Modeling Epidemics with Noncompliance: A Discrete-Time Mean-Field Approach
Presentation Type
Poster
Presentation Type
Submission
Keywords
Epidemic simulation, Behavioral isolation, Edge-deletion dynamics, Adaptive networks, Basic reproductive number
Department
Mathematics
Abstract
Building upon an established compartmental model that captures the social contagion of noncompliance alongside infectious disease dynamics, this study investigates the impact of adaptive network topology on epidemic spread. While the foundational ordinary differential equation (ODE) framework establishes the baseline dynamics of compliant and noncompliant populations, our work introduces an adaptive network simulation where infectious individuals face behavioral isolation. In this simulation, edge-deletion events are triggered when an individual reaches a specific threshold (h) of infectious neighbors. To quantify this localized behavioral response, we derive an adaptive basic reproductive number formulated as a weighted average of static and adaptive network regimes.
Numerical simulations of 10,000 realizations per threshold step validate this theoretical derivation and reveal two distinct epidemiological phases. In the adaptive phase (h < 10), the overall reproductive ratio is heavily governed by the probability of behavioral isolation, with numerical results closely tracking the weighted theory. Conversely, in the static phase (h >= 10), isolation probability effectively vanishes, causing the system to converge to the deterministic mass-action limit. This probabilistic extension provides a robust framework for evaluating how localized isolation thresholds influence overarching epidemic trajectories.
Faculty Mentor
Christina Duron
Funding Source or Research Program
Academic Year Undergraduate Research Initiative
Location
Waves Cafeteria
Start Date
10-4-2026 1:00 PM
End Date
10-4-2026 2:00 PM
Modeling Epidemics with Noncompliance: A Discrete-Time Mean-Field Approach
Waves Cafeteria
Building upon an established compartmental model that captures the social contagion of noncompliance alongside infectious disease dynamics, this study investigates the impact of adaptive network topology on epidemic spread. While the foundational ordinary differential equation (ODE) framework establishes the baseline dynamics of compliant and noncompliant populations, our work introduces an adaptive network simulation where infectious individuals face behavioral isolation. In this simulation, edge-deletion events are triggered when an individual reaches a specific threshold (h) of infectious neighbors. To quantify this localized behavioral response, we derive an adaptive basic reproductive number formulated as a weighted average of static and adaptive network regimes.
Numerical simulations of 10,000 realizations per threshold step validate this theoretical derivation and reveal two distinct epidemiological phases. In the adaptive phase (h < 10), the overall reproductive ratio is heavily governed by the probability of behavioral isolation, with numerical results closely tracking the weighted theory. Conversely, in the static phase (h >= 10), isolation probability effectively vanishes, causing the system to converge to the deterministic mass-action limit. This probabilistic extension provides a robust framework for evaluating how localized isolation thresholds influence overarching epidemic trajectories.