Explicit Formula of the Basic Reproduction Number for Heterogeneous Age‐Structured SIR Epidemic Model

ABSTRACT There are still a lot of unsolved problems in the classical age‐structured SIR epidemic model. Generally, the explicit formula of basic reproduction number is only available under the case of separable mixing. The explicit formula of for heterogeneous age‐structured SIR model is given in this paper. The existence, uniqueness, and stability results of the heterogeneous model are discussed. We conclude that the disease free steady states is global stable if , the endemic steady state is exists, unique and locally stable if . A number of numerical examples are given to support the theory. The result is a generalization of isolation, separability and proportion mixing.