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The Well-posedness of Solutions to PDE Model of Infectious Dynamics

RONG Cui-xian,SHENG Qi-rong(College of Mathematics and Systems Science,Xinjiang University,Wulumuqi,Xinjiang 830046,China)  
Infectious dynamics inspects the influence of infectious disease for population distribution and searches for developing trend and law of infectious disease so that we can take precautions against it and control it by suitable measures and improve population quality and living standard of the whole nation.Considering people's subjective efforts for guarding against infections,in this paper,an infectious model with preventive-separated measure is discussed and theory basis is provided for forecasting infectious developing process by using the model.We get local existence uniqueness of the solution by characteristic method and fixed point theorem and prove the whole existence uniqueness of the solution and continuously dependent of solutions for initial value by making use of prior estimation and important Gronwell inequality.In the end,smooth of the solution is discussed.
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