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

By Robeva R.S., et al.

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A POPULATION GROWTH MODEL WITH DELAY Despite substantial improvement over the ‘‘unlimited’’ population dP ¼ rPðtÞ; the logistic growth model (1-12) has one major growth model dt drawback—replacing r with the factor rðPðtÞÞ ¼ að1 À PðtÞ=KÞ only provides a mechanism for the net per capita growth rate to adjust itself based on current population size. The logistic model (1-24) is entirely based on the present and disregards, to a large extent, the past. In reality, certain delay effects are essential, although this logistic model does not account for them.

The total concentration at 12:00 noon is then equal to: CeÀ11r þ CeÀ8r þ CeÀ5r þ CeÀ2r ¼ CeÀ2r ðeÀ9r þ eÀ6r þ eÀ3r þ 1Þ: (1-31) For a more compact form of Eq. (1-31), observe that if b ¼ eÀ3r, then b2 ¼ eÀ6r, and b3 ¼ eÀ9r. Thus, the concentration becomes: CeÀ2r ðb3 þ b2 þ b þ 1Þ: (1-32) From this example, we can extract a more general result. In the term eÀ3r, the number 3 arises from the time between dosages. M. M. M. M. 2 CeÀ2r Time of Dose TABLE 1-6. Contribution of multiple doses to serum drug concentration.

Taubes, C. H. (2001). Modeling differential equations in biology. Upper Saddle River, NJ: Prentice Hall. S. Environmental Protection Agency. (2000, April). Global warming and our changing climate. Answers to frequently asked questions (EPA Publication No. 430-F-00-011). S. Government Printing Office. com Home page for BERKELEY MADONNA. Download a fully functional trial version, and investigate the tutorials here. com Introduction to Dynamical Systems An Invitation to Biomathematics Home page for the suppliers of MATLAB.