Effect of incubation delay and pollution on the transmission dynamics of infectious disease.

Emerging infectious diseases pose serious threat to human population. Studies suggest that there is correlation between population's pollution status and emerging infectious diseases. We propose a delayed SIS model to examine the effects of environmental contamination on human health, which can lead to the spread of numerous diseases. A threshold parameter called basic reproduction number has been obtained for the system. Within the sight of time delay, stability analysis for equilibrium points has been obtained. The existence of Hopf bifurcation around endemic equilibrium point pertaining to time delay as a critical parameter is observed. Our study suggests that pollution can have detrimental effects on the spread of disease. Analytical results are supported by numerical simulations.