1. China-Australia Joint Research Centre for Infectious Diseases, School of Public Health, Xi’an Jiaotong University Health Science Center
2. Key Laboratory for Disease Prevention and Control and Health Promotion of Shaanxi
3. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, China
4. Department of Mathematics, University of Florida, Gainesville, Florida, USA
5. State Key Laboratory of Infectious Disease Prevention and Control (SKLID), National Center for AIDS/STD Control and Prevention (NCAIDS), Chinese Center for Disease Control and Prevention (China CDC), Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, Beijing
6. Guangxi Key Laboratory of Major Infectious Disease Prevention Control and Biosafety Emergency Response, Guangxi Center for Disease Control and Prevention, Nanning, China.