A new generalized version of logistic growth is proposed to study the dynamics of logistically growing population with a chronic infection in the population. A modification is made due to the change in the birth and death rates in the infectious population with chronic disease. A nonlinear mathematical model is proposed for each of the cases when growth rate (birth minus death rate) in the infected class is positive and negative. There are three nonnegative equilibrium points out of which two are boundary equilibrium points in which there is no disease and the endemic equilibrium in which disease remains present. The local as well as global stability depends on the basic reproduction number . The disease free equilibrium is globally stable if basic reproduction number is smaller than one. The endemic equilibrium point exists and become globally stable when basic reproduction number exceeds one.

Logistic growth; carrying capacity; infectious disease; basic reproduction number; stability.