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

TL;DR

This paper develops an age-structured PDE model with nonlinear recidivism, identifying conditions for backward bifurcation and providing a numerical framework for analyzing multiple infectious equilibria.

Contribution

It introduces a novel age-structured PDE model with nonlinear recidivism and derives conditions for backward bifurcation, along with a general numerical implementation.

Findings

Backward bifurcation exists under specific conditions.

Numerical framework enables exploration of multiple infectious equilibria.

Model captures complex age-dependent recidivism dynamics.

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.