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MMChapter4_4p8

# P=plot(t,x,1,’b’,t,x,2,’r.’ xlabel(’time’

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Unformatted text preview: p=plot(t,x(:,1),’b’,t,x(:,2),’r-.’); xlabel(’Time’); ylabel(’Drug Concentration’); title(’Pharmacokinetics Model’); set(p,’LineWidth’,3); pLegnd=legend(’GI tract’,’Blood’); set(pLegnd,’Location’, ’NorthWest’) end J. D. Flores ( USD ) Math-735: Math Modeling Spring 2013 37 / 41 Consider the case where drug injection is periodic. This is a reasonable situation because prescription drugs are often taken at specific intervals of time. Suppose a drug is prescribed as follows: d ( t ) = 2 , ≤ t ≤ 1 / 2 , , 1 / 2 < t < 6 , where d ( t + 6) = d ( t ) ([Yeargers, E. K., Shonkwiler, R.W. & Herod J.V., 1996]). The drug is taken orally every six hours and released into GI tract over a half-hour period. J. D. Flores ( USD ) Math-735: Math Modeling Spring 2013 38 / 41 Outline 1. Phase Plane Analysis 2. Eigenvalues. Real Eigenvalues Complex Eigenvalues Examples 3. Gershgorin’s Theorem 4. An Example: Pharmacokinetics Model 5. References J. D. Flores ( USD ) Math-735: Math Modeling Spring 2013 39 / 41 References I F. Brauer & J. A. Nohel Qualitative Theory of Ordinary Differential Equations. Reprint , Dover 1989. J. M. Cushing Differential Equations: An Applied Approach. Prentice Hall 2004. C. Moler & C. Van Loan Nineteen dubious ways to compute the exponential of a matrix. SIAM Review 20:801-836, 1978. C. Moler & C. Van Loan Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review 45:3-49, 2003. J. D. Flores ( USD ) Math-735: Math Modeling Spring 2013 40 / 41 References II B. Noble Applied Linear Algebra. Prentice Hall 1969. E. K. Yeargers, R. W. Shonkwiler & J. V. Herod An Introduction to the Mathematics of Biology. Birkh ¨ auser , 1996. J. D. Flores ( USD ) Math-735: Math Modeling Spring 2013 41 / 41...
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