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Sensitivity Analysis on Ms2 Viral Dynamics Using Interval Mathematics

Ozlem Yilmaz, Luke E. K. Achenie, and Ranjan Srivastava. University of Connecticut, 191 Auditorium Rd. Unit 3222, Storrs, CT 06269

Validated solutions of initial value problems (IVPs) can be obtained using interval analysis. A significant advantage over standard numerical methods is that an enclosure of the true solution is obtained. Since there are often measurement errors in an experiment, parameters determined based on the experimental data are also prone to errors. In this paper we employ a MATLAB version of the interval ODE solver VNODE (Nedialkov, 1999) to identify the most sensitive parameters in a biological model. The model under study explains how lytic RNA phage infects Escherichia coli C-3000 and the viral dynamics between the phage and its host at the intercellular level. Experimental data consisted of uninfected cell density (sensitive and resistant type), infected cell density, free phage density and substrate (glucose) concentration. There were 9 parameters determined experimentally and 6 parameters estimated using regression analysis (Jain et al., 2006, submitted). In our preliminary studies, each parameter was defined over an interval. Among all, the parameter corresponding to the rate of infection was found to be the most sensitive one. In the above studies, we note that the interval Hermite-Obreschkoff (IHO) method converges better than the interval Taylor series (ITS). The IHO unfortunately has high computational overhead and has convergence problems when the intervals are large. To alleviate these problems we have been investigating hybrid approaches that combine constraint satisfaction (Granvilliers et al., 2004 and Janssen et al., 2002) with IHO.

References: 1. Nedialkov N., Computing rigorous bounds on the solution of an initial value problem, Ph.D. thesis, University of Toronto, 1999. 2. Jain R., Knorr A.L., Bernacki J. and R. Srivastava, Investigation of bacteriophage MS2 viral dynamics using model discrimination analysis, submitted 2006. 3. Granvilliers L., Cruz J. and P. Barahona, Parameter estimation using interval computations, SIAM J. Sci. Comput., 26:2, 591-612. 4. Janssen M., Hentenryck P.V. and Y. Deville, A constraint satisfaction approach for enclosing solutions to parametric ordinary differential equations, SIAM J. Numer. Anal. 40:5, 1896-1939