Backward bifurcation of an age-structured epidemic model with partial immunity: The Lyapunov–Schmidt approach

Abstract

In this paper, we propose an age-structured SVIRS model with two loss routes of immunity. Employing the Lyapunov–Schmidt approach, we derive a necessary and sufficient condition for the occurrence of a backward bifurcation. We identify that the combined action of such two losses of immunity plays a vital role in producing a bistable phenomena.