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Global stability analysis for a model with carriers and non-linear incidence rate
Miller Cerón Gómez1, Eduardo Ibarguen Mondragon1, Patricia Lopez Molano2
1Departmento de Matemáticas, Universidad de Nariño, Pasto, Colombia.
Journal of Biological Dynamics
|June 6, 2020
Summary
This study analyzes a Susceptible-Carrier-Infectious-Recovered (SCIR) epidemiological model with a non-linear incidence rate. The research proves the global asymptotic stability of both disease-free and disease equilibrium states.
Area of Science:
- Epidemiology
- Mathematical Biology
- Dynamical Systems
Background:
- Understanding disease dynamics is crucial for public health interventions.
- Mathematical models are essential tools for analyzing infectious disease spread.
- Previous models often used linear incidence rates, which may not capture complex transmission dynamics.
Purpose of the Study:
- To analyze a Susceptible-Carrier-Infectious-Recovered (SCIR) epidemiological model.
- To investigate the impact of a general non-linear incidence rate on disease dynamics.
- To determine the stability of disease-free and disease equilibrium states.
Main Methods:
- Development of a SCIR epidemiological model.
- Inclusion of a general non-linear incidence rate function.
- Application of the Lyapunov direct method for stability analysis.
Main Results:
- The model demonstrates two equilibrium points: one disease-free and one with disease presence.
- Sufficient conditions were identified for the global asymptotic stability of both equilibrium points.
- The non-linear incidence rate significantly influences the model's stability properties.
Conclusions:
- The SCIR model with a non-linear incidence rate provides a robust framework for studying infectious diseases.
- The stability analysis confirms predictable long-term outcomes under specific conditions.
- This research contributes to the theoretical understanding of disease persistence and eradication.
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