A proportion (p) of the infected individuals get treatment and their natural recovery rate (γ1) increases
by the relative rate of shedding λ. Recovered Individuals increases by the inflow of infected
individuals who get recover from cholera infection (either by natural recovery or by recovery due to effect
of treatment). Recover class decreases due to natural death rate (d3) and those individuals who losses
natural immunity to cholera at a rate (δ). Vibrio cholerae in infected human intestines (VI ) increases at
a growth rate (α). It decreases due to natural death at a rate (d4) and also due to human shedding at
a rate (η). Those humans who get treated have their relative rate of shedding is reduced by a fraction
ψ. Vibrio cholerae in the environment is increases due to natural shedding of the infected human at a
rate (η) and decreases due to natural death in the environment at a rate (d4). We consider the cholera
transmission to be a bilinear functional interaction between susceptible human population and the vibrio
cholerae population in the environment (VE), which has the following form: