The needs of mitigating COVID-19 epidemic prompt policymakers to make public health-related decision under the guidelines of science. Tremendous unstructured COVID-19 publications make it challenging for policymakers to obtain relevant evidence. Knowledge graphs (KGs) can formalize unstructured knowledge into structured form and have been used in supporting decision-making recently. Here, we introduce a novel framework that can extract the COVID-19 public health evidence knowledge graph (CPHE-KG) from papers relating to a modelling study. We screen out a corpus of 3096 COVID-19 modelling study papers by performing a literature assessment process. We define a novel annotation schema to construct the COVID-19 modelling study-related IE dataset (CPHIE). We also propose a novel multi-tasks document-level information extraction model SS-DYGIE++ based on the dataset. Leveraging the model on the new corpus, we construct CPHE-KG containing 60,967 entities and 51,140 relations. Finally, we seek to apply our KG to support evidence querying and evidence mapping visualization. Our SS-DYGIE++(SpanBERT) model has achieved a F1 score of 0.77 and 0.55 respectively in document-level entity recognition and coreference resolution tasks. It has also shown high performance in the relation identification task. With evidence querying, our KG can present the dynamic transmissions of COVID-19 pandemic in different countries and regions. The evidence mapping of our KG can show the impacts of variable non-pharmacological interventions to COVID-19 pandemic. Analysis demonstrates the quality of our KG and shows that it has the potential to support COVID-19 policy making in public health.