Global dynamics for an SIR patchy model with susceptibles dispersal

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• Understanding disease spread in interconnected populations is crucial.
• Dispersal of susceptible individuals can influence disease dynamics.
• Threshold parameters like the basic reproduction number are key to predicting disease persistence.

Purpose of the Study:

• To analyze an epidemiological model with susceptible dispersal between two patches.
• To determine the conditions for disease-free and endemic equilibria.
• To investigate the impact of susceptible dispersal on disease dynamics.

Main Methods:

• Development of a two-patch epidemiological model.
• Definition and analysis of basic reproduction numbers (R01 and R02).
• Application of comparison principles for cooperative systems and Lyapunov functions.

Main Results:

• Disease-free equilibrium is globally asymptotically stable if R01 and R02 are below unity.
• Disease persistence in patch 1 if R01 > 1, R02 < 1, and specific conditions on R01 and R02 are met.
• Endemic equilibrium is globally asymptotically stable if R01 and R02 are above unity and other conditions are satisfied.
• Susceptible dispersal does not alter the qualitative behavior of the model.

Conclusions:

• The stability of the epidemiological model is primarily determined by basic reproduction numbers.
• Susceptible dispersal between populations does not change the fundamental disease dynamics.
• The model provides insights into disease control strategies in metapopulations.