Stability analysis of hand foot and mouth infectious disease model with time delay and non monotonic contact rate
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Based on the epidemic characteristics of the hand- foot- mouth disease, using non monotonic contact rate of the dependent variable function K (S) to represent a series of external and internal factors, not in the hand, foot and mouth disease dynamics model introduced in double time delay, and thus establish a touch delay and have not monotonous content, foot and mouth disease model, and then linearized model can be converted to a linear system, discusses the model disease- free equilibrium and the existence and stability of the endemic equilibrium, told of the disease- free equilibrium model is the only, and in 5 cases, the existence of the endemic equilibrium is discussed. Finally, it is found that the disease- free equilibrium is unstable when the basic regeneration number is greater than 1, and the local disease equilibrium is asymptotically stable.
Hand-foot-mouth disease, basic regeneration number, no disease equilibrium, local disease equilibrium