Abstract
In this paper, considering the impact of environmental change on trachoma transmission, we establish a periodic trachoma epidemic model on heterogeneous networks, which is a non-autonomous model. We prove theoretically the existence of basic reproduction number shown by R0. And then, we demonstrate that the disease-free periodic solution is globally asymptotically stable if R0<1, and there exists a unique positive periodic solution which is also is globally asymptotically stable if R0>1. The method obtained in this paper can be seen as an extension for proving the global stability of the high-dimensional periodic epidemic model on heterogeneous networks. And our results provide theoretical basis for decision-makers to make control strategies.
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