Vol. 9, No. 2 (2020): Regular Issue

Vineyard replacement is a common practice in every wine-growing farm since the grapevine production decays over time and requires a new vine to ensure the business sustainability. In this paper, we formulate a simple discrete model that captures the vineyard’s main dynamics such as production values and grape quality. Then, by applying binary non-linear programming methods to find the vineyard replacement trigger, we seek the optimal solution concerning different governmental subsidies to the target producer.

Computer viruses are a serious threat to the general society, due to their implications for private life and corporative systems. This paper begins to briefly illustrate the dynamics of computer viruses within a network system, by taking advantage of the EpiModel R package and using a SIR (Susceptible–Infected–Recovered) epidemic model. However, since devices are not constantly immune to cyberattacks, a SIRS model with an optimal control application is proposed to minimize the levels of infections caused by malicious objects. Additionally, real numerical data related to the number of reported cybercrimes in Japan from 2012 to 2017 are considered. The existence and uniqueness of an optimal control for the proposed control problem are proved. Under proper investment costs, numerical simulations in Matlab show the effectiveness of the proposed control strategy in increasing the rate of immunity and decreasing the chances of re–susceptibility to cyberattacks.

Themain contribution of this paper consists of introducing a novelmodel of three-dimensional reconstruction from multiple two-dimensional images. Actually, our proposedmodel presents the followingmain advantages; first, we improve the original region fitting energy in the general region-based level set method by an anisotropic diffusion to evolve the contour. Second, we use the Dijkstra algorithm to improve and allow simple and free initializations. Third, we adopt the domain decomposition method to reduce the computational cost for high-resolution images. Finally, in order to prove the efficiency and accuracy of our proposed method, experiments were performed on synthetic and real images.

In this paper, we propose a generalized reaction-diffusion epidemic model with time delay. The proposed model is governed by partial differential equations (PDEs). The global existence, positivity and boundedness of solutions are obtained. By analyzing the corresponding characteristic equation and constructing appropriate Lyapunov functionals, the local/global stability of homogeneous steady states are investigated. Finally, an application of our analytical results is given.

In the present work we study a predator-prey harvesting model with Monod-Haldane functional response. The mathematical features of the model have been analyzed in terms of stability, bifurcations and harvesting. Threshold values for some parameters indicating the feasibility and stability conditions of all equilibria are determined. The range of significant parameters under which the system admits different types of bifurcations are investigated. Optimal harvesting criteria and the net economic revenue are analyzed. Numerical illustrations are performed finally in order to confirm the analytical findings.

In this paper, we are focused upon the results on existence, uniqueness and stability of mild solution of impulsive stochastic partial neutral functional differential equations with infinite delays and poisson jumps. The results are obtained by using the method of successive approximation and Bihari’s inequality.

The aim of this paper is to investigate, the characterizations of different classes of non-associative and non-commutative ordered semigroups in terms of intuitionistic fuzzy left (right, bi-, generalized bi-, (1,2)-) ideals.

In this paper we prove the existence of solutions of fractional neutral integrodifferential equations with deviating arguments by using the resolvent operators and fixed point theorem. Examples are discussed to illustrate the theory.

The theoretical model of uncolonised by antagonist, colonised by the antagonist and infected by ther pathogen in the biological control has been discussed. In this article, we present the non-steady state solutions for biological control. The simple analytical expressions of the dimensionless concentrations are derived for non-linear boundary value problem using the variational iteration method. Numerical solutions are obtained and the results are discussed graphically. We also compared our analytical results with numerical simulation, it gives a satisfactory agreement is noted.

For driven time dependent harmonic oscillator a detailed and systematic study of several methods for the building of Integrals is carried out. The central feature of the present discussion is the establishment of Integrals for the dynamical system. In spite of their different procedural details all the approaches lead to the same invariant for the given classical system. Advantage and limitations of different methods are briefly highlighted.

This paper formulates and analyzes a predator-prey model with disease in the prey. Mathematical analysis of the model system concerns the existence, uniqueness and uniform boundedness of solutions in the positive octant. The threshold condition for epidemic and the conditions for persistence are obtained. Moreover, the system is analyzed for local stability, global stability around several equilibria. Hopf-bifurcation with its nature and the stability of the bifurcating limit cycle are studied around the disease free equilibrium point. Numerical simulations are performed to justify the analytical findings. Eco-epidemilogical significance and implications of the concluded results are discussed as well.

This article presents the result on existence, uniqueness and stability of mild solution of impulsive stochastic partial neutral functional differential equations driven by a fractional Brownian motion. The results are obtained by using the method of successive approximation and Bihari’s inequality.