On the Dynamics of an Epidemic Model with Multiple Transmission Ways and Pollution

An epidemiological model with existence of disease and pollutant has been proposed and analyzed, the formulation of the model is described and the uniqueness and boundness of solution of the system are discussed. The stability analysis of the non-negative equilibrium points is performed. Finally numerical simulation is used to show that increasing the values of external disease transmit ion rate and rates at which the susceptible, infected and recovered individuals decreasing due to the toxicant in proposed model, the population will die out.