Chowdhury Atiqur, Tanveer Saleh, Wang Xueying
Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88001, USA.
Department of Mathematics, Ohio State University, Columbus, OH 43210, USA.
Proc Math Phys Eng Sci. 2020 Feb;476(2234):20190673. doi: 10.1098/rspa.2019.0673. Epub 2020 Feb 26.
This paper is concerned primarily with constructive mathematical analysis of a general system of nonlinear two-point boundary value problem when an empirically constructed candidate for an approximate solution () satisfies verifiable conditions. A local analysis in a neighbour- hood of a assures the existence and uniqueness of solutions and, at the same time, provides error bounds for approximate solutions. Applying this method to a cholera epidemic model, we obtain an analytical approximation of the steady-state solution with rigorous error bounds that also displays dependence on a parameter. In connection with this epidemic model, we also analyse the basic reproduction number, an important threshold quantity in the epidemiology context. Through a complex analytic approach, we determine the principal eigenvalue to be real and positive in a range of parameter values.
本文主要关注当一个通过经验构建的近似解候选函数（）满足可验证条件时，非线性两点边值问题一般系统的构造性数学分析。在一个邻域内的局部分析确保了解的存在性和唯一性，同时为近似解提供了误差界。将此方法应用于霍乱流行模型，我们得到了具有严格误差界的稳态解的解析近似，该近似也显示了对一个参数的依赖性。关于这个流行模型，我们还分析了基本再生数，这是流行病学背景下一个重要的阈值量。通过复分析方法，我们确定在一系列参数值范围内主特征值为实且正。
