  The mathematical modeling of the propagation of illnesses has an important
role from both mathematical and biological points of view. In this article, we
observe an SEIR-type model with a general incidence rate and a non-constant
recruitment rate function. First, we observe the qualitative properties of
different methods: first-order and higher-order strong stability preserving
Runge-Kutta methods \cite{shu}. We give different conditions under which the
numerical schemes behave as expected. Then, the theoretical results are
demonstrated by some numerical experiments. \keywords{positivity preservation,
general SEIR model, SSP Runge-Kutta methods}
