s.n eluozo - Subaka Nigeria Limited Port Harcourt Rivers State of Nigeria.

Bacterial migration in soil and water environment under the influence of various soil characteristics has been expressed, the concepts is to monitor the transport process at various condition, bacterial known to have a lot of variety of behaviour, these condition were considered when the system are developed, the major variables in the system are porosity of the soil, these parameters determine the rate of bacterial deposition at every formation, degree of porosity also has a lots of variation, therefore bacterial behaviour are influenced by the rate of soil porosity, the system developed an equation considering this parameters as a major role in fast migration of bacterial under the influence of this variables, other variables were considered that played other role in the transport were expressed .in the system, the developed mathematical equation that expresses this study of bacterial were derived, applying slit method techniques and Bernoulli’s method of separation of variables, the developed equation are derived applying these concept were the equation express the parameters at various state with their functions at different phase of the transport process expressed denoted with mathematical tools, the model express base on the behaviour of the bacterial at different phase on the transport process to soil and water environment.

Mathematical model; Bacterial migration; Soil; Water; Environment