Chaos: making a new science
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
A mathematical study of a model for childhood diseases with non-permanent immunity
Journal of Computational and Applied Mathematics
A second-order, unconditionally positive, mass-conserving integration scheme for biochemical systems
Applied Numerical Mathematics
Nonstandard finite-difference methods for predator-prey models with general functional response
Mathematics and Computers in Simulation
Nonstandard numerical methods for a mathematical model for influenza disease
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
A nonstandard numerical scheme of predictor-corrector type for epidemic models
Computers & Mathematics with Applications
Topological structure preserving numerical simulations of dynamical models
Journal of Computational and Applied Mathematics
Matrix nonstandard numerical schemes for epidemic models
WSEAS Transactions on Mathematics
Mathematics and Computers in Simulation
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The SEIR (susceptible, exposed, infectious, recovered) model has been discussed by many authors, in particular with reference to the spread of measles in an epidemic. In this paper, the SEIR model with constant rate of infection is solved using a first-order, finite-difference method in the form of a system of one-point iteration functions. This discrete system is seen to have two fixed points which are identical to the critical points of the (continuous) equations of the SEIR model and it is shown that they have the same stability properties. It is shown further that the solution sequence is attracted from any set of initial conditions to the correct (stable) fixed point for an arbitrarily large time step. Simulations confirm this and results are compared with well-known numerical methods.