Open AccessDynamics of a malaria infection model with time delay
Author(s) -
Qian Ding,
Jian Liu,
Zhiming Guo
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019246
Subject(s) - hopf bifurcation , center manifold , malaria , stability (learning theory) , basic reproduction number , delay differential equation , bifurcation , stability theory , dynamics (music) , mathematics , control theory (sociology) , physics , mathematical analysis , differential equation , biology , immunology , nonlinear system , computer science , demography , population , quantum mechanics , control (management) , machine learning , artificial intelligence , sociology , acoustics
In this paper, a new mathematical model (a system of delay differential equation) is proposed to describe dynamical behaviors of malaria in an infected host with red blood cells (RBCs), infected red blood cells (iRBCs) and immune factors. The basic reproduction number R0 of the malaria infection is derived. If R 0 ≤1, the uninfected equilibrium E 0 is globally asymptotically stable. If R 0 >1, there exists two kinds of infection equilibria. The conditions of these equilibria with respect to the existence, stability and uniform persistence are given. Furthermore, fluctuations occur when the model undergoes Hopf bifurcation, and periodic solution appears near the positive equilibrium. The direction and stability of Hopf bifurcation are also obtained by applying the center manifold method and the normal form theory. Numerical simulations are provided to demonstrate the theoretical results.