North Carolina State University Department of Mathematics Introduction to Applied Mathematics MA 325 Assignment #2 DUE Date: June 29, 2017 A. Successful HCV treatment also called sustained virology response (SVR) is de ned as a patient's viral load below the lower limit of quanti cation at a follow-up evaluation at 24 weeks after the completion of the treatment. On the other hand, patients who do not attain SVR, the viral load either rebounds to pretreatment levels during the therapy (partial virology response (PVR) or breakthrough (undetectable viral load followed by increase during treatment)) or returns to pretreatment levels upon cessation of therapy (relapse). Consider the following mathematical model for HCV viral kinetic with interferon- therapy ( ) that was discussed in class: dT dt dI dt dV dt = s dT VT = VT I = (1 )pI cV: 1. Implement the above model in SimBiology with the initial conditions T (0) = 1:4984e+06, I(0) = 0:4724e + 06, V (0) = 4:3881e + 06 and parameter values = 4:1684e 09, = 0:1211, p = 25:1, c = 2:7018, = 0:61382, s = 61:7e + 3, d = 0:003. Simulate the solutions for 336 days and describe the results. Is the treatment successful? 2. Repeat part 1. with the initial conditions T (0) = 0:9167e + 06, I(0) = 0:1009e + 06, V (0) = 5:3591e + 06 and parameter values = 1:2e 08, = 0:58411, p = 25:1, c = 0:47268, = 1:0, s = 61:7e + 3, d = 0:003. B. Write a summary (one to two page) of this module. Notes: (i) Your write-up should include, among other things, the differential equations that you exported from SimBiology for each problem, the plots for each simulation, and your responses to the