ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Immune Impairment and Immunodeficiency Thresholds in HIV Infection with General Incidence Rate


Alireza Ansari

Department of mathematics,
Sharif University of Technology,
P.O.Box: 11155-9414,
Tehran, Iran.

Mahmoud Hesaaraki

Department of mathematics,
Sharif University of Technology,
P.O.Box: 11155-9414,
Tehran, Iran.



In previous works we used a linear incidence rate into a mathematical model to examine the immune impairment for a proliferation model of CTL responses in the immune response to HIV. Under the assumption that the immune impairment increases over the HIV infection, they classified four processes of the disease progression dynamics, according to their virological properties. In particular they showed that a typical disease progression presents a risky threshold and an immunodeficiency threshold. Moreover the immune system might collapse when the impairment rate of HIV exceeds a threshold value. On the other hand if the immune impairment rate never exceeds the threshold value, the viral replication is well controlled by CTL responses. In this paper we show that all of the above results remain valid if we use a general functional response as the incidence rate into the above mathematical model.


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