Study of a Host-pathogen Reaction Diffusion Model with Asymptomatic Infection and Multiple Infection Routes
Based on the spatial heterogeneity,the asymptomatic hosts and the mul-tiplicity of pathogen transmission routes,a model of reactive diffusion host-pathogen with asymptomatic hosts and multiple infection routes is proposed,which is discussed the existence and uniqueness of the global positive solution of the model by using semi-group theory.Further,according to the spectral radius method of the next generation operator,the basic reproduction number R0 of the model is given,and the extinction and persistence of the disease are described.That is,if R0＜1,the disease-free steady state is globally asymptotically stable;while if R0＞1,the disease is uniformly persis-tent and the model admits at least one endemic steady state.In addition,the global asymptotic stability of the disease-free and endemic equilibrium states of the model in a spatially homogeneous environment is obtained by constructing suitable Lyapunov functions.Finally,some numerical simulations are conducted to explain the main the-oretical results and to explore the influence of diffusion rates on the distribution of infected hosts.
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