Analysis of the Dynamics of SI-SI-SEIR Avian Influenza A(H7N9) Epidemic Model with Re-infection

  • Oluwafemi I. Bada Department of Mathematics, University of Benin, Nigeria
  • Abayomi S. Oke Department of Mathematical Sciences, Adekunle Ajasin University, Nigeria and Department of Mathematics and Actuarial Science, Kenyatta University, Kenya
  • Winfred N. Mutuku Department of Mathematics and Actuarial Science, Kenyatta University, Kenya
  • Patrick O. Aye Department of Mathematical Sciences, Adekunle Ajasin University, Nigeria
Keywords: avian influenza A(H7N9), reproduction number, Lyapunov functions, next generation matrix, re-infections


The spread of Avian influenza in Asia, Europe and Africa ever since its emergence in 2003, has been endemic in many countries. In this study, a non-linear SI-SI-SEIR Mathematical model with re-infection as a result of continuous contact with both infected poultry from farm and market is proposed. Local and global stability of the three equilibrium points are established and numerical simulations are used to validate the results.


V. C. C. Cheng, S-C. Wong, K. K. W. To, P. L. Ho and K-Y. Yuen, Preparedness and proactive infection control measures against the emerging novel coronavirus in China, Journal of Hospital Infection 104(3) (2020), 254-255.

Fengxiang Song, Nannan Shi, Fei Shan, Zhiyong Zhang, Jie Shen, Hongzhou Lu, Yun Ling, Yebin Jiang and Yuxin Shi, Emerging 2019 novel coronavirus (2019-{nCoV}) pneumonia, Radiology 295(1) (2020), 210-217.

Junbo Chen, Huachen Zhu, Peter W. Horby, Qianli Wang, Jiaxin Zhou, Hui Jiang, Liwei Liu, Tianchen Zhang, Yongli Zhang, Xinhua Chen, Xiaowei Deng, Birgit Nikolay, Wei Wang, Simon Cauchemez, Yi Guan, Timothy M. Uyeki and Hongjie Yu, Specificity, kinetics and longevity of antibody responses to avian influenza A(H7N9) virus infection in humans, Journal of Infection 80 (2020), 310-319.

S. Iwami, Y. Takeuchi and X. Liu, Avian-human influenza epidemic model, Mathematical Biosciences 207(1) (2007), 1-25.

Z. Liu and C. T. Fang, A modeling study of human infections with avian influenza A H7N9 virus in mainland China, International Journal of Infectious Diseases 41 (2015), 73-78.

S. Che, Y. Xue and L. Ma, The stability of highly pathogenic avian influenza epidemic model with saturated contact rate, Applied Mathematics 5(21) (2014), 3365-3371.

Y. Chen and Y. Wen, Global dynamic analysis of a H7N9 avian-human influenza model in an outbreak region, Journal of Theoretical Biology 367 (2015), 180-188.

S. Sharma and V. H. Badshah and V. Gupta, The highly pathogenic avian influenza epidemic model with vertical transmission function in poultry, IOSR Journal of Mathematics (IOSR-JM) 12 (2016), 40-48.

Yun Li, Peng Qin and Juping Zhang, Dynamics analysis of avian influenza A(H7N9) epidemic model, Discrete Dynamics in Nature and Society 2018 (2018), Art. ID 7485310, 12 pp.

A. S. Oke and O. I. Bada, Analysis of the dynamics of avian influenza A(H7N9) epidemic model with re-infection, Open Journal of Mathematical Sciences 3 (2019), 417-432.

Shuo Su, Yuhai Bi, Gary Wong, Gregory C. Gray, George F. Gao and Shoujun Lia, Epidemiology, evolution, and recent outbreaks of avian influenza virus in China, J. Virol. 89 (2015), 8671-8676.

Mai-Juan Ma, Yang Yang and Li-Qun Fang, Highly pathogenic avian H7N9 influenza viruses: recent challenges, Trends in Microbiology 27(2) (2019), 93-95.

Juping Zhang, Yun Li, Zhen Jin and Huaiping Zhu, Dynamics analysis of an avian influenza A (H7N9) epidemic model with vaccination and seasonality, Complexity 2019 (2019), Art. ID 4161287, 15 pp.

Zeng Li, Jingying Fu, Gang Lin and Dong Jiang, Spatiotemporal variation and hotspot detection of the avian influenza A(H7N9) virus in China, 2013-2017, International Journal of Environmental Research and Public Health 16(4) (2019), 648.

Wenming Jiang, Guangyu Hou, Jinping Li, Cheng Peng, Suchun Wang, Shuo Liu, Qingye Zhuang, Liping Yuan, Xiaohui Yu, Yang Li, Jingjing Wang and Hualei Liu, Antigenic variant of highly pathogenic avian influenza A(H7N9) virus, China, 2019, Emerging Infectious Diseases 26(2) (2020), 379-380.

Chang Gao, Yeming Wang, Xiaoying Gu, Xinghua Shen, Daming Zhou, Shujun Zhou, Jian-an Huang, Bin Cao and Qiang Guo, Association between cardiac injury and mortality in hospitalized patients infected with avian influenza A (H7N9) virus, Critical Care Medicine 48 (2020), 451-458.

P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences 180 (2002), 29-48.

J. P. LaSalle, Stability theory for ordinary differential equations, Journal of Differential Equations 4(1) (1968), 57-65.

J. P. LaSalle, The Stability of Dynamical Systems, SIAM, America 25 (1976).

WHO, Cumulative number of confirmed human cases of avian influenza A(H5N1) reported to WHO, World Health Organization, 2017.

WHO, Number of confirmed human cases of avian influenza A (H7N9) reported to World Health Organization, World Health Organization, 2013.

D. J. Alexander, A review of avian influenza in different bird species, Veterinary Microbiology 74(1-2) (2000), 3-13.

E. C. J. Claas, A. D. M. E. Osterhaus and R. van Beek, Human influenza A H5N1 virus related to a highly pathogenic avian influenza virus, The Lancet 351(9101) (1998), 472-477.

How to Cite
Bada, O. I., Oke, A. S., Mutuku, W. N., & Aye, P. O. (2020). Analysis of the Dynamics of SI-SI-SEIR Avian Influenza A(H7N9) Epidemic Model with Re-infection. Earthline Journal of Mathematical Sciences, 5(1), 43-73.