Anguelov R, Dumont Y, Lubuma J M-S
Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa.
CIRAD, Umr AMAP, Montpellier, France.
AIP Conf Proc. 2012 Oct 2;1487(1):212-223. doi: 10.1063/1.4758961.
We design, analyze and implement nonstandard finite difference (NSFD) schemes for some differential models in biosciences. The NSFD schemes are reliable in three directions. They are topologically dynamically consistent for onedimensional models. They can replicate the global asymptotic stability of the disease-free equilibrium of the MSEIR model in epidemiology whenever the basic reproduction number is less than 1. They preserve the positivity and boundedness property of solutions of advection-reaction and reaction-diffusion equations.
我们为生物科学中的一些微分模型设计、分析并实现了非标准有限差分（NSFD）格式。NSFD格式在三个方面是可靠的。对于一维模型，它们在拓扑动力学上是一致的。每当基本再生数小于1时，它们能够复制流行病学中MSEIR模型无病平衡点的全局渐近稳定性。它们保持了对流反应方程和反应扩散方程解的正性和有界性。
