A cattle rancher discovers a viral disease spreading among his 4000 cattle. Suppose the rate at which the disease spreads is proportional to the product of the number of cattle that have the disease and the number that do not. Write a differential equation that describes this scenario.

Question

A cattle rancher discovers a viral disease spreading among his 4000 cattle.  Suppose the rate at which the disease spreads is proportional to the product of the number of cattle that have the disease and the number that do not.  Write a differential equation that describes this scenario.

anonymous · Answer

let P be the diseased cattle
$$\frac{ dP }{ dt } = kP(4000-P)$$