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

Abstract

The mathematical modeling of the propagation of diseases 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 the continuous system and then apply different numerical methods: first-order and higher-order strong stability preserving Runge-Kutta methods. We give different conditions under which the numerical schemes preserve the positivity and the boundedness of the continuous-time solution. Then, the theoretical results are demonstrated by some numerical experiments.