Dynamical behavior of a Rotavirus transmission model with an environmental effects

Rotavirus is one of the leading to severe diarrhea in infants and children throughout both developed and developing countries. Rotavirus infection is still a significant cause of death in infants and children. It has various mode of transmissions, those are, human to human, human to environment, and environment to human. In this paper, a SIRE (Susceptible, Infected, Recovered and Environment of pathogens) epidemic model is proposed and the dynamics of this model is analyzed by both theoretical and numerical means. Firstly, the basic reproduction number ( R0) which determines whether the disease is extinct or not, is derived. By Routh-Hurwitz criterion theory, we prove that the disease-free equilibrium is unstable and the endemic equilibrium is asymptotically stable when R0 is greater than one. The analysis results are confirmed by some numerical simulations.