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

Abstract

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.