The Stability Analysis and Transmission Dynamics of the SIR Model with Nonlinear Recovery and Incidence Rates
Mathematical Problems in Engineering
; 2022, 2022.
Article
in English
| ProQuest Central | ID: covidwho-2053425
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 well as to strengthen the theoretical results. Numerical simulations specify that the NSFD scheme preserves the important properties of the continuous model. Consequently, they can produce estimates which are entirely according to the solutions of the model.
Engineering; Infections; Infectious diseases; Population; Partial differential equations; Pneumonia; Mathematical models; Epidemiology; Finite difference method; Dynamic stability; Pandemics; Equilibrium; Epidemics; Quarantine; Recovery; Stability analysis; Dynamic tests; Disease prevention; Liapunov functions; Coronaviruses; Tuberculosis; Tropical diseases; COVID-19; Disease transmission
Full text:
Available
Collection:
Databases of international organizations
Database:
ProQuest Central
Type of study:
Observational study
Language:
English
Journal:
Mathematical Problems in Engineering
Year:
2022
Document Type:
Article
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