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Modelling and stability of epidemic model with free-living pathogens growing in the environment
Yifan Xing,Liang Zhang
Keywords:Epidemics, Free-living pathogen, Basic reproduction number, Global stability.
Abstract:
      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 $R_0$. If $R_0<1$, the disease free equilibrium is globally asymptotically stable, and if $R_0>1$, the endemic equilibrium is globally asymptotically stable. Some numerical simulations are also carried out to illustrate our analytical results.