Modelling the spread of carrier-dependent infectious diseases with environmental effect

Many infectious diseases spread by carriers such as flies, ticks, mites, snails, etc. In this paper an SIS model for carrier-dependent infectious diseases, like cholera, diarrhea, etc. caused by direct contact of susceptibles with infectives as well as by carriers is proposed and analyzed assuming the growth of both the human and the carrier populations logistic. It is assumed further that the density of carrier population increases with the increase in the cumulative density of discharges by the human population into the environment. The mathematical model is analyzed for the following two cases: (i) the rate of cumulative environmental discharges Q is a constant, and (ii) the rate of cumulative environmental discharges Q is a function of the population density. This model is analyzed using usual theory of differential equations and computer simulation. By computer simulation it is concluded that if the growth of carrier population caused by conducive household discharges increases, the spread of the infectious disease increases. 2003 Elsevier Inc. All rights reserved.