Backward bifurcation and saddle-node bifurcation in virus-immune dynamics

TL;DR

This paper investigates complex bifurcation phenomena, including backward and saddle-node bifurcations, in virus-immune dynamics models, revealing thresholds critical for disease control and immune response stability.

Contribution

It demonstrates the existence of backward and saddle-node bifurcations in virus-immune models, extending previous work on thresholds and bi-stability.

Findings

Identification of backward bifurcation point as control threshold

Detection of saddle node bifurcation as post-treatment threshold

Existence of bi-stable interval between thresholds

Abstract

Recently, Wang and Xu [ Appl. Math. Lett. 78 (2018) 105-111] studied thresholds and bi-stability in virus-immune dynamics. In this paper, we show there also exist backward bifurcation and saddle node bifurcation in this model. Our investigation demonstrates the existence of post-bifurcation phenomenon in the system when the immune strength was selected as the bifurcation parameter. The bifurcation of saddle knot is then analyzed. The values of backward bifurcation point and saddle node bifurcation point are the elite control threshold and post-treatment control threshold respectively. The time interval between the two thresholds is the bi-stable interval.