#### Çankaya University Analysis and Applied Math Seminar Series

Mathematical Models of the Dynamics of HIV-1 Decline in Patients on Protease Inhibitor Monotherapy
Elvan Akın
Missouri University S&T, United States of America
Özet : Mathematical models have shed light on the dynamics of HIV- 1 infection in vivo. In this study, we propose alternative discrete models to one of the early models of the dynamics of HIV-1 introduced by Perelson et al. in [3] that is given as a system of first order differential equations. Our main goal is to compare these mathematical models including the model of Perelson et al. when the unit of time is in days and in hours. To achieve our goal, we first generalize the model of the interaction of the immune system with HIV-1 in [3] on a nonempty closed subset of real numbers and find an alternative discrete model departing from the generalization. Then, we derive the unique solutions to these mathematical models to retrieve the total concentration of plasma virions. For the comparison, we use MATLAB with nonlinear least squares method to estimate the parameters such as the virion clearance rate and the rate of loss of infected cells and calculate Adjusted R-squared values by fitting the total concentration of plasma virions to experimental data collected in [3]. Our results show that systems obtained from the generalization describe the best fit regardless of unit of time. On the other hand, the system of first order difference equations is found to be the best fit in hours.
 Tarih : 25.05.2018 Saat : 13:30 Yer : Department of Mathematics, Cankaya University Dil : English Web : http://math.cankaya.edu.tr