Modeling the effect of time delay in controlling the carrier dependent infectious disease – Cholera

A delay mathematical model for the control of cholera epidemic is proposed and analyzed. It is assumed that the disease spreads through carriers, which makes the human food contaminated by transporting bacteria from the environment. It is also assumed that insecticides are used to control the carriers with the rate proportional to the density of carriers. The analysis of model shows that the disease may be controlled by spraying insecticides but a longer delay in spraying insecticides may destabilize the system. Simulation is also carried out to support the analytical results.