purpose & introduction

Why not kill all S. mutans in our cavity?

Without S. mutans, other bacteria will grow rampantly, so we build a model to demonstrate the multi-species competition of dental plaque bacterium.

system

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

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

$x_i$:dental plaque bacteria population

$s$:substrate of bacteria, such as glucose.

$\mu_{x_i}$:population growth rate of species i

$k_s$:amount of substrate remaining when the growth rate is half of maximum

$k_{d_i}$:population death rate of species i

$Y_i$:bacteria yield ratio of species i