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

$$\frac{dx_i}{dt} = \mu_{x_i}{x_i} = ( {\mu_{\max_i}}\frac{s}{k_s+s}-k_{d_i} )x_i$$

$$\frac{ds}{dt} = \sum\limits_i(-\frac{\mu_{x_i}x_i}{Y_i})$$

$$\frac{d[\text{acidic substance}]}{dt} = \sum\limits_i(\alpha_i\frac{dx_i}{dt}+\beta{x_i})$$

$\alpha_i,\beta_i$: related coefficient