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arXiv · 1712.09105

A Partial Differential Equation Model with Age-Structure and Nonlinear Recidivism: Conditions for a Backward Bifurcation and a General Numerical Implementation

Fabio Sanchez·Juan G. Calvo·Esteban Segura·Zhilan Feng
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Abstract

\noindent We formulate an age-structured three-staged nonlinear partial differential equation model that features {\it nonlinear} recidivism to the infected ({\it infectious}) class from the {\it temporarily} recovered class. Equilibria are computed, as well as local and global stability of the {\it 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 {\it infectious} class.

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Fabio Sanchez, Juan G. Calvo, Esteban Segura, Zhilan Feng. 2017-12-25. A Partial Differential Equation Model with Age-Structure and Nonlinear Recidivism: Conditions for a Backward Bifurcation and a General Numerical Implementation. https://doi.org/10.1016/j.camwa.2019.06.021

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