Modelling the spread of bacterial infectious disease with environmental effect in a logistically growing human population

In this paper, an SIS model for bacterial infectious disease is proposed and analyzed where the growth of human population is logistic. It is assumed that disease is transmitted by direct contact of susceptibles with infectives as well as by bacteria. Further it is assumed that bacteria population too is growing logistically in the environment and it's growth is enhanced due to the environmental discharges caused by human sources. The stability of the equilibria are studied by using the theory of differential equation and computer simulation. It is concluded from the analysis that the spread of the infectious disease increases when the growth of bacteria caused by conducive environmental discharge due to human sources increases.