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Team:NYMU-Taipei/modeling/m2
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<p>$$\frac{dx_i}{dt} = \mu_{x_i}{x_i} = ( {\mu_{\max_i}}\frac{s}{k_s+s}-k_{d_i} )x_i$$</p> | <p>$$\frac{dx_i}{dt} = \mu_{x_i}{x_i} = ( {\mu_{\max_i}}\frac{s}{k_s+s}-k_{d_i} )x_i$$</p> | ||
<p>$$\frac{ds}{dt} = \sum\limits_i(-\frac{\mu_{x_i}x_i}{Y_i})$$</p> | <p>$$\frac{ds}{dt} = \sum\limits_i(-\frac{\mu_{x_i}x_i}{Y_i})$$</p> | ||
| - | <p>$$\frac{d[acidic | + | <p>$$\frac{d[\text{acidic substance}]}{dt} = \sum\limits_i(\alpha_i\frac{dx_i}{dt}+\beta{x_i})$$</p> |
<p>$\alpha_i,\beta_i$: related coefficient</p> | <p>$\alpha_i,\beta_i$: related coefficient</p> | ||
<h1>result</h1> | <h1>result</h1> | ||
Revision as of 11:13, 5 August 2014
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purpose & introduction
How many S. mutans should we kill?
It is bacteria’s acid production that causes caries, so we build a model to know how much S. mutans we should kill to prevent caries.
system
(equation from competition model):
$$\frac{dx_i}{dt} = \mu_{x_i}{x_i} = ( {\mu_{\max_i}}\frac{s}{k_s+s}-k_{d_i} )x_i$$
$$\frac{ds}{dt} = \sum\limits_i(-\frac{\mu_{x_i}x_i}{Y_i})$$
$$\frac{d[\text{acidic substance}]}{dt} = \sum\limits_i(\alpha_i\frac{dx_i}{dt}+\beta{x_i})$$
$\alpha_i,\beta_i$: related coefficient
