High-order reliable numerical methods for epidemic models with non-constant recruitment rate

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}