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Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidence
M G M Gomes1, A Margheri, G F Medley
1Instituto Gulbenkian de Ciência, Apartado 14, 2781-901 Oeiras, Portugal.
Journal of Mathematical Biology
|June 9, 2005
Summary
This study analyzes epidemiological models transitioning between SIR and SIS frameworks, exploring nonlinear infection forces. It identifies conditions for complex dynamics like backwards bifurcations and oscillations.
Area of Science:
- Epidemiology
- Mathematical Biology
- Dynamical Systems Theory
Background:
- Epidemiological models are crucial for understanding disease spread.
- Transitions between Susceptible-Infectious-Resistant (SIR) and Susceptible-Infectious-Susceptible (SIS) frameworks represent different disease dynamics.
- Nonlinear force of infection functions can lead to complex population dynamics.
Purpose of the Study:
- To analyze the dynamics of two families of epidemiological models.
- To investigate transitions from SIR to SIS frameworks.
- To determine conditions for specific dynamic behaviors like backwards bifurcations, oscillations, and Bogdanov-Takens points.
Main Methods:
- Analysis of epidemiological models.
- Mathematical modeling of disease transmission dynamics.
- Investigation of nonlinear force of infection functions based on infectious individuals' density.
Main Results:
- Characterization of two model families representing SIR to SIS transitions.
- Identification of conditions leading to backwards bifurcations.
- Determination of criteria for oscillations and Bogdanov-Takens points in the models.
Conclusions:
- The study provides insights into the complex dynamics of epidemiological models.
- Understanding these dynamics is essential for predicting and controlling infectious diseases.
- The findings contribute to the theoretical framework of epidemiological modeling.