Showing papers in "Journal of Applied Mathematics and Computing in 2021"

Impact of social media advertisements on the transmission dynamics of COVID-19 pandemic in India.

Abstract: In this paper, we propose a mathematical model to assess the impact of social media advertisements in combating the coronavirus pandemic in India. We assume that dissemination of awareness among susceptible individuals modifies public attitudes and behaviours towards this contagious disease which results in reducing the chance of contact with the coronavirus and hence decreasing the disease transmission. Moreover, the individual's behavioral response in the presence of global information campaigns accelerate the rate of hospitalization of symptomatic individuals and also encourage the asymptomatic individuals for conducting health protocols, such as self-isolation, social distancing, etc. We calibrate the proposed model with the cumulative confirmed COVID-19 cases for the Republic of India. We estimate eight epidemiologically important parameters, and also the size of basic reproduction number for India. We find that the basic reproduction number for India is greater than unity, which represents the substantial outbreak of COVID-19 in the country. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected population. Our results reveal that to reduce disease burden in India, non-pharmaceutical interventions strategies should be implemented effectively to decrease basic reproduction number below unity. Continuous propagation of awareness through the internet and social media platforms should be regularly circulated by the health authorities/government officials for hospitalization of symptomatic individuals and quarantine of asymptomatic individuals to control the prevalence of disease in India.

On relations between Sombor and other degree-based indices

Abstract: Recently, a novel topological invariant based on degrees of end-vertices of an edge in a graph was put forward. It was named Sombor index. The definition of the Sombor invariant suggests another, rather a geometric view onto graph edges. Here, the mathematical relations between the Sombor index and some other well-known degree-based descriptors are investigated. Then, a few results of Nordhaus–Gaddum-type are obtained. Finally, computational testing and comparison with other well-established indices are presented.

Mathematical modeling of COVID-19 spreading with asymptomatic infected and interacting peoples.

Abstract: In this article we propose a modified compartmental model describing the transmission of COVID-19 in Morocco. It takes account on the asymptomatic people and the strategies involving hospital isolation of the confirmed infected person, quarantine of people contacting them, and home containment of all population to restrict mobility. We establish a relationship between the containment control coefficient $$c_0$$ and the basic reproduction number $${\mathscr {R}}_0$$ . Different scenarios are tested with different values of $$c_0$$ , for which the stability of a Disease Free Equilibrium point is correlated with the condition linking $${\mathscr {R}}_0$$ and $$c_0$$ . A worst scenario in which the containment is not respected in the same way during the period of confinement leads to several rebound in the evolution of the pandemic. It is shown that home containment, if it is strictly respected, played a crucial role in controlling the disease spreading.

Decision-making analysis based on q-rung picture fuzzy graph structures

Abstract: In this research article, we introduce the notion of q-rung picture fuzzy graph structures (q-RPFGSs). Further, we present the concepts of $$S_{i}$$ -strongly regular q-RPFGSs and $$S_{i}$$ -uniform q-RPFGSs. We study $$S_{i}$$ -bipartite q-RPFGSs and $$S_{i}$$ -r-partite q-RPFGSs and investigate some useful results of their $$S_{i}$$ -regularity. In addition, we discuss drug trafficking in particular region by using complete 6-partite 15-RPFGS. Moreover, power and economy based dominating relationships of developed countries with rich, progressing and underdeveloped countries are represented by a 4-partite 12-RPFGS. Finally, we describe general procedures of our proposed models by algorithms.

The locating number of hexagonal Möbius ladder network

Abstract: Due to the immense applications of interconnection networks, various new networks are designed and extensively used in computer sciences and engineering fields. Networks can be expressed in the form of graphs, where node become vertex and links between nodes are called edges. To obtain the exact location of a specific node which is unique from all the nodes, several nodes are selected this is called locating/resolving set. Minimum number of nodes in the locating set is called locating number. In this article, we find the exact value of locating number of newly designed hexagonal Mobius ladder network.

Controllability results for fractional semilinear delay control systems

Abstract: In this article, we have presented the controllability relationship between the semilinear control system of fractional order (1, 2] with delay and that of the semilinear control system without delay. Suppose X and U be Hilbert spaces which are separable and $$Z=L_2[0,b;X],\;Z_h=L_2[-h,b;X],\;0\le h\le b$$ and $$Y=L_2[0,b;U]$$ be the function spaces. Let the semilinear control system of fractional order with delay as $$\begin{aligned} ^CD_\tau ^\alpha z(\tau )= & {} Az(\tau )+Bv(\tau )+g(\tau ,z(\tau -h)),\;0\le \tau \le b;\\ z_0(\theta )= & {} \phi (\theta ),\;\;\;\; \theta \in [-h,0]\\ z'(0)= & {} z_0. \end{aligned}$$ where $$1<\alpha \le 2$$ , fractional Caputo derivative is denoted as $$^CD_{\tau }^\alpha $$ , time constant b is positive and finite. $$A:D(A)\subseteq X\rightarrow X$$ is a operator which is linear and closed having densed domain X and A is the infinitesimal generator of solution operator $$\{C_\alpha (\tau )\}_{\tau \ge 0}$$ . The control function is denoted by $$v(\tau )$$ and defined as $$v:[0,b]\rightarrow U$$ . The continuous state variable $$z(\tau )\in Z$$ , $$\phi \in L_2[-h,0;X]$$ . The operator $$B:Y\rightarrow Z$$ is linear and bounded. The function $$g:[0,b]\times X\rightarrow V$$ is purely nonlinear and satisfies Lipschitz continuity. We assumed that the fractional semilinear system without delay is approximate/exact controllable and by imposing some conditions on the range of the nonlinear term, we obtained the controllability results of the fractional semilinear system with delay. Approximate controllability of proposed problem is discussed under three different sets of assumptions. Exact controllability of proposed problem is also discussed. Finally an example is given to understand the theoretical results in better manner.

$${\pmb {{\mathbb {Z}}}}_p{\pmb {{\mathbb {Z}}}}_p[v]$$ Z p Z p [ v ] -additive cyclic codes are asymptotically good

Abstract: We construct a class of $${\mathbb {Z}}_p{\mathbb {Z}}_p[v]$$ -additive cyclic codes, where p is a prime number and $$v^2=v$$ . We determine the asymptotic properties of the relative minimum distance and rate of this class of codes. We prove that, for any positive real number $$0<\delta <1$$ such that the p-ary entropy at $$\frac{k+l}{2}\delta $$ is less than $$\frac{1}{2}$$ , the relative minimum distance of the random code is convergent to $$\delta $$ and the rate of the random code is convergent to $$\frac{1}{k+l}$$ , where p, k, l are pairwise coprime positive integers.

Stationary distribution and extinction of a multi-stage HIV model with nonlinear stochastic perturbation

Abstract: In this paper, we investigate a stochastic multi-stage model to evaluate the influence of treatment intensification with the integrase inhibitor raltegravir on viral load and 2-LTR dynamics in HIV patients under suppressive therapy. Firstly, it is proven that the model has a unique global positive solution. Secondly, by constructing a Lyapunov function, we establish sufficient conditions for the existence of a unique ergodic stationary distribution if $$R_{0}^{S}>1$$ . Thirdly, we obtain sufficient criterions $$R_{0}^{s}<1$$ for disease extinction. Finally, the analytical results are demonstrated via two simulation examples. Our contribution also concentrates on proposing a method constructing Lyapunov function, which can be successfully used for the research about stationary distribution of epidemic model with nonlinear stochastic perturbation.

Fractional methicillin-resistant Staphylococcus aureus infection model under Caputo operator.

Abstract: This study provides a detailed exposition of in-hospital community-acquired methicillin-resistant S. aureus (CA-MRSA) which is a new strain of MRSA, and hospital-acquired methicillin-resistant S. aureus (HA-MRSA) employing Caputo fractional operator. These two strains of MRSA, referred to as staph, have been a serious problem in hospitals and it is known that they give rise to more deaths per year than AIDS. Hence, the transmission dynamics determining whether the CA-MRSA overtakes HA-MRSA is analyzed by means of a non-local fractional derivative. We show the existence and uniqueness of the solutions of the fractional staph infection model through fixed-point theorems. Moreover, stability analysis and iterative solutions are furnished by the recursive procedure. We make use of the parameter values obtained from the Beth Israel Deaconess Medical Center. Analysis of the model under investigation shows that the disease-free equilibrium existing for all parameters is globally asymptotically stable when both $${\mathscr {R}}_0^H$$ and $${\mathscr {R}}_0^C$$ are less than one. We also carry out the sensitivity analysis to identify the most sensitive parameters for controlling the spread of the infection. Additionally, the solution for the above-mentioned model is obtained by the Laplace-Adomian decomposition method and various simulations are performed by using convenient fractional-order $$\alpha $$ .

Convergence of $$\lambda $$ λ -Bernstein operators via power series summability method

Abstract: In this paper we present uniform convergence of a sequence of $$\lambda $$ -Bernstein operators via A-statistical convergence and power summability method. A rate of convergence of the sequence of operators are also investigated by means of above mentioned summability methods. The last section is devoted to pointwise convergence (A-statistical convergence) of the sequence of operators in terms of Voronovskaya and Gru ss–Voronovskaya type theorems.

New results on symmetric division deg index

Abstract: The symmetric division deg index (or simply sdd-index) was proposed by Vukicevic et al as a remarkable predictor of total surface area of polychlorobiphenyls It is one of discrete Adriatic indices that showed good predictive properties on the testing sets provided by International Academy of Mathematical Chemistry In this paper, we investigate some properties of this graph invariant in terms of orbit structure of a graph and then we explore new bounds for sdd-index In continuing, the inverse symmetric division deg index is defined and new results concerning these two graph indices are stablished Finally, some bounds for both indices are presented

Generalized neutrosophic planar graphs and its application

Abstract: In the existing definition of a neutrosophic planar graph, there is a limitation. In that definition, the value of falsity in degree of planarity is 1, even then the crisp underline graph is planar. This limitation is removed in the proposed definition. In this study, an advanced concept of the neutrosophic planar graphs is given and investigated the generalized neutrosophic planar graphs (GNPG). The score of planarity is calculated based on the true, falsity and indeterminacy values of degree of planarity to measure the overall planarity of a GNPG. And a few related properties are investigated. A real-life application is presented and solved by this concept of a GNPG.

Cacti with maximal general sum-connectivity index

Abstract: Let V(G) and E(G) be, respectively, the vertex set and edge set of a graph G. The general sum-connectivity index of a graph G is denoted by $$\chi _\alpha (G)$$ and is defined as $$\sum \limits _{uv\in E(G)}(d_u+d_v)^\alpha $$ , where uv is an edge that connect the vertices $$u,v\in V(G)$$ , $$d_u$$ is the degree of a vertex u and $$\alpha $$ is any non-zero real number. A cactus is a graph in which any two cycles have at most one common vertex. Let $$\mathscr {C}_{n,t}$$ denote the class of all cacti with order n and t pendant vertices. In this paper, a maximum general sum-connectivity index ( $$\chi _\alpha (G)$$ , $$\alpha >1$$ ) of a cacti graph with order n and t pendant vertices is considered. We determine the maximum general sum-connectivity index of n-vertex cacti graph. Based on our obtained results, we characterize the cactus with a perfect matching having the maximum general sum-connectivity index.

Exponential-sum-approximation technique for variable-order time-fractional diffusion equations

Abstract: In this paper, we study the variable-order (VO) time-fractional diffusion equations. For a VO function $$\alpha (t)\in (0,1)$$ , we develop an exponential-sum-approximation (ESA) technique to approach the VO Caputo fractional derivative. The ESA technique keeps both the quadrature exponents and the number of exponentials in the summation unchanged at different time level. Approximating parameters are properly selected to achieve the efficient accuracy. Compared with the general direct method, the proposed method reduces the storage requirement from $${\mathcal {O}}(n)$$ to $${\mathcal {O}}(\log ^2 n)$$ and the computational cost from $${\mathcal {O}}(n^2)$$ to $$\mathcal {O}(n\log ^2 n)$$ , respectively, with n being the number of the time levels. When this fast algorithm is exploited to construct a fast ESA scheme for the VO time-fractional diffusion equations, the computational complexity of the proposed scheme is only of $${\mathcal {O}}(mn\log ^2 n)$$ with $${\mathcal {O}}(m\log ^2n)$$ storage requirement, where m denotes the number of spatial grid points. Theoretically, the unconditional stability and error analysis of the fast ESA scheme are given. The effectiveness of the proposed algorithm is verified by numerical examples.

Bifurcations in a modified Leslie–Gower predator–prey discrete model with Michaelis–Menten prey harvesting

Abstract: In this paper, a modified Leslie–Gower predator–prey discrete model with Michaelis–Menten type prey harvesting is investigated. It is shown that the model exhibits several bifurcations of codimension 1 viz. Neimark–Sacker bifurcation, transcritical bifurcation and flip bifurcation on varying one parameter. Bifurcation theory and center manifold theory are used to establish the conditions for the existence of these bifurcations. Moreover, existence of Bogdanov–Takens bifurcation of codimension 2 (i.e. two parameters must be varied for the occurrence of bifurcation) is exhibited. The non-degeneracy conditions are determined for occurrence of Bogdanov–Takens bifurcation. The extensive numerical simulation is performed to demonstrate the analytical findings. The system exhibits periodic solutions including flip bifurcation and Neimark–Sacker bifurcation followed by the wide range of dense chaos.

Global asymptotic dynamics of a nonlinear illicit drug use system

Abstract: In this paper, a nonlinear mathematical model of illicit drug use in a population is studied using dynamical system theory. The work is largely concerned with the analysis of asymptotic behaviour of solutions to a six-dimensional system of differential equations modeling the influence of illicit drug use in the population. The model is mathematically well-posed based on positivity and boundedness of solutions. A key threshold which measures the potential spread of the illicit drug use in the population is derived analytically. The model is shown to exhibit forward bifurcation property, implying the existence, uniqueness and local stability of an illicit drug-present equilibrium. Furthermore, the global asymptotic dynamics of the model around the illicit drug-free and drug-present equilibria are extensively investigated using appropriate Lyapunov functions. Numerical simulations are carried out to complement the obtained theoretical results, and to examine the effects of some parameters, such as influence rate, rehabilitation rates of drug users and relapse rate, on the dynamical spread of illicit drug use in the population. Measures to guide against the menace of the illicit drug use are suggested.

Splitting preconditioning based on sine transform for time-dependent Riesz space fractional diffusion equations

Abstract: We study the sine-transform-based splitting preconditioning technique for the linear systems arising in the numerical discretization of time-dependent one dimensional and two dimensional Riesz space fractional diffusion equations. Those linear systems are Toeplitz-like. By making use of diagonal-plus-Toeplitz splitting iteration technique, a sine-transform-based splitting preconditioner is proposed to accelerate the convergence rate efficiently when the Krylov subspace method is implemented. Theoretically, we prove that the spectrum of the preconditioned matrix of the proposed method is clustering around 1. In practical computations, by the fast sine transform the computational complexity at each time level can be done in $${{\mathcal {O}}}(n\log n)$$ operations where n is the matrix size. Numerical examples are presented to illustrate the effectiveness of the proposed algorithm.

Approximation of fixed point and its application to fractional differential equation

Abstract: In this study, we prove some convergence results for generalized $$\alpha $$ -Reich–Suzuki non-expansive mappings via a fast iterative scheme. We validate our result by constructing a numerical example. Also, we compare our results with the other well known iterative schemes. Finally, we calculate the approximate solution of nonlinear fractional differential equation.

Some weighted statistical convergence and associated Korovkin and Voronovskaya type theorems

Abstract: In this paper, we propose to investigate a new weighted statistical convergence by applying the Norlund–Cesaro summability method. Based upon this definition, we prove some properties of statistically convergent sequences and a kind of the Korovkin type theorems. We also study the rate of the convergence for this kind of weighted statistical convergence and a Voronovskaya type theorem.

Randic index of bipolar fuzzy graphs and its application in network systems

Abstract: Connectivity can be used to measure the strength and combined power of a connected network system. Randic index of graph is one such parameter and it can measure the total combined power of a connected graphical transmission system. For two opposite sided opinion of vertices as well as edges in a bipolar fuzzy graph, it can measure the uncertainty of vertices and edges along positive and negative sides. In this article, the Randic index of bipolar fuzzy graph and bipolar fuzzy subgraph are introduced with their properties. The upper and lower boundaries of Randic index of bipolar fuzzy graphs are studied with some isomorphic properties. Randic index of directed bipolar fuzzy graphs are introduced. Several formula’s are presented to calculate the Randic index of different types of regular bipolar fuzzy graphs and bipolar fuzzy cycles. Finally, two real life applications of Randic index in bipolar fuzzy graphs are described.

Two sufficient descent three-term conjugate gradient methods for unconstrained optimization problems with applications in compressive sensing

Abstract: In this paper, we present two new three-term conjugate gradient methods which can generate sufficient descent directions for the large-scale optimization problems. Note that this property is independent of the line search used. We prove that these three-term conjugate gradient methods are global convergence under the Wolfe line search. Numerical experiments and comparisons demonstrate that the proposed algorithms are efficient approaches for test functions. Moreover, we use the proposed methods to solve the $$\ell _1-\alpha \ell _2$$ regularization problem of sparse signal decoding in compressed sensing, and the results show that our methods have certain advantages over the existing solvers on such problems.

Novel neighbourhood redefined first and second Zagreb indices on carborundum structures

Abstract: Graph theory offers experts with a useful tool called the topological index which analyses the characteristics of chemical compounds. Motivated by the recent work of redefined Zagreb indices ( $$ReZG_{1}$$ , $$ReZG_{2}$$ , $$ ReZG_{3}$$ ), novel topological indices such as Neighbourhood redefined first and second Zagreb indices ( $$NReZ_{1}$$ , $$NReZ_{2}$$ ) are proposed and computed for a molecular graph G of two carborundum structures. The correlation coefficient of $$NReZ_{1}$$ , $$NReZ_{2}$$ with ten properties of octane isomers are determined, of which entropy and acentric factor showed a good correlation. Also, the lower and upper bounds of redefined Zagreb indices are determined using classic results, Polya–Szego and Cauchy–Schwarz inequalities for simple graphs and trees.

Mathematical modeling of stagnation region nanofluid flow through Darcy–Forchheimer space taking into account inconsistent heat source/sink

Abstract: The primary target of present research is to examine the application of OHAM (optimal homotopy asymptotic method) for a nanofluid transport through Darcy Forchheimer space toward the stagnation region by comparing stretching and straining forces. The porous matrix is suspended with nanofluid, and the flow field is under inconsistent heat source/sink influence. The solutions of guiding boundary layer equations report that pattern of primary velocity profiles are inverted by stagnation region flow strength. Straightforward relation of Forchheimer number with heat transfer has also been observed when stagnation forces dominate stretching forces. The novelty of present article lies in vector form presentation to OHAM and in the comparative analysis of stretching and straining forces.

Adomian decomposition and homotopy perturbation method for the solution of time fractional partial integro-differential equations

Abstract: This article deals with two different methods to solve a time fractional partial integro-differential equation. The fractional derivatives are defined here in Caputo sense. The model problem is solved using the Adomian decomposition method and homotopy perturbation method. Moreover, this paper proves the convergence analysis of the solution based on the present methods. Numerical evidences are illustrated in support of the theoretical analysis.

A computational procedure for exact solutions of Burgers’ hierarchy of nonlinear partial differential equations

Abstract: This paper considers the exact solution of Burgers’ hierarchy of nonlinear evolution equations. We construct the general nth conservation law of the hierarchy and prove that these expressions may be transformed into ordinary differential equations. In particular, a coordinate transformation leads to the systematic reduction of the conservation law properties of the Burgers’ hierarchy. Such an approach yields a nonlinear equation, where a second transformation is derived to linearize the expression. Consequently, this approach describes a procedure for finding the exact solutions of the hierarchy. A formula of the nth solution is provided, and to demonstrate its application, we discuss the solution to several members of the nonlinear hierarchy.

On Connected Graphs Having the Maximum Connective Eccentricity Index

Abstract: The connective eccentricity index (CEI) of a connected graph G is defined as $$\xi ^{ee}(G)=\sum _{u\in V_G}[d_G(u)/\varepsilon _G(u)]$$ , where $$d_G(u)$$ and $$\varepsilon _G(u)$$ are the degree and eccentricity, respectively, of the vertex $$u\in V_G$$ of G. In this paper, graphs with the maximum CEI are characterized from the class of all connected graphs of a fixed order and size. Graphs having maximum CEI are also determined from some other well-known classes of connected graphs of a given order; namely, the Halin graphs, triangle-free graphs, planar graphs and outer-planar graphs.

Iterative regularization methods with new stepsize rules for solving variational inclusions

Abstract: The paper concerns with three iterative regularization methods for solving a variational inclusion problem of the sum of two operators, the one is maximally monotone and the another is monotone and Lipschitz continuous, in a Hilbert space. We first describe how to incorporate regularization terms in the methods of forward-backward types, and then establish the strong convergence of the resulting methods. With several new stepsize rules considered, the methods can work with or without knowing previously the Lipschitz constant of cost operator. Unlike known hybrid methods, the strong convergence of the proposed methods comes from the regularization technique. Several applications to signal recovery problems and optimal control problems together with numerical experiments are also presented in this paper. Our numerical results have illustrated the fast convergence and computational effectiveness of the new methods over known hybrid methods.

Relations on neutrosophic soft set and their application in decision making

Abstract: Neutrosophic soft sets are a mathematical model put forward to overcome uncertainty with the contribution of a parameterization tool and neutrosophic logic by considering of information a falsity membership function, an indeterminacy membership function and a truth membership function. This set theory which is a very successful mathematical model, especially as it handles information in three different aspects, was first introduced to the literature by Maji (Ann Fuzzy Math Inf 5(1):157–168, 2013) and later modified by Deli and Broumi (J Intell Fuzzy Syst 28(5):2233–2241, 2015). In this way, they aimed to use neutrosophic soft sets more effectively for uncertainty problems encountered in most real life problems. Relations are a method preferred by researchers to explain the correspondences between objects. In this paper, neutrosophic soft relationships are discuss and define by referring to the theory of neutrosophic soft set proposed by Deli and Broumi (Ann Fuzzy Math Inf 9:169–182, 2015). Then, we present the concepts of composition, inverse of neutrosophic soft relations and functions along with some related properties and theorems. Moreover, the equivalence classes and equivalence relations of soft relations are given with support from real life examples and some of their properties are analyzed. Finally, we propose an algorithm to be used in expressing the correspondence between objects in solving uncertainty problems by using the soft relationship defined and an example is given to show how this algorithm can be applied for uncertainty problems.

Bounded positive solutions of an iterative three-point boundary-value problem with integral boundary condtions

Abstract: The aim of this paper is to investigate the existence, uniqueness and continuous dependence of solutions for a class of third order iterative differential equations with integral boundary conditions. The method applied here is based on Schauder’s fixed point theorem. The main idea consists to convert the considered equation into an integral one before using the fixed point theorem. Moreover, an example is given to illustrate our main results.

On the existence of the solution of Hammerstein integral equations and fractional differential equations

Abstract: Nonlinear integral equations (particularly Hammerstein integral equations) and fractional differential equations have been the center of extensive research for various scientists because of their practical and physical significance In this article, our focus is to find the sufficient conditions for the existence of solutions of some class of Hammerstein integral equations and fractional differential equations For this purpose, we extend the notion of Kannan mappings in view of F-contraction in the setting of b-metric like spaces Moreover, to address conceptual depth within this approach, we supply series of innovative and nontrivial examples to illustrate the established results along with computer simulation, thereby propounding the concept in a quite novel way At the other end, some open problems are proposed for enthusiastic readers