Dispersal, disease and life-history evolution

Area of Science:

• Epidemiology
• Mathematical Biology
• Non-linear Dynamics

Background:

• Discrete-time susceptible-infective-susceptible (S-I-S) models frequently demonstrate bistability.
• Bistability refers to the existence of multiple stable states in a system.
• Understanding factors influencing disease persistence and spread is crucial.

Purpose of the Study:

• To explore the impact of inter-patch dispersal on disease dynamics in a two-patch S-I-S model.
• To investigate how dispersal, whether disease-enhanced or disease-suppressed, influences model bistability.
• To demonstrate the complex behaviors arising from simple non-linear systems.

Main Methods:

• Utilized discrete-time susceptible-infective-susceptible (S-I-S) epidemic modeling.
• Developed a two-patch model incorporating disease-dependent dispersal rates.
• Analyzed model behavior across a range of parameter values to identify bistability.

Main Results:

• Dispersal between patches significantly alters local disease dynamics.
• Inter-patch dispersal can induce bistability in parameter regimes where single patches do not exhibit it.
• Disease-enhanced and disease-suppressed dispersal can lead to distinct emergent behaviors.

Conclusions:

• Spatial structure and dispersal are critical determinants of epidemic patterns.
• Even simple non-linear models with dispersal can generate rich and complex epidemiological outcomes.
• The study highlights the importance of considering connectivity when analyzing disease spread.