Construction of a discrete-time model for periodic diseases with integer-valued populations

摘要

We demonstrate by means of an explicit construction that it is possible to have a discrete-time model for periodic diseases, consisting of these interacting populations, such that if the initial populations are integer-valued, future populations are also integer-valued. This particular work indicates that the problem of "small values" for solutions can be overcome and, as a consequence, more realistic mathematical models can be constructed for dynamical systems involving the spread of disease in a population.