Open Journal of Mathematical Sciences

Vol. 3 (2019), Issue 1, pp. 417 – 432
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2019.0084

Analysis of the dynamics of avian influenza A(H7N9) epidemic model with re-infection

Abayomi Samuel OKE\(^1\), Oluwafemi Isaac BADA
Department of Mathematical Sciences, Adekunle Ajasin University, P.M.B. 001, Akungba Akoko, Ondo State, Nigeria.; (A.S.O)
Department of Mathematical Sciences, University of Benin, P.M.B. 1154, Benin City, Nigeria.; (O.I.B)
\(^{1}\)Corresponding Author: okeabayomisamuel@gmail.com, abayomi.oke@aaua.edu.ng

Copyright © 2019 Abayomi Samuel OKE, Oluwafemi Isaac BADA. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Received: May 13, 2019 – Accepted: November 15, 2019 – Published: December 7, 2019

Abstract

Since the emergence of the avian influenza A(H7N9) in the year 2013 in China, several researches have been carried out to investigate the spread. In this paper, a mathematical model describing the transmission dynamics of avian influenza A(H7N9) between human and poultry proposed by Li et al. [1] is modified by introducing re-infections into the susceptible human compartment. The method of next generation matrix is used to calculate the reproduction number. We also establish the local and global stability of the equilibria using Lyapunov functions. Finally, we use numerical simulations to validate our results.

Keywords:

Avian influenza A(H7N9), reproduction number, Lyapunov functions, next generation matrix, re-infections.