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Nonlinear two-point boundary value problems: applications to a cholera epidemic model.

ABSTRACT: 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 (quasi-solution) satisfies verifiable conditions. A local analysis in a neighbour- hood of a quasi-solution 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.

SUBMITTER: Chowdhury A

PROVIDER: S-EPMC7069490 | biostudies-literature | 2020 Feb

REPOSITORIES: biostudies-literature

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Nonlinear two-point boundary value problems: applications to a cholera epidemic model.

Chowdhury Atiqur A Tanveer Saleh S Wang Xueying X

Proceedings. Mathematical, physical, and engineering sciences 20200226 2234

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 (<i>quasi-solution</i>) satisfies verifiable conditions. A local analysis in a neighbour- hood of a <i>quasi-solution</i> 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 mod ...[more]

PMID: 32201479

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