Analysis of an HIV Pandemic Model with Cure Rateand CTL Response Delay

2020 ◽  
Vol 14 (5) ◽  
Keyword(s):  
Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6247-6267 ◽  
Author(s):  
Elham Shamsara ◽  
Zahra Afsharnezhad ◽  
Reihaneh Mostolizadeh

Developing accurate mathematical models for host immune response in immunosuppressive diseases such as HIV and HTLV-1 are essential to achieve an optimal drug therapy regime. Since for HTLV-1 specific CTL response typically occurs after a time lag, we consider a discontinuous response function to better describe this lagged response during the early stage of the infectious, thus the system of HTLV-1 model will be a discontinuous system. For analyzing the dynamic of the system we use Filippov theory and find conditions in which the Filippov system undergoes a Hopf bifurcation. The Hopf bifurcation help us to find stable and unstable periodic oscillations and can be used to predict whether the CTL response can return to a steady state condition. Also, Hopf bifurcation in sliding mode is investigated. In this case the solutions will remain in the hyper-surface of discontinuity and as a consequence the disease cannot progress, at least for a long time. Finally we use numerical simulations to demonstrate the results by example.


2007 ◽  
Vol 82 (1) ◽  
pp. 196-206 ◽  
Author(s):  
Andreas Jung ◽  
Hiroki Kato ◽  
Yutaro Kumagai ◽  
Himanshu Kumar ◽  
Taro Kawai ◽  
...  

ABSTRACTToll-like receptors (TLRs) and retinoic acid-inducible gene I-like helicases (RLHs) are two major machineries recognizing RNA virus infection of innate immune cells. Intracellular signaling for TLRs and RLHs is mediated by their cytoplasmic adaptors, i.e., MyD88 or TRIF and IPS-1, respectively. In the present study, we investigated the contributions of TLRs and RLHs to the cytotoxic T-lymphocyte (CTL) response by using lymphocytoid choriomeningitis virus (LCMV) as a model virus. The generation of virus-specific cytotoxic T lymphocytes was critically dependent on MyD88 but not on IPS-1. Type I interferons (IFNs) are known to be important for the development of the CTL response to LCMV infection. Serum levels of type I IFNs and proinflammatory cytokines were mainly dependent on the presence of MyD88, although IPS-1−/−mice showed a decrease in IFN-α levels but not in IFN-β and proinflammatory cytokine levels. Analysis ofIfna6+/GFPreporter mice revealed that plasmacytoid dendritic cells (DCs) are the major source of IFN-α in LCMV infection. MyD88−/−mice were highly susceptible to LCMV infection in vivo. These results suggest that recognition of LCMV by plasmacytoid DCs via TLRs is responsible for the production of type I IFNs in vivo. Furthermore, the activation of a MyD88-dependent innate mechanism induces a CTL response, which eventually leads to virus elimination.


2000 ◽  
Vol 191 (9) ◽  
pp. 1499-1512 ◽  
Author(s):  
Franziska Lechner ◽  
David K.H. Wong ◽  
P. Rod Dunbar ◽  
Roger Chapman ◽  
Raymond T. Chung ◽  
...  

Although hepatitis C virus (HCV) infection is very common, identification of patients during acute infection is rare. Consequently, little is known about the immune response during this critical stage of the disease. We analyzed the T lymphocyte response during and after acute resolving HCV infection in three persons, using interferon (IFN)-γ enzyme-linked immunospot (ELISPOT) and human histocompatibility leukocyte antigen (HLA) peptide tetramer assays. Acute infection was associated with a broadly directed T helper and cytotoxic T lymphocyte (CTL) response, which persisted after resolution of clinical hepatitis and clearance of viremia. At the earliest time point studied, highly activated CTL populations were observed that temporarily failed to secrete IFN-γ, a “stunned” phenotype, from which they recovered as viremia declined. In long-term HCV-seropositive persons, CTL responses were more common in persons who had cleared viremia compared with those with persistent viremia, although the frequencies of HCV-specific CTLs were lower than those found in persons during and after resolution of acute HCV infection. These studies demonstrate a strong and persistent CTL response in resolving acute HCV infection, and provide rationale to explore immune augmentation as a therapeutic intervention in chronic HCV infection.


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