A spatial SIS point pattern model with movement

Area of Science:

• Epidemiology
• Mathematical Biology
• Spatial Statistics

Background:

• Spatial epidemic dynamics are influenced by local interactions and individual movement.
• Existing models often simplify movement or focus on discrete spaces.
• Understanding these dynamics is crucial for disease control.

Purpose of the Study:

• To develop and analyze a spatial susceptible-infected-susceptible (SIS) model incorporating continuous individual movement.
• To investigate the impact of different distance-dependent infection kernels on epidemic spread.
• To explore how movement patterns and transmission kernels jointly influence spatial disease dynamics.

Main Methods:

• Developed a spatial SIS model based on point pattern dynamics with continuous movement for susceptible and infected individuals.
• Employed distance-dependent infection kernels (Gaussian, step-function, exponential) to model disease transmission.
• Derived heuristic singlet and pair-density equations to analyze spatial distributions and temporal evolution.
• Utilized numerical simulations to assess the effects of kernel shape, infection range, and movement.

Main Results:

• Individual movement and distance-dependent transmission significantly shape spatial epidemic spread.
• Different infection kernel shapes (Gaussian, step-function, exponential) lead to varying spatial patterns and spread dynamics.
• Movement parameters and infection range critically influence the temporal evolution of susceptible and infected individuals.
• The interplay between movement and transmission determines the overall spatial distribution of the disease.

Conclusions:

• Spatial movement and distance-dependent transmission are key drivers of recurrent infection dynamics.
• The developed model provides a framework for understanding complex spatial epidemic behaviors.
• Findings highlight the importance of considering individual movement in epidemiological models for accurate predictions and control strategies.