A Delay Mathematical Model for Spread of Carrier Dependent Infectious Diseases

Abstract

In this paper, a non-linear delay mathematical model for spread of carrier dependent infectious diseases has been proposed and analyzed. In the modeling process it is assumed that disease spreads due to the direct contact between susceptible and infective as well as through carriers. It is also assumed that the infective individuals transmit disease to susceptible individuals after some time lag ‘τ ’. It is further assumed that carriers follow logistic growth, whose growth rate depends on the human related activities. The equilibriums of the model have been obtained and their stability discussed. The critical value of time delay τ for Hopf-bifurcation has been obtained analytically.