Extensions of mean-field approximations for environmentally-transmitted pathogen networks.

Area of Science:

• Epidemiology
• Mathematical Modeling
• Network Theory

Background:

• Pathogen spread often occurs via environmental transmission, distinct from direct host-to-host contact.
• Existing environmental transmission models frequently use intuitive structures similar to direct transmission models.
• Model accuracy is highly sensitive to underlying assumptions, necessitating rigorous analysis.

Purpose of the Study:

• To construct and analyze a network model for environmentally transmitted pathogens.
• To rigorously derive systems of ordinary differential equations (ODEs) under varying assumptions.
• To compare ODE approximations with a stochastic network model implementation.

Main Methods:

• Development of a simple network model for environmental pathogen transmission.
• Rigorous derivation of ordinary differential equation (ODE) systems based on homogeneity and independence assumptions.
• Comparison of derived ODE models against a stochastic network model simulation across diverse parameters and network structures.

Main Results:

• Relaxing homogeneity and independence assumptions leads to more accurate ODE approximations of pathogen transmission.
• Fewer restrictive assumptions improve approximation accuracy but result in more complex ODE systems.
• The study precisely identifies errors arising from specific assumptions and proposes resolutions.

Conclusions:

• Rigorously derived ODE models with less restrictive assumptions offer superior accuracy for environmental transmission.
• Complex ODE systems may arise from relaxing assumptions, potentially leading to unstable solutions.
• Understanding and addressing assumption-driven errors is crucial for reliable pathogen transmission modeling.