We present an SIR epidemic model with constant recruitment and two control variables. We intend to control the susceptible and infected individuals with vaccination and treatment strategies. We analyze the local stability of the disease-free and endemic equilibrium, respectively. The main theorem shows that if  then the disease-free equilibrium is locally asymptotically stable and the phase will vanish out of the host and if  then a unique endemic equilibrium is also locally asymptotically stable and the disease persists at the endemic steady state. We established the effect of the control strategies on the dynamical behaviour of the system using numerical simulation to illustrate.

SIR epidemic model, stability, Lyapunov function, equilibrium state, vaccination, treatment, numerical simulation.

Received: July 5, 2021; Revised: September 25, 2021; Accepted: October 16, 2021; Published: December 7, 2021

How to cite this article: A. Nwagwo and E. A. Bakare, Stability analysis of an SIR epidemic model and effect of control strategy with constant recruitment, Far East Journal of Dynamical Systems 33(2) (2021), 115-130. DOI: 10.17654/0972111821002

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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