Abstract
BackgroundMathematical modeling of virus dynamics has provided quantitative insights into viral infections such as influenza, the simian immunodeficiency virus/human immunodeficiency virus, hepatitis B, and hepatitis C. Through modeling, we can estimate the half-life of infected cells, the exponential growth rate, and the basic reproduction number (R0). To calculate R0 from virus load data, the death rate of productively infected cells is required. This can be readily estimated from treatment data collected during the chronic phase, but is difficult to determine from acute infection data. Here, we propose two new models that can reliably estimate the average life span of infected cells from acute-phase data, and apply both methods to experimental data from humanized mice infected with HIV-1.MethodsBoth new models, called as the reduced quasi-steady state (RQS) model and the piece-wise regression (PWR) model, are derived by simplification of a standard model for the acute-phase dynamics of target cells, viruses and infected cells. By having only a limited number of parameters, both models allow us to reliably estimate the death rate of productively infected cells. Simulated datasets with plausible parameter values are generated with the standard model to compare the performance of the new models with that of the major previous model (i.e., the simple exponential model). Finally, we fit models to time course data from HIV-1 infected humanized mice to estimate the several important parameters characterizing their acute infection.Results and conclusionsThe new models provided much better estimates than the previous model because they more precisely capture the de novo infection process. Both models describe the acute phase of HIV-1 infected humanized mice reasonably well, and we estimated an average death rate of infected cells of 0.61 and 0.61, an average exponential growth rate of 0.69 and 0.76, and an average basic reproduction number of 2.30 and 2.38 in the RQS model and the PWR model, respectively. These estimates are fairly close to those obtained in humans.
Highlights
Mathematical modeling of virus dynamics has provided quantitative insights into viral infections such as influenza, the simian immunodeficiency virus/ human immunodeficiency virus, hepatitis B, and hepatitis C
Mathematical models describing the acute phase of virus infection (I) Reduced quasi-steady state (RQS) model The standard model for viral infection consists of three differential equations for target cells, T(t), infected cells, I(t), and viral particles, V(t) [7,8,9]
Since, during the acute phase of several virus infections, such as human immunodeficiency virus (HIV), simian immunodeficiency virus (SIV) and simian–human immunodeficiency virus (SHIV), the decrease in number of target cells in peripheral blood (PB) is preceded by an initial flat phase [14,15,16,17,18,19,20,26,27,28], we propose a phenomenological model for the target cells consisting of an initial flat phase, and a second phase of exponential loss (Figure 1)
Summary
Mathematical modeling of virus dynamics has provided quantitative insights into viral infections such as influenza, the simian immunodeficiency virus/ human immunodeficiency virus, hepatitis B, and hepatitis C. In chronic viral infections, such as human immunodeficiency virus (HIV) and hepatitis C virus (HCV) infections, contraction slows down such that the viral load approaches a steady state, called the virological set point [3,4] In both infection types, the expansion and contraction of the viral load have been modeled as single exponential functions, with parameters determined by linear regression of the log transformed data [3,5,6,7]. The expansion and contraction of the viral load have been modeled as single exponential functions, with parameters determined by linear regression of the log transformed data [3,5,6,7] This simple approach is reasonable as long as the conditions, e.g., the availability of target cells or the immune response, hardly change within each phase. Once the basic reproduction number is estimated, the critical inhibition, 1–1/R0, induced by vaccines, or by antiviral drugs, to prevent primary virus infection can be calculated [6]
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