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To understand the impact of free-living pathogens (FLP) on the epidemics, an epidemic model with FLP is constructed. The global dynamics of our model are determined by the basic reproduction number R0. If R0 < 1, the disease free equilibrium is globally asymptotically stable, and if R0 > 1, the endemic equilibrium is globally asymptotically stable. Some numerical simulations are also carried out to illustrate our analytical results.

MODELLING AND STABILITY OF EPIDEMIC MODEL WITH FREE-LIVING PATHOGENS GROWING IN THE ENVIRONMENT