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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.

Experimental investigations on gamma - rays attenuation parameters and dielectric spectroscopic properties were done on a polymeric mixture with chemical composition (100-x) polyethylene + x basalt, where x = 0, 1, 3, 5, 10, and 20 wt%. Using the melting blending technique,six nanocomposite polymeric samples were prepared. The linear attenuation coefficient μ of each prepared set of samples was measured using a gamma-ray spectrometer including High Purity Germanium detector (HPGe) at energies 662.5, 1173.24, and 1332.51 keV. Based on the measured values of (μ) and sample density, the other effective shielding parameters were calculated. the values of μ showed an increase with increasing the dopant ratios from 0.0 up to 20.0 wt%. In addition, the μ values decreased with the photon's energy. The μ values were found 0.0847 up to 0.1175 cm−1, 0.0571 up to 0.0855 cm−1, and 0.0543 up to 0.075 cm−1 at 662.5, 1173.24, and 1332.51 keV. for B0 up to B20, respectively. The ATR spectroscopy was done on the prepared samples, and a good evidence of adding the filler to the pure polyethylene (HDPE) was obtained. Besides, an enhancement in dielectric constant by insertion of basalt NPs also recorded and can be attributed to the large dielectric constant of basalt compared to pure HDPE.

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.

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.

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.

Oxyfluoride glasses of compositions 50 LiF-x P2O5-(50-x) B2O3 (all in mol%) with the value of x = 0, 5, 10, and 50 mol% were prepared and labeled as LFPB0, LFPB40, LFPB45, and LFPB50, respectively. Physical, luminescence, and ionizing radiation shielding properties of lithium borate glasses have been investigated. The highest TL response was obtained at reducing the percentage of P2O5 to 5 mol%. The mass attenuation coefficient was calculated using theoretical software program Phy-x/PSD. The highest MAC values were recorded to LFPB0 glasses. It was found that the linear attenuation coefficient LAC values (14.429 cm−1, 0.051 cm−1), (7.178 cm−1, 0.046 cm−1), (5.672 cm−1, 0.045 cm−1) and (3.934 cm−1, 0.044 cm−1) at 0.015 and 15 MeV for LFPB0, LFPB40, LFPB45, and LFPB50, respectively. LFPB glasses took the following order from the mean free path point of view; LFPB0