Mathematical analysis of a within-host model of malaria with immune effectors and Holling type II functional response
Applicationes Mathematicae, Tome 42 (2015) no. 2-3, pp. 137-158
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $R_0 1$. Then the disease is controllable and dies out. In the absence of immune effectors, when $R_0 > 1$, 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 $R_0 > 1$, 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.
DOI :
10.4064/am42-2-2
Keywords:
paper consider within host model malaria holling type functional response model describes dynamics blood stage parasites their interaction host cells particular red blood cells immune effectors first obtain equilibrium points system global stability disease free equilibrium point established basic reproduction ratio infection disease controllable dies out absence immune effectors there exists unique endemic equilibrium point global analysis point given which uses lyapunov functions other results theory competitive systems stability periodic orbits therefore malaria infection persists host finally presence immune effectors endemic equilibrium unstable parameter values using routh hurwitz criterion numerical simulations model results
Affiliations des auteurs :
F. Gazori 1 ; M. Hesaaraki 1
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author = {F. Gazori and M. Hesaaraki},
title = {Mathematical analysis of a within-host model of malaria with immune effectors and {Holling} type {II} functional response},
journal = {Applicationes Mathematicae},
pages = {137--158},
publisher = {mathdoc},
volume = {42},
number = {2-3},
year = {2015},
doi = {10.4064/am42-2-2},
zbl = {06506202},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am42-2-2/}
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%0 Journal Article %A F. Gazori %A M. Hesaaraki %T Mathematical analysis of a within-host model of malaria with immune effectors and Holling type II functional response %J Applicationes Mathematicae %D 2015 %P 137-158 %V 42 %N 2-3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/am42-2-2/ %R 10.4064/am42-2-2 %G en %F 10_4064_am42_2_2
F. Gazori; M. Hesaaraki. Mathematical analysis of a within-host model of malaria with immune effectors and Holling type II functional response. Applicationes Mathematicae, Tome 42 (2015) no. 2-3, pp. 137-158. doi: 10.4064/am42-2-2
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