3.5.1. Chemotaxis

The *E. coli* bacteria moves inside the human intestine searching for a nutrient-rich location with the help of locomotory organelles called flagella. This search of the bacteria for nutrients is called chemotaxis. With the help of flagella, the bacterium can swim or tumble, and these are the basic functions performed by the bacterium during the chemotaxis process [75]. In the swimming case, the bacterium moves continuously in some direction, but in the tumble case, it changes its direction randomly. The chemotactic method in terms of a mathematical equation is given as:

$$\theta^{\rm i}(\mathbf{j}+1,\mathbf{k},\mathbf{l}) = \theta^{\rm i}(\mathbf{j},\mathbf{k},\mathbf{l}) + \mathbf{C}(\mathbf{i}) \frac{\Delta(\mathbf{i})}{\sqrt{\Delta^{\rm T}(\mathbf{i})}.\Delta(\mathbf{i})} \tag{19}$$

where

θ<sup>i</sup>(j + 1, k, l) is the ith bacterium at jth chemotactic for kth reproductive and lth elimination dispersal step

