1. Numerical threshold stability of a nonlinear age-structured reaction diffusion heroin transmission model.
- Author
-
Liu, X., Zhang, M., and Yang, Z.W.
- Subjects
- *
BASIC reproduction number , *HEROIN , *DISCRETE systems , *NUMERICAL analysis - Abstract
This paper deals with the numerical threshold stability of a nonlinear age-space structured heroin transmission model. A semi-discrete system is established by spatially domain discretization of the original nonlinear age-space structured model. A threshold value is proposed in stability analysis of the semi-discrete system and named as a numerical basic reproduction number. Besides the role it plays in numerical threshold stability analysis, the numerical basic reproduction number can preserve qualitative properties of the exact basic reproduction number and converge to the latter while stepsizes vanish. A fully discrete system is established via a time discretization of the semi-discrete system, in which an implicit-explicit technique is implemented to ensure the preservation of the biological meanings (such as positivity) without CFL restriction. Some numerical experiments are exhibited in the end to confirm the conclusions and explore the final state. • A numerical scheme is constructed for nonlinear age-structured reaction-diffusion models. • A numerical stability threshold is proposed in numerical stability analysis. • The numerical stability threshold we proposed can preserve qualitative properties of the exact stability threshold. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF