Relative prevalence-based dispersal in an epidemic patch model.

Area of Science:

• Mathematical epidemiology
• Dynamical systems theory
• Population dynamics

Background:

• Understanding infectious disease dynamics in spatially structured populations is crucial for effective control strategies.
• Previous models often assume simplified incidence and dispersal rates, limiting their applicability to real-world scenarios.
• The interplay between local disease transmission and individual movement between patches significantly influences overall disease prevalence.

Purpose of the Study:

• To develop and analyze a two-patch SIRS epidemiological model incorporating nonlinear incidence and nonconstant, relative-prevalence-dependent dispersal rates.
• To investigate the complex dynamics, including bifurcations and multiple coexistent states, in both isolated and connected environments.
• To explore the impact of different dispersal strategies (constant vs. relative prevalence-based) on disease extinction, persistence, and overall prevalence.

Main Methods:

• Formulation of a two-patch SIRS model with nonlinear incidence and state-dependent dispersal rates.
• Analysis of local and global dynamics using bifurcation theory (Bogdanov-Takens, Hopf bifurcations) in an isolated environment.
• Numerical simulations to examine the effects of constant and relative prevalence-based dispersal on disease spread in a connected environment.

Main Results:

• In isolation, the model exhibits rich dynamics, including cusp and Hopf bifurcations, multiple equilibria, periodic orbits, and bistability.
• A threshold determines disease extinction versus uniform persistence in a connected environment.
• Relative prevalence-based dispersal can reduce overall disease prevalence compared to constant dispersal; constant dispersal can increase prevalence.
• Unidirectional dispersal can lead to complex oscillations or disease extinction in one patch, while relative prevalence-based dispersal can accelerate periodic outbreaks.

Conclusions:

• The proposed model captures complex epidemiological behaviors arising from nonlinear incidence and adaptive dispersal.
• Dispersal strategies significantly influence disease dynamics, with relative prevalence-based movement potentially offering a more effective control mechanism.
• The findings highlight the importance of considering realistic dispersal patterns in epidemiological modeling for predicting and managing disease spread.