Viral dynamics of primary viremia and antiretroviral therapy in simian immunodeficiency virus infection

Abstract

Mathematical modeling of viral replication dynamics, based on sequential measurements of levels of virion-associated RNA in plasma during antiretroviral treatment, has led to fundamental new insights into human immunodeficiency virus type 1 pathogenesis. We took advantage of the simian immunodeficiency virus (SIV)-infected macaque model to perform detailed measurements and mathematical modeling during primary infection and during treatment of established infection with the antiretroviral drug (R)-9-(2-phosphonylmethoxypropyl)adenine (PMPA). The calculated clearance half-life for productively infected cells during resolution of the peak viremia of primary infection was on the order of 1 day, with slightly shorter clearance half-lives calculated during PMPA treatment. Viral reproduction rates upon discontinuation of PMPA treatment after 2 weeks were approximately twofold greater than those obtained just prior to initiation of treatment in the same animals, likely reflecting accumulation of susceptible target cells during treatment. The basic reproductive ratio (R0) for the spread of SIV infection in vivo, which represents the number of productively infected cells derived from each productively infected cell at the beginning of infection, was also estimated. This parameter quantifies the extent to which antiviral therapy or vaccination must limit the initial spread of virus to prevent establishment of chronic disseminated infection. The results thus provide an important guide for efforts to develop vaccines against SIV and, by extension, human immunodeficiency virus.

Perspectives on the basic reproductive ratio

“…As an example, consider Nowak et al (1997) and Lloyd (2001a), who studied the within-host dynamics of viral disease. From standard models of viral dynamics, they find that the relationship between R 0 and r 0 is…”

Comparative estimation of the reproduction number for pandemic influenza from daily case notification data

“…These approaches include the estimation of the initial intrinsic growth rate of the epidemic followed by its substitution into a formula derived from the linearization of the deterministic epidemic model (e.g. Anderson & May 1991;Nowak et al 1997;Lloyd 2001;Lipsitch 2003), trajectory matching (least-square fitting) of epidemic models to epidemic curve data (examples of recent work include Riley et al 2003;Chowell et al 2006) and sequential Bayesian inference to estimate the effective reproduction number R t at a given time t, from a stochastic formulation of a SIR model (Bettencourt & Ribeiro 2006).…”

A new SEIR epidemic model with applications to the theory of eradication and control of diseases, and to the calculation of

“…Therefore, we assume, as given above, that s ranges from 0.5 and 1.0 days, and r ranges from 1.0 to 2.0 days.Our result suggests that each SIV infected macaque cell will infect in average (6:8 þ 22:1Þ=2 $ 15 cells over the course of its life span when CD4 target cells are not limiting. In [47], the estimated R 0 values vary drastically under different models: R 0 ranges from 4.2 to 17 in the exponentially distributed model with a mean latent period of 0.5 days, and R 0 ranges from 5.4 to 68 in the fixed time delay model with a mean latent period of 1.0 days. * Sources: Benenson [3] and 'The Pink Book' of CDC, 9th Ed., 2006 [6].…”

“…i SIV stands for simian immunodeficiency virus. Our estimation of the mean infectious period r for SIV cells is based on [47] from SIV infected macaques, by which the infectious period r is equal to the reciprocal of the infected cell loss rate a (i.e., r ¼ 1=a). It was estimated (see Table I of [47]) that the values of a range from 0.51 to 0.96.…”

“…Moreover, it was known (cf. [47,37]) that the latent period s for SIV is between 0.5 and 1.0 days. Therefore, we assume, as given above, that s ranges from 0.5 and 1.0 days, and r ranges from 1.0 to 2.0 days.Our result suggests that each SIV infected macaque cell will infect in average (6:8 þ 22:1Þ=2 $ 15 cells over the course of its life span when CD4 target cells are not limiting.…”