Multiple stable recurrent outbreaks and predictability in seasonally forced nonlinear epidemic models

Area of Science:

• Mathematical epidemiology
• Nonlinear dynamics
• Computational modeling

Background:

• Epidemic modeling is crucial for understanding disease dynamics.
• Nonlinear models can exhibit complex behaviors, including multiple stable states.
• Seasonal forcing influences disease transmission patterns.

Purpose of the Study:

• To investigate the dynamics of a seasonally forced nonlinear SEIR epidemic model.
• To explore the phenomenon of bistability in epidemic outbreak patterns.
• To analyze the basins of attraction for coexisting stable outbreaks.

Main Methods:

• Development and simulation of a nonlinear Susceptible-Exposed-Infectious-Recovered (SEIR) model.
• Inclusion of seasonal forcing to represent environmental influences on transmission.
• Computation of basins of attraction to visualize the stability of different outbreak regimes.

Main Results:

• The SEIR model demonstrates bistable behavior, supporting two distinct types of periodic outbreaks (small and large amplitude).
• Basins of attraction for these coexisting outbreaks are intricately intertwined.
• Uncertainty in initial conditions (susceptible and infectious populations) complicates long-term prediction of outbreak type.

Conclusions:

• The model highlights the potential for complex, coexisting epidemic dynamics.
• The intertwined nature of basins of attraction poses significant challenges for predictive epidemiology.
• Understanding these nonlinear dynamics is essential for effective public health interventions.