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

2024/02/16 by Bálint Takács, Takács, B. M., G. Svantnerné Sebestyén +3 · 1 citation
Mathematics · #34C60 (Secondary) #65L05 (Primary) 92D30 #COVID-19 epidemiological studies #FOS: Mathematics #G.1.7 #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2402.10549

openalex publication_date 2024/02/16 · openalex created_date 2024/02/20 · openalex updated_date 2026/08/01

Abstract

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 \citeshu. We give different conditions under which the numerical schemes behave as expected. Then, the theoretical results are demonstrated by some numerical experiments. \keywordspositivity preservation, general SEIR model, SSP Runge-Kutta methods

Cited by

• An insight on some properties of high order nonstandard linear multistep methods

Related

• Navigating Epidemic Mathematics: Exploring Tools for Mathematical Modelling in Biology
• Stochastic Partial Differential Equation SEIRS Epidemic Models: Well-posedness and Longtime Behavior
• Domain preserving and strongly converging explicit scheme for the stochastic SIS epidemic model
• A non-autonomous SEIRS model with general incidence rate
• Global dynamics of a periodic SEIRS model with general incidence rate