The Stability Analysis and Transmission Dynamics of the SIR Model with Nonlinear Recovery and Incidence Rates (original) (raw)

Abstract

In the present paper, the SIR model with nonlinear recovery and Monod type equation as incidence rates is proposed and analyzed. The expression for basic reproduction number is obtained which plays a main role in the stability of disease-free and endemic equilibria. The nonstandard finite difference (NSFD) scheme is constructed for the model and the denominator function is chosen such that the suggested scheme ensures solutions boundedness. It is shown that the NSFD scheme does not depend on the step size and gives better results in all respects. To prove the local stability of disease-free equilibrium point, the Jacobean method is used; however, Schur–Cohn conditions are applied to discuss the local stability of the endemic equilibrium point for the discrete NSFD scheme. The Enatsu criterion and Lyapunov function are employed to prove the global stability of disease-free and endemic equilibria. Numerical simulations are also presented to discuss the advantages of NSFD scheme as wel...

Key takeaways

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  1. The NSFD scheme provides reliable numerical solutions for SIR models with nonlinear recovery and incidence rates.
  2. Basic reproduction number (R0) is pivotal for assessing local and global stability of equilibria.
  3. The model demonstrates both local asymptotic stability (LAS) and global asymptotic stability (GAS) for disease equilibria.
  4. Numerical simulations validate theoretical findings and highlight the NSFD scheme's advantages over traditional methods.
  5. Monod type equations account for preventive measures in disease transmission dynamics, enhancing model accuracy.

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