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# 1: Natural Progression of HIV The viral load is shown in red, and the CD + 4 cell counts in blue. (Figure adapted from Giorgi, 2011)

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## Contexts in source publication

**Context 1**

... processes and in particular the Semi-Markov models have been employed in the field of biomedicine, for example, in applications to prevent, screen, and design cancer prevention trials, see in (Zelen & Davidov, 2000). (Mathieu, Loup, Dellamonica, & Daures, 2005, argued that, the use of reversible disease states defined on both CD + 4 and V L levels is quite innovative. They considered four states which are characteristics of the disease stages, the states were defined on crossed values of both Viral load and CD + 4 cell count as shown below. and CD + 4 > 200 represents a stable state in the evolution of seropositive patients. In their analysis, they ignored the fact that the disease progression is dependent on other factors like time and age. ( Mathieu et al., 2007) extended his previous study ) by modeling the HIV evolution using Non -Homogeneous Semi-Markov Model (NHSMM) in continuous time. They considered four states of the disease evolution and assumed that patients move through these states according to ten transitions as in Figure 2.3: Figure 2.3: HIV disease progression They used a parametric approach and computed the interval transition ...

**Context 2**

... processes and in particular the Semi-Markov models have been employed in the field of biomedicine, for example, in applications to prevent, screen, and design cancer prevention trials, see in (Zelen & Davidov, 2000). (Mathieu, Loup, Dellamonica, & Daures, 2005, argued that, the use of reversible disease states defined on both CD + 4 and V L levels is quite innovative. They considered four states which are characteristics of the disease stages, the states were defined on crossed values of both Viral load and CD + 4 cell count as shown below. and CD + 4 > 200 represents a stable state in the evolution of seropositive patients. In their analysis, they ignored the fact that the disease progression is dependent on other factors like time and age. ( Mathieu et al., 2007) extended his previous study ) by modeling the HIV evolution using Non -Homogeneous Semi-Markov Model (NHSMM) in continuous time. They considered four states of the disease evolution and assumed that patients move through these states according to ten transitions as in Figure 2.3: Figure 2.3: HIV disease progression They used a parametric approach and computed the interval transition ...

**Context 3**

... summary of the HIV evolution dynamics review is shown in Figure 2.5: Figure 2.5: Literature summary on stochastic ...

**Context 4**

... summary of the HIV evolution dynamics review is shown in Figure 2.5: Figure 2.5: Literature summary on stochastic ...

**Context 5**

... initial variable values and parameter values for the model are described in Tables 3.4 the simulations, it is clear that in the primary stage of the infection (period before treatment), a dramatically decrease in the level of the CD4-T cells occur and the number of the free virions increase with time. With the introduction of intra- cellular delay, the virus population drops as well as an increase in the CD4 cells but then they stabilize at some point and coexist in the host as shown in Figures 3.2 and 3.3. This analysis shows that the intracellular delay plays a big role in slowing down the progression of HIV in an infected person. A typical life-cycle of HIV virus and immune system interaction with therapeutic intervention effect is shown in Figure ...