations.

Abstract This research focuses on the design of a novel fractional model for simulating the ongoing spread of the coronavirus (COVID-19). The model is composed of multiple categories named susceptible $$S(t)$$ S ( t ) , infected $$I(t)$$ I ( t ) , treated $$T(t)$$ T ( t ) , and recovered $$R(t)$$ R ( t ) with the susceptible category further divided into two subcategories $${S}_{1} (t)$$ S 1 ( t ) and $${S}_{2} (t)$$ S 2 ( t ) . In light of the need for restrictive measures such as mandatory masks and social distancing to control the virus, the study of the dynamics and spread of the virus is an important topic. In addition, we investigate the positivity of the solution and its boundedness to ensure positive results. Furthermore, equilibrium points for the system are determined, and a stability analysis is conducted. Additionally, this study employs the analytical technique of the Laplace Adomian decomposition method (LADM) to simulate the different compartments of the model, taking into account various scenarios. The Laplace transform is used to convert the nonlinear resulting equations into an equivalent linear form, and the Adomian polynomials are utilized to treat the nonlinear terms. Solving this set of equations yields the solution for the state variables. To further assess the dynamics of the model, numerical simulations are conducted and compared with the results from LADM. Additionally, a comparison with real data from Italy is demonstrated, which shows a perfect agreement between the obtained data using the numerical and Laplace Adomian techniques. The graphical simulation is employed to investigate the effect of fractional-order terms, and an analysis of parameters is done to observe how quickly stabilization can be achieved with or without confinement rules. It is demonstrated that if no confinement rules are applied, it will take longer for stabilization after more people have been affected; however, if strict measures and a low contact rate are implemented, stabilization can be reached sooner.

This work investigates the transmission dynamics of a proposed fractional-order cotton leaf curl virus (CLCuV) model considering the effects of climate change. High temperatures resulting from climate change and global warming significantly impact the cotton crop and CLCuV transmission, causing substantial economic losses for farmers and agricultural industries. The study aims to address these impacts and contribute to the Sustainable Development Goals (SDGs) by promoting well-being and healthy lives. The characteristics of the CLCuV model’s solution are examined, including equilibrium points and the basic reproduction number. The stability of equilibrium points is analyzed in relation to key parameters, and sensitivity analysis of controllable parameters is performed. Additionally, optimal management strategies for controlling CLCuV spread are explored, aiming for minimal cost, improved health, and reduced climate change hazards. Numerical simulations are conducted to validate the theoretical findings.

In this paper, we introduce a novel model that simulates the spread of the monkeypox virus. The new model takes into account the effect of the interaction between the human and rodent population along with some realistic factors that have not been introduced before such as imperfect vaccination and nonlinear incidence rates. Moreover, the human population is further divided into low-risk and high-risk groups to better reflect recent observations. To understand the dynamics of the new model, the existence, uniqueness, and continuous dependence on initial conditions, as well as its positivity and boundedness of the model are investigated in detail. The obtained solution is proved to be positive and has bounded behavior. Furthermore, the reproduction number R0 for the proposed system is computed and detailed bifurcation analysis is performed to reveal major qualitative changes in the model's dynamics. In addition, we investigate the influence of key parameters on the basic reproduction number. We also explore and analyze the stability of equilibrium points in the space of parameters. The new findings reveal that the virus is more frequently witnessed among the high-risk group, which may provide some restrictions to stop the spread through social limitations. To validate our theoretical results, we conduct numerical simulations, which provide insights into the behavior of the model under different conditions. The new findings aim in developing preventive control measures to suppress the spread of the virus and to develop effective strategies for controlling and preventing outbreaks, ultimately protecting public health and minimizing the impact of the disease.

Lumpy skin disease is a viral disease that affects cattle and is caused by the lumpy skin disease virus. This work is devoted to presenting and analyzing the nonlinear dynamics of a novel discrete fractional model for lumpy skin disease. The equilibrium points of the proposed discrete fractional model are found. The stability analysis of equilibrium points is carried out. The influences of key parameters in the model are investigated, and then the stability regions of a disease-free steady state in the space of parameters are obtained. A proposed efficient control scheme is implemented to stabilize the disease-free equilibrium point when it is unstable. The influences of fractional-order parameters on the applied control scheme are explored. Finally, numerical simulations are performed to verify the theoretical findings obtained and confirm the effectiveness of the employed control scheme.

In this paper, a novel fractional-order monkeypox epidemic model is introduced, where fractional-order derivatives in the sense of Caputo are applied to achieve more realistic results for the proposed nonlinear model. The newly developed model, which models the transmission and spread of monkeypox across the interacting populations of humans and rodents, is controlled by a 14-dimensional system of fractional-order differential equations. To comply with empirical and reported observations, the state variables of the proposed model are categorized into three main groups of state variables: the population who are at high risk of being infected, people with low infection probability, and finally, rodents who can carry and transmit the virus. The high-risk group represents individuals who might be more vulnerable to the virus due to their habits, workplace, or hygienic behaviors. The existence, uniqueness, non-negativity, and boundedness of the solution to the proposed model are proved. The next-generation matrix approach is used to determine the control monkeypox reproduction number, R0, and the equilibrium points for the proposed model are obtained. The effect of the main parameters in the model is thoroughly investigated to provide new insight into the new dynamics of the model. The region of stability of the disease-free points (DFE) is obtained in the space of parameters, and the effect of the parameters is examined. In addition, the optimal control strategy is applied to the model to provide insight into some prevention control to stop the disease from spreading and to provide new control strategies during the monkeypox outbreak. Numerical simulations are performed to validate the theoretical results of the different optimal control strategies.

In this research paper, we investigate the numerical solutions of the nonlinear complex Layla and Majnun fractional mathematical model, which describes the emotional behavior of two lovers. The fractional model is defined using the Liouville-Caputo derivative. The model is solved using a spectral collocation matrix method and a quasilinearization method with the aid of Schröder polynomials as basis functions. The existence of solutions for the model is investigated to ensure a unique solution, and a stability analysis is performed to highlight the stability regions ensuring stable solutions. In addition, the convergence analysis and error bound for the main model are illustrated in detail, and the theoretical findings are verified by several examples. The acquired results prove the ability of the proposed technique to find accurate solutions and to capture the effect of heredity of the fractional order model. The proposed techniques are proven to be effective in providing accurate solutions and can be extended to simulate similar complex problems.

Graph theory is a powerful and essential tool for applied scientists and engineers in analyzing and designing algorithms for several problems. Graph theory has a vital role in complex systems, especially in computer sciences. Applications of graph theory can be found in many scientific disciplines such as operational research, engineering, life sciences, management sciences, coding, and computer science. In the literature, there are two algorithms for constructing decompositions for the circulant graphs C2r,r with 2r vertices and r degree. For r,m⩾2, a circulant-balanced complete multipartite graph Cmr,(m-1)r is a generalization to C2r,r. Here, the major contributions are the generalization of the algorithms used for constructing the decompositions for the circulant graphs C2r,r to generalized algorithms that can be used for the decomposition of Cmr,(m-1)r that have mr vertices and (m-1)r degree. These generalized algorithms manage us to decompose the circulant graphs Cmr,(m-1)r by different graph classes. The paper's novelty is demonstrated by the fact that it is the first to suggest general approaches for decomposing circulant-balanced complete multipartite graphs. The constructed results in the present paper are suitable for generating different codes and also have great importance in the design of experiments.

Many structural models in chemistry, biology, computer science, sociology, and operations research can be analyzed using graph theory. Some examples of these structure models are species movement between regions, molecular bonds, shortest spanning trees, development of computer algorithms. This paper introduces the edge decomposition of circulant graphs with 2n vertices by different graph classes. These circulant graphs are denoted as C2n,n, where n is the degree of the graph C2n,n. We propose two algorithmic approaches for constructing edge decomposition of C2n,n. With aid of the proposed algorithmic approaches, we construct paths decompositions, trees decompositions, disjoint unions of cycles and trees decompositions, and complete bipartite graphs decompositions of C2n,n. In the end, a recursive construction of an edge decomposition, based on orthogonal edge decompositions, is proposed. This helps in using the mutually orthogonal decompositions of the circulant graphs C2n,n in several applications, such as the design of experiments and binary codes generation.

For over a hundred years, the model of prey–predator has been handled extensively. It has been proved that Lotka–Volterra (LV) models are not stable from all previous studies. In these models, there is divergent extinction of one species or cyclic oscillation. There is no solution for asymptotic stability for the prey–predator models. In this paper, a Caputo fractional-order one prey-two predators’ model with an immigration effect is investigated. Then, the effect of adding a small immigration term to the prey or predators’ populations is studied. The extension is both the inclusion of a second predator and the use of Caputo derivatives. Although LV systems have been extensively investigated, there are no previous studies on our proposed nonlinear modifications. The Grünwald–Letnikov method was applied to find numerical solutions for the proposed model to validate our findings. Several different cases were studied to reach confirmed conclusions. The effect of the variation of fractional-order derivative is handled in this study. From all the results, the effect of adding the small immigration terms is positive for stability. Hence, it can be concluded that the proposed small immigration terms can stabilize the natural populations of the one prey-two predators’ model. An optimal control strategy for the proposed model is shown at the end of the paper.

Security of personal information has become a major concern due to the increasing use of the Internet by individuals in the digital world. The main purpose here is to prevent an unauthorized person from gaining access to confidential information. The solution to such a problem is by authentication of users. Authentication has a very important role in achieving security. Mutually orthogonal graph squares (MOGS) are considered the generalization of mutually orthogonal Latin squares (MOLS). Also, MOGS are generated from edge decompositions of complete bipartite graphs by isomorphic graphs. Graph-orthogonal arrays can be constructed by MOGS. In this paper, graph-orthogonal arrays are used for constructing authentication codes. These arrays are the encoding matrices of authentication tags. We introduce the concepts and basic theorems of MOGS, graph-orthogonal arrays, and authentication codes. After constructing graph-orthogonal arrays by MOGS, then there is an established mapping between graph-orthogonal arrays and message set. This manages us to construct perfect non-splitting and splitting Cartesian authentication codes. In both cases, we calculate the probabilities of successful impersonation attacks and substitution attacks. Besides that, the performance of constructed non-splitting and splitting authentication codes is analyzed. In the end, optimal authentication codes and secure authentication codes are constructed.

Partial balanced incomplete block designs have a wide range of applications in many areas. Such designs provide advantages over fully balanced incomplete block designs as they allow for designs with a low number of blocks and different associations. This paper introduces a class of partially balanced incomplete designs. We call it partially balanced network designs (PBNDs). The fundamentals and properties of PBNDs are studied. We are concerned with modeling PBNDs as graph designs. Some direct constructions of small PBNDs and generalized PBNDs are introduced. Besides that, we show that our modeling yields an effective utilization of PNBDs in constructing graph codes. Here, we are interested in constructing graph codes from bipartite graphs. We have proved that these codes have good characteristics for error detection and correction. In the end, the paper introduces a novel technique for generating new codes from already constructed codes. This technique results in increasing the ability to correct errors.

The subject of mutually orthogonal Latin squares (MOLSs) has fascinated researchers for many years. Although there is a number of intriguing results in this area, many open problems remain to which the answers seem as elusive as ever. Mutually orthogonal graph squares (MOGSs) are considered a generalization to MOLS. MOLS are considered an area of combinatorial design theory which has many applications in optical communications, cryptography, storage system design, wireless communications, communication protocols, and algorithm design and analysis, to mention just a few areas. In this paper, we introduce a technique for constructing the mutually orthogonal disjoint union of graphs squares and the generalization of the Kronecker product of MOGS as a generalization to the MacNeish’s Kronecker product of MOLS. These are useful for constructing many new results concerned with the MOGS.

In this study, we generalize the Lotka-Volterra (LV) model. Our generalization is done via two simultaneous techniques. The first technique is done by incorporating a general term to model the immigrations to the predator or prey populace. The second technique is to utilize the Caputo fractional derivative. This study is done via different five cases. We show the impact of changing the fractional order to the proposed model response. We display that including a generalized immigration to the predator or prey populace produces stabilization of the LV model in context of Caputo fractional derivatives in all executed cases. In addition, we present the generalized model via graph and utilizing the graph theory concepts, we display several hidden features of the model.

Sets of mutually orthogonal Latin squares prescribe the order in which to apply different treatments in designing an experiment to permit effective statistical analysis of results, they encode the incidence structure of finite geometries, they encapsulate the structure of finite groups and more general algebraic objects known as quasigroups, and they produce optimal density error-correcting codes. This paper gives some new results on mutually orthogonal graph squares. Mutually orthogonal graph squares generalize orthogonal Latin squares interestingly. Mutually orthogonal graph squares are an area of combinatorial design theory that has many applications in optical communications, wireless communications, cryptography, storage system design, algorithm design and analysis, and communication protocols, to mention just a few areas. In this paper, novel product techniques of mutually orthogonal graph squares are considered. Proposed product techniques are the half-starters’ vectors Cartesian product, half-starters’ function product, and tensor product of graphs. It is shown that by taking mutually orthogonal subgraphs of complete bipartite graphs, one can obtain enough mutually orthogonal subgraphs in some larger complete bipartite graphs. Also, we try to find the minimum number of mutually orthogonal subgraphs for certain graphs based on the proposed product techniques. As a direct application to the proposed different product techniques, mutually orthogonal graph squares for disjoint unions of stars are constructed. All the constructed results in this paper can be used to generate new graph-orthogonal arrays and new authentication codes.

In this paper, DSEK model with fractional derivatives of the Atangana-Baleanu Caputo (ABC) is proposed. This paper gives a brief overview of the ABC fractional derivative and its attributes. Fixed point theory has been used to establish the uniqueness and existence of solutions for the fractional DSEK model. According to this theory, we will define two operators based on Lipschitzian and prove that they are contraction mapping and relatively compact. Ulam-Hyers stability theorem is implemented to prove the fractional DSEK model’s stability in Banach space. Also, fractional Euler’s numerical method is derived for initial value problems with ABC fractional derivative and implemented on fractional DSEK model. The symmetric properties contribute to determining the appropriate method for finding the correct solution to fractional differential equations. The numerical solutions generated using fractional Euler’s method have been plotted for different values of α where α∈0,1 and different step sizes h. Result discussion will be given, describing the changes that occur due to the step size h.

Combinatorial designs have many interesting and genuine wide applications in areas including analysis and design of algorithms, cryptography, analysis and design of experiments, storage system design, tournament scheduling, optical communications, and computer networks to mention just a few areas. In this paper, we are concerned with the transversal designs and authentication codes as direct applications of combinatorial designs. The novelty of the current paper is demonstrated by the fact that it is the first to introduce the transversal designs and authentication codes by the mutually orthogonal graph squares (MOGS); we call them graph-transversal designs and graph-authentication codes, respectively. Here, the major contributions are the constructions of graph-transversal designs and graph-authentication codes based on several classes of graphs. Also, we present several results such as path-transversal designs, cycle-transversal designs, and disjoint unions of stars-transversal designs.

For applied scientists and engineers, graph theory is a strong and vital tool for evaluating and inventing solutions for a variety of issues. Graph theory is extremely important in complex systems, particularly in computer science. Many scientific areas use graph theory, including biological sciences, engineering, coding, and operational research. A strategy for the orthogonal labelling of a bipartite graph G with n edges has been proposed in the literature, yielding cyclic decompositions of balanced complete bipartite graphs Kn,n by the graph G. A generalization to circulant-balanced complete multipartite graphs Kn,n,⋯,n⏟m;m,n≥2, is our objective here. In this paper, we expand the orthogonal labelling approach used to generate cyclic decompositions for Kn,n to a generalized orthogonal labelling approach that may be used for decomposing Kn,n,⋯,n⏟m. We can decompose Kn,n,⋯,n⏟m into distinct graph classes based on the proposed generalized orthogonal labelling approach.

The victim-predator model has been investigated in several papers in the literature since it is considered one of the very important models. The relation between predator and victim is an important aspect of ecology. The principal object of this research is to propose a new Caputo fractional one victim-two predators model with variable parameters. In addition, we study its stability and prove the existence and uniqueness of its solution. We calculate its approximate solution using Laplace transform coupled with the Adomian Decomposition Method (ADM) in two cases. Also, in order to complete the study of the proposed paradigm, we simulate and show its fractional dynamics plus the effect of changing certain parameters on its fractional dynamics against various fractional orders.

In this paper, the notions of fuzzy F∗-simply connected spaces and fuzzy F∗-structure homeomorphisms are introduced, and further fuzzy F∗-structure homeomorphism between fuzzy F∗-path-connected spaces are studied. Also, it is shown that every fuzzy F∗-structure subspace of fuzzy F∗-simply connected space is fuzzy F∗-simply connected subspace. Further, the concepts of fuzzy F∗-contractible spaces and fuzzy F∗-retracts are introduced, and it is proved that every fuzzy F∗-contractible space is fuzzy F∗-simply connected.

Graph theory is considered an attractive field for finding the proof techniques in discrete mathematics. The results of graph theory have applications in many areas of social, computing, and natural sciences. Graph labelings and decompositions have received much attention in the literature. Several types of graph labeling were proposed for solving the problem of decomposing different graph classes. In the present paper, we propose a technique for labeling the vertices of a bipartite graph G with n edges, called orthogonal labeling, to yield cyclic decompositions of balanced complete bipartite graphs Kn,n by the graph G. By applying the proposed orthogonal labeling technique, we had constructed decompositions of Kn,n by paths, trees, one factorization, disjoint union of cycles, complete bipartite graphs, disjoint union of trees, caterpillars, and so forth. From the constructed results, we can confirm that the proposed orthogonal labeling technique is effective.

This paper is devoted to the model of Lassa hemorrhagic fever (LHF) disease in pregnant women. This disease is a biocidal fever and epidemic. LHF disease in pregnant women has negative impacts that were initially appeared in Africa. In the present study, we find an approximate solution to the fractional-order model that describes the fatal LHF disease. Laplace transforms coupled with the Adomian decomposition method (ADM) are applied. In addition, the fractional-order LHF model is numerically simulated in terms of a varied fractional order. Furthermore, a fractional order optimal control for the LHF model is studied.

In this article, a technique to construct cyclic orthogonal double covers (CODCs) of regular circulant graphs by certain infinite graph classes such as complete bipartite and tripartite graphs and disjoint union of butterfly and is introduced.

During the last two centuries, after the question asked by Euler concerning mutually orthogonal Latin squares (MOLS), essential advances have been made. MOLS are considered as a construction tool for orthogonal arrays. Although Latin squares have numerous helpful properties, for some factual applications these structures are excessively prohibitive. The more general concepts of graph squares and mutually orthogonal graph squares (MOGS) offer more flexibility. MOGS generalize MOLS in an interesting way. As such, the topic is attractive. Orthogonal arrays are essential in statistics and are related to finite fields, geometry, combinatorics and error-correcting codes. Furthermore, they are used in cryptography and computer science. In this paper, our current efforts have concentrated on the definition of the graph-orthogonal arrays and on proving that if there are k MOGS of order n, then there is a graph-orthogonal array, and we denote this array by G-OA(n2,k,n,2). In addition, several new results for the orthogonal arrays obtained from the MOGS are given. Furthermore, we introduce a recursive construction method for constructing the graph-orthogonal arrays.

In this paper, we generalize the orthogonal double covers (ODC) of Kn,n as follows. The circular intensely orthogonal double cover design (CIODCD) of X=Kn,n,…,n︸m is defined as a collection T={G00,G10,…,G(n−1)0}∪{G01,G11,…,G(n−1)1} of isomorphic spanning subgraphs of X such that every edge of X appears twice in the collection T,E(Gi0)∩E(Gj0)=E(Gi1)∩E(Gj1)=0,i≠jand E(Gi0)∩E(Gj1)=λ=m2,i,j∈ℤn. We define the half starters and the symmetric starters matrices as constructing methods for the CIODCD of X. Then, we introduce some results as a direct application to the construction of CIODCD of X by the symmetric starters matrices.

An orthogonal double cover (ODC) of a graph H is a collection G={Gv:v∈V(H)} of |V(H)| subgraphs of H such that every edge of H is contained in exactly two members of G and for any two members Gu and Gv in G, |E(Gu)∩E(Gv)| is 1 if u and v are adjacent in H and it is 0 if u and v are nonadjacent in H. In this paper, we are concerned with the Cartesian product of symmetric starter vectors of orthogonal double covers of the complete bipartite graphs and using this method to construct ODCs for new graph classes.