text: Several mathematical models of chemotaxis were developed depending on the type of
  * Migration (e.g., basic differences of bacterial swimming, movement of unicellular eukaryotes with cilia/flagellum and amoeboid migration)
  * Physico-chemical characteristics of the chemicals (e.g., diffusion) working as ligands
  * Biological characteristics of the ligands (attractant, neutral, and repellent molecules)
  * Assay systems applied to evaluate chemotaxis (see incubation times, development, and stability of concentration gradients)
  * Other environmental effects possessing direct or indirect influence on the migration (lighting, temperature, magnetic fields, etc.)
  Although interactions of the factors listed above make the behavior of the solutions of mathematical models of chemotaxis rather complex, it is possible to describe the basic phenomenon of chemotaxis-driven motion in a straightforward way. Indeed, let us denote with  the spatially non-uniform concentration of the chemo-attractant and  as its gradient. Then the chemotactic cellular flow (also called current)  that is generated by the chemotaxis is linked to the above gradient by the law:where  is the spatial density of the cells and  is the so-called Chemotactic coefficient -  is often not constant, but a decreasing function of the chemo-attractant. For some quantity  that is subject to total flux  and generation/destruction term , it is possible to formulate a continuity equation:
  where  is the divergence. This general equation applies to both the cell density and the chemo-attractant. Therefore, incorporating a diffusion flux into the total flux term, the interactions between these quantities are governed by a set of coupled reaction-diffusion partial differential equations describing the change in  and :where  describes the growth in cell density,  is the kinetics/source term for the chemo-attractant, and the diffusion coefficients for cell density and the chemo-attractant are respectively  and .
  Spatial ecology of soil microorganisms is a function of their chemotactic sensitivities towards substrate and fellow organisms. The chemotactic behavior of the bacteria was proven to lead to non-trivial population patterns even in the absence of environmental heterogeneities. The presence of structural pore scale heterogeneities has an extra impact on the emerging bacterial patterns.