A. Successful HCV treatment also called sustained virology response (SVR) is defined as a patient’s

viral load below the lower limit of quantification 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-α therapy ()

that was discussed in class:

dT

dt = s - dT - βV T

dI

dt = βV T - δI

dV

dt = (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 β = 4:1684e - 09,

δ = 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 β = 1:2e - 08, δ = 0:58411, p = 25:1, c =

0:47268, = 1:0, s = 61:7e + 3, d = 0:003.

B. Write  (10 to 15 page) on 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

question.

(ii) Since I will be on travel the week of March 16th, please turn in hard copy of your assignment

in class on the due date (i.e., do not email me the assignment like you did with the first

assignment)

North Carolina State UniversityDepartment of MathematicsIntroduction to Applied MathematicsMA 325Assignment #2DUE Date: March 18, 2015A. Successful HCV treatment also called sustained virology response (SVR) is defined as a patient’sviral load below the lower limit of quantification at a follow-up evaluation at 24 weeks afterthe completion of the treatment. On the other hand, patients who do not attain SVR, theviral load either rebounds to pretreatment levels during the therapy (partial virology response(PVR) or breakthrough (undetectable viral load followed by increase during treatment)) orreturns to pretreatment levels upon cessation of therapy (relapse).Consider the following mathematical model for HCV viral kinetic with interferon-αtherapy (±)that was discussed in class:dTdt=s-dT-βV TdIdt=βV T-δIdVdt= (1-±)pI-cV.1. Implement the above model in SimBiology with the initial conditionsT(0) = 1.4984e+06,I(0) = 0.4724e+ 06,V(0) = 4.3881e+ 06 and parameter valuesβ= 4.1684e-09,δ= 0.1211,p= 25.1,c= 2.7018,±= 0.61382,s= 61.7e+ 3,d= 0.003. Simulate thesolutions for 336 days and describe the results. Is the treatment successful?2. Repeat part 1. with the initial conditionsT(0) = 0.9167e+ 06,I(0) = 0.1009e+ 06,V(0) = 5.3591e+ 06 and parameter valuesβ= 1.2e-08,δ= 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 exportedfrom SimBiology for each problem, the plots for each simulation, and your responses to thequestion.(ii) Since I will be on travel the week of March 16th, please turn in hard copy of your assignmentin class on the due date (i.e., do not email me the assignment like you did with the firstassignment).

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