Abstract
Mathematical modeling has contributed to quantitative understanding of viral infections. The basic model, T'(t)=－βT(t)V(t), I'(t)=βT(t)V(t)－δI(t) and V'(t)=pI(t)－cV(t), has been analyzed which clinical or experimental data sets for many kinds of virus infections so far. However, in the basic model, we implicitly assume that punctual removal of cells and virions due to experimental sampling in cell cultures is described by an exponentially decay. However, the removal of cells and virions is performed instantaneously in viral infection experiments. Therefore, there might be differences among estimated parameters when we use the basic model or an explicit model including the punctual removal. Here, we constructed a hybrid dynamical model which describes the punctual removal by piecewise continuous function to the basic model. We analyzed time course of experimental data for SHIV-KS661 and SHIV-#64 infection in vitro by the basic model and the hybrid dynamical model, and compared the estimated parameters. Interestingly, we found that these two models give similar parameter estimations, and well capture the experimental virus infections. Our results provide a validation of the exponential decay assumption for the punctual removal in terms of parameter estimations.
