A partial differential equation model with age-structure and nonlinear recidivism: Conditions for a backward bifurcation and a general numerical implementation

被引：8

作者：

Sanchez, Fabio ^{[1
]}

Calvo, Juan G. ^{[1
]}

Segura, Esteban ^{[1
]}

Feng, Zhilan ^{[2
]}

机构：

[1] Univ Costa Rica, Escuela Matemat, Ctr Invest Matemat Pura & Aplicada, San Jose 11501, Costa Rica

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2019年 / 78卷 / 12期

关键词：

Backward bifurcation; Age-structured model; Epidemic models; Finite difference methods; EPIDEMIC MODEL; VACCINATION; TUBERCULOSIS; INFECTION;

D O I：

10.1016/j.camwa.2019.06.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We formulate an age-structured three-staged nonlinear partial differential equation model that features nonlinear recidivism to the infected (infectious) class from the temporarily recovered class. Equilibria are computed, as well as local and global stability of the infection-free equilibrium. As a result, a backward-bifurcation exists under necessary and sufficient conditions. A generalized numerical framework is established and numerical experiments are explored for two positive solutions to exist in the infectious class. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：3916 / 3930

页数：15

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