The Mathematics of Infectious Diseases
SIAM Review
An unconditionally convergent discretization of the SEIR Model
Mathematics and Computers in Simulation
A competitive numerical method for a chemotherapy model of two HIV subtypes
Applied Mathematics and Computation
Nonstandard finite difference method by nonlocal approximation
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Mathematics and Computers in Simulation - Special issue: Nonlinear waves: computation and theory IV
Combined nonstandard numerical methods for ODEs with polynomial right-hand sides
Mathematics and Computers in Simulation - Special issue: Applied and computational mathematics - selected papers of the fifth PanAmerican workshop - June 21-25, 2004, Tegucigalpa, Honduras
Non-standard numerical method for a mathematical model of RSV epidemiological transmission
Computers & Mathematics with Applications
Nonstandard numerical methods for a mathematical model for influenza disease
Mathematics and Computers in Simulation
Numerical simulation of multi-species biofilms in porous media for different kinetics
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
Modeling the spread of seasonal epidemiological diseases: Theory and applications
Mathematical and Computer Modelling: An International Journal
Nonstandard discrete approximationspreserving stability properties of continuous mathematical models
Mathematical and Computer Modelling: An International Journal
Computers & Mathematics with Applications
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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 is an autonomous differential equation system, and the second one is a nonautonomous one which generally is more difficult to be solved. The numerical schemes developed here can be used in other general epidemic models based on ordinary differential equations. One advantage of the developed methodology is that can be used easily by the scientific community without special knowledge. In addition, these NSFD schemes which are based on the the nonstandard finite difference methods developed by Mickens solve numerically systems describing epidemics with less computational effort. Finally, with these matrix NSFD schemes it can be exploited more easily matrix operations advantages.