Model of bacteria growth and death with killing gene endowed

Generally in the open environment, the population density of bacteriaΨ, the nutrition density φ_i, and the killing signal density ρ can be modeled by the following system of partial differential equation:

With

Where the functional dependence of ρ is to be determined case by case.

Special case

In our project, we assumed a lactose analogue in close environment and homogeneous bacteria culture:

This is a system of two asymptotic equations with environment dependent parameters, which will have to be determined experimentally.