Global Stability Analysis of Typhoid Fever Model

  • Olumuyiwa James Peter Department of Mathematics, University of Ilorin, Ilorin, Nigeria
  • Ajimot Folasade Adebisi Department of Mathematics, Osun State University, Oshogbo, Osun State, Nigeria
  • Michael Oyelami Ajisope Department of Mathematics, Federal University Oye-Ekiti, Oye-Ekiti, Nigeria
  • Fidelis Odedishemi Ajibade Department of Civil Engineering, Federal University of Technology, Akure, Nigeria
  • Adesoye Idowu Abioye Department of Mathematics, University of Ilorin, Ilorin, Nigeria
  • Festus Abiodun Oguntolu Department of Mathematics, Federal University of Technology, Minna, Niger State, Nigeria
Keywords: typhoid fever, equilibria, stability, nonlinear mathematical model

Abstract

We analyze with four compartments a deterministic nonlinear mathematical model of typhoid fever transmission dynamics. Using the Lipchitz condition, we verified the existence and uniqueness of the model solutions to establish the validity of the model and derive the equilibria states of the model, i.e. disease-free equilibrium (DFE) and endemic equilibrium (EE). The computed basic reproductive number R0 was used to establish that the disease-free equilibrium is globally asymptotically stable when its numerical values are less than one while the endemic equilibrium is locally asymptotically stable when its values are greater than one. In addition, the Lyapunov function was applied to investigate the stability property for the (DFE). The model was numerically simulated to validate the results of the analysis.

Published
2020-06-30
Issue
Vol 20 No 2 (2020): Advances in Systems Science and Applications
Section
Articles