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

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arxiv 1712.09105 v3 pith:M6CDBJC3 submitted 2017-12-25 math.DS q-bio.PE

Fabio Sanchez , Juan G. Calvo , Esteban Segura , Zhilan Feng This is my paper
classification math.DSq-bio.PE
keywords classnonlinearnumericalconditionsdifferentialequationinfectiousmodel
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\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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Cited by 1 Pith paper

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  1. A two-patch epidemic model with nonlinear reinfection

    q-bio.PE 2019-07 unverdicted novelty 4.0 of 10

    A two-patch epidemic model with nonlinear reinfection shows that population movement can enlarge the stability region of the disease-free steady state.

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