Discrete dynamical systems: theory and applications
Discrete dynamical systems: theory and applications
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
An introduction to difference equations
An introduction to difference equations
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
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
Nonstandard finite-difference methods for predator-prey models with general functional response
Mathematics and Computers in Simulation
Numerical simulation of multi-species biofilms in porous media for different kinetics
Mathematics and Computers in Simulation
A nonstandard numerical scheme of predictor-corrector type for epidemic models
Computers & Mathematics with Applications
Matrix nonstandard numerical schemes for epidemic models
WSEAS Transactions on Mathematics
Dynamics of a discretized SIR epidemic model with pulse vaccination and time delay
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
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In this paper we construct and develop two competitive implicit finite difference scheme for a deterministic mathematical model associated with the evolution of influenza A disease in human population. Qualitative dynamics of the model is determined by the basic reproduction number, R"0. Numerical schemes developed here are based on nonstandard finite difference methods. Our aim is to transfer essential properties of the continuous model to the discrete schemes and to obtain unconditional stable schemes. The proposed numerical schemes have two fixed points which are identical to the critical points of the continuous model and it is shown that they have the same stability properties. Numerical simulations with different initial conditions, parameters values and time step sizes are developed for different values of parameter R"0, convergence to the disease free equilibrium point when R"01 are obtained independent of the time step size. These numerical integration schemes are useful since can reproduce the dynamics of original differential equations.