Strong Resonance Bifurcations in a Discrete-time In-host Model with a Saturating Infection Rate

Abstract

The complex dynamics of a two-dimensional discrete-time in-host infection model with a saturating infection rate are discussed. The local stability of fixed points of the model is investigated. The model undergoes both flip and Neimark-Sacker bifurcations. Moreover, codimension-two bifurcations of the infected fixed point are discussed using bifurcation theory and normal forms. The model exhibits 1:2, 1:3, and 1:4 strong resonances. Numerical simulations are performed to verify our analysis. In addition, bifurcations of higher iterations are extracted from the numerical continuation. In order to reduce the disease burden, a control strategy is applied to the discrete-time model.