Mathematical analysis of a within-host model of malaria with immune effectors and Holling type II functional response

F. Gazori, and M. Hesaaraki. "Mathematical analysis of a within-host model of malaria with immune effectors and Holling type II functional response." Applicationes Mathematicae 42.2-3 (2015): 137-158. <http://eudml.org/doc/280012>.

@article{F2015,
abstract = {In this paper, we consider a within-host model of malaria with Holling type II functional response. The model describes the dynamics of the blood-stage of parasites and their interaction with host cells, in particular red blood cells and immune effectors. First, we obtain equilibrium points of the system. The global stability of the disease-free equilibrium point is established when the basic reproduction ratio of infection is R₀< 1. Then the disease is controllable and dies out. In the absence of immune effectors, when R₀ > 1, there exists a unique endemic equilibrium point. Global analysis of this point is given, which uses on the one hand Lyapunov functions and on the other hand results of the theory of competitive systems and stability of periodic orbits. Therefore, if R₀ > 1, the malaria infection persists in the host. Finally, in the presence of immune effectors, we find that the endemic equilibrium is unstable for some parameter values using the Routh-Hurwitz criterion; numerical simulations of the model also show the same results.},
author = {F. Gazori, M. Hesaaraki},
journal = {Applicationes Mathematicae},
keywords = {within-host model of malaria; immune effectors; basic reproduction ratio of infection; global stability},
language = {eng},
number = {2-3},
pages = {137-158},
title = {Mathematical analysis of a within-host model of malaria with immune effectors and Holling type II functional response},
url = {http://eudml.org/doc/280012},
volume = {42},
year = {2015},
}

TY - JOUR
AU - F. Gazori
AU - M. Hesaaraki
TI - Mathematical analysis of a within-host model of malaria with immune effectors and Holling type II functional response
JO - Applicationes Mathematicae
PY - 2015
VL - 42
IS - 2-3
SP - 137
EP - 158
AB - In this paper, we consider a within-host model of malaria with Holling type II functional response. The model describes the dynamics of the blood-stage of parasites and their interaction with host cells, in particular red blood cells and immune effectors. First, we obtain equilibrium points of the system. The global stability of the disease-free equilibrium point is established when the basic reproduction ratio of infection is R₀< 1. Then the disease is controllable and dies out. In the absence of immune effectors, when R₀ > 1, there exists a unique endemic equilibrium point. Global analysis of this point is given, which uses on the one hand Lyapunov functions and on the other hand results of the theory of competitive systems and stability of periodic orbits. Therefore, if R₀ > 1, the malaria infection persists in the host. Finally, in the presence of immune effectors, we find that the endemic equilibrium is unstable for some parameter values using the Routh-Hurwitz criterion; numerical simulations of the model also show the same results.
LA - eng
KW - within-host model of malaria; immune effectors; basic reproduction ratio of infection; global stability
UR - http://eudml.org/doc/280012
ER -