Bifurcation analysis for an in-host Mycobacterium tuberculosis model

Miaoran Yao, Key Laboratory of Eco-environments in Three Gorges Reservoir Region, School of Mathematics and Statistics, Southwest University, Chongqing 400715, China, Yongxin Zhang, Wendi Wang
2017 Discrete and continuous dynamical systems. Series B  
Tuberculosis infection is still a major threat to humans and it may progress slowly or rapidly to clearance, latent infection, or active disease. In this paper, considering T cells can perform acceleration effect on their own recruitment, an in-host model of Mycobacterium tuberculosis is studied. Focus type and elliptic type of nilpotent singularities of codimension 3 are analyzed in this four dimensional model. Complex dynamical behaviors such as homoclinic loop, saddle-node bifurcation of
more » ... t cycle and co-existence of two limit cycles are revealed by bifurcation analysis. Especially, the slow-fast periodic solution with large-amplitude or small-amplitude is observed in numerical simulations, which provides a perfect explanation for the reactivation of latent infection. 2020 Mathematics Subject Classification. Primary: 92D30; Secondary: 34C23.
doi:10.3934/dcdsb.2020324 fatcat:cbjjpi75yfhz5o3a5nu5o4gpoi