Equilibrium properties of the spatial SIS model as a point pattern dynamics - How is infection distributed over...

Area of Science:

• Epidemiology
• Mathematical Ecology
• Spatial Statistics

Background:

• The classical Susceptible-Infectious-Susceptible (SIS) model is foundational in epidemiology.
• Understanding spatial distribution is crucial for disease dynamics and control.
• Previous models often simplified spatial interactions.

Purpose of the Study:

• To analyze the equilibrium spatial distribution of the SIS model using a stochastic point pattern framework.
• To investigate how distance-dependent infection kernels influence spatial clustering of infectious individuals.
• To demonstrate the utility of the point pattern approach for ecological dynamics.

Main Methods:

• Revisiting the SIS model as a stochastic point pattern process.
• Mathematically describing the dynamics using probabilities of point configurations (singlets, pairs, triplets).
• Employing a closure approximation for triplet probabilities to derive equilibrium distributions.

Main Results:

• Explicit derivation of average singlet and pair probabilities at equilibrium.
• Demonstrated that infectious individuals (I) exhibit spatial clustering.
• The degree of clustering is directly related to the spatial scale of the infection kernel.

Conclusions:

• The point pattern approach provides a powerful tool for modeling spatially explicit population dynamics.
• Local interactions, dependent on distance, are effectively captured by this framework.
• This method offers insights into disease spread and spatial ecology.