Control, bi-stability, and preference for chaos in time-dependent vaccination campaign

Area of Science:

• Epidemiology
• Mathematical Biology
• Dynamical Systems

Background:

• The Susceptible-Exposed-Infected-Recovered-Susceptible (SEIRS) model is crucial for understanding infectious disease dynamics.
• Vaccination strategies significantly impact disease transmission and population health.
• Investigating complex dynamics, including chaos, is essential for robust epidemiological modeling.

Purpose of the Study:

• To analyze the impact of constant and time-dependent vaccination rates on the SEIRS model.
• To explore the emergence of complex structures and chaotic behavior under different vaccination scenarios.
• To assess the potential of time-dependent vaccination for controlling epidemic dynamics.

Main Methods:

• Utilized the SEIRS epidemiological model.
• Employed Lyapunov exponent calculations to identify chaotic dynamics.
• Introduced time-dependent vaccination via periodic functions with varying amplitude and frequency.
• Analyzed system behavior in bi-stable dynamics with coexisting chaotic and periodic attractors.

Main Results:

• Constant vaccination can lead to complex structures (e.g., shrimps) and does not always suppress chaos, even at high rates (>0.95).
• Linear and non-linear relationships were found between control parameters and constant vaccination for disease-free states.
• Total infected numbers remained consistent regardless of chaotic or periodic dynamics.
• Time-dependent vaccination, depending on its parameters, can control chaos, leading to periodic structures, often via crisis or period-doubling.
• Time-dependent vaccination effectively controlled bi-stable dynamics by suppressing periodic attractors, favoring chaotic ones.

Conclusions:

• Vaccination rates, both constant and time-dependent, profoundly influence SEIRS model dynamics, including the emergence of chaos.
• Time-dependent vaccination offers a promising strategy for controlling epidemic spread, particularly in bi-stable scenarios, by manipulating attractor landscapes.
• Chaotic attractors may possess more favorable characteristics for epidemic control in certain bi-stable states compared to periodic ones.