About the Authors

Sanyi Tang

Affiliation College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, People's Republic of China

Yanni Xiao

Affiliation Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, People's Republic of China

Youping Yang

Affiliation Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, People's Republic of China

Yicang Zhou

Affiliation Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, People's Republic of China

Jianhong Wu

Affiliation Centre for Disease Modeling, York University, Toronto, Ontario, Canada

Zhien Ma

zhma@mail.xjtu.edu.cn

Affiliation Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, People's Republic of China

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: ST YX YZ JW ZM. Analyzed the data: ST. Contributed reagents/materials/analysis tools: ST YY. Wrote the paper: ST YX JW.