In the present paper, SIR model with nonlinear recovery and Monod type equation as incidence rates is proposed analyzed. The expression for basic reproduction number obtained which plays a main role in stability of disease-free endemic equilibria. nonstandard finite difference (NSFD) scheme constructed denominator function chosen such that suggested ensures solutions boundedness. It shown NSFD ...

PROTOSOLID is a solid modeler that represents solids with planar surfaces and manipulates the solids with regularized set operations. This paper looks at the internal structures and operations of PROTOSOLID and is intended as a programmer user guide. A boundary of a solid is represented by a/edge-based data structure. It is developed in ComrnonLisp. IThill work hILS been supported in part by an...

Fuzziness or uncertainties arise due to insufficient knowledge, experimental errors, operating conditions and parameters that provide inaccurate information. The concepts of susceptible, infectious recovered are uncertain the different degrees in susceptibility, infectivity recovery among individuals population. differences can arise, when population groups under consideration having distinct h...

Abstract— The aim of this work is to construct high-order numerical schemes that preserve the dynamical properties a mathematical model describing spread computer viruses on Internet. For purpose, we first apply Mickens’ methodology formulate dynamically consistent nonstandard finite difference (NSFD) scheme for under consid­eration. After that, constructed NSFD combined with Richardson’s extra...

In this work, a novel second-order nonstandard finite difference (NSFD) method that preserves simultaneously the positivity and local asymptotic stability of one-dimensional autonomous dynamical systems is introduced analyzed. This based on non-local approximations for right-hand side functions differential equations in combination with denominator functions. The obtained results not only resol...

In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solution of the model in fractional order is presented. Then the local stability analysis of the model in fractional order is discussed. Finally, the general solutions are presented an...

This paper is concerned with the construction and developing of several nonstandard finite difference (NSFD) schemes in matrix form in order to obtain numerical solutions of epidemic models. In particular, we deal with a classical SIR epidemic model and a seasonal model associated with the evolution of the transmission of respiratory syncytial virus RSV in the human population. The first model ...

In this paper, the Black–Scholes equation is solved using a new technique. This scheme derived by combining Laplace transform method and nonstandard finite difference (NSFD) strategy. The qualitative properties of are discussed, it shown that positive, stable, consistent when low volatility assumed. efficiency demonstrated numerical example.

Nowadays, numerical models have great importance in every field of science, especially for solving the nonlinear differential equations, partial differential equations, biochemical reactions, etc. The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by the Runge-Kutta of order four (RK4) and by nonstandard finite difference (NSFD) method. A...

The main aim of this contribution is to construct a numerical scheme for solving stochastic time-dependent partial differential equations (PDEs). This has the advantage problems with positive solutions. provides conditions obtaining solutions, which existing Euler–Maruyama method cannot do. In addition, it more accurate than non-standard finite difference (NSFD) method. Theoretically, suggested...