By Robeva R.S., et al.

ISBN-10: 0120887711

ISBN-13: 9780120887712

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1. Indeed, using Eq. 1 CeÀTr 1 À ðeÀTr Þn CeÀTr C : ¼ ¼ ÀTr 1Àe 1 À eÀTr e Tr À 1 (1-42) Thus, for a sufficiently large number of doses, the residual concentrations stabilize around the value R, which depends on the dose C, the fixed time between doses T, and the elimination rate constant r. EXERCISE 1-19 Is Rn larger or smaller than R? Explain why. What is the physiological meaning of R? 1 hoursÀ1, T ¼ 8 hours. Knowing the MEC, the MTC, and the drug’s half-life (or its elimination rate constant r), we now want to design a therapeutic regimen with maximal benefits.

The yield b a achieves its maximum at b ¼ (the reader YðbÞ ¼ bP ¼ bK 1 À a 2 should verify this), which shows that the maximum sustainable yield in this case is a a a aK MSY ¼ Ymax ¼ Y : ¼ K 1À ¼ 2 2 2a 4 In this example, we made the assumption that yield is proportional to population size. This assumption is certainly justified when fishing or hunting is involved. As our next exercise shows, in more controlled environments, the harvesting rate may be independent from the population size.

For P(0) < K, the population size P(t) is continuously increasing to K when t ! 1 while if P(0) > K, the population size P(t) is continuously decreasing to K when t ! 1 (Figure 1-8). The Verhulst model offers cases of considerably more complex long-term behavior—the system could converge to an equilibrium state through oscillations, exhibit lack of convergence because of periodic oscillatory behavior, or be driven to chaos. Pn so that xn is the fraction of the maximum K population the environment can sustain.

### An invitation to biomathematics by Robeva R.S., et al.

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