Model for disease dynamics of a waterborne pathogen on a random network

Area of Science:

• Epidemiology
• Mathematical Biology
• Network Science

Background:

• Cholera and other environmentally transmitted diseases pose significant public health challenges.
• Existing models often simplify transmission pathways, limiting their applicability to complex real-world scenarios.
• Understanding disease dynamics in networks is crucial for effective intervention.

Purpose of the Study:

• To develop and analyze a novel network epidemic SIWR (Susceptible-Infectious-Water-Recovered) model for diseases transmitted via environment and person-to-person contact.
• To investigate the impact of network structure on disease transmission dynamics.
• To compute reproduction numbers and derive equations for final epidemic size to inform control strategies.

Main Methods:

• Developed a network epidemic SIWR model incorporating both random contact networks for person-to-person transmission and an external node representing the contagious environment.
• Adapted the model from the Miller network SIR model.
• Validated model dynamics against stochastic simulations.
• Computed the basic reproduction number ([Formula: see text]) and type reproduction numbers.

Main Results:

• The model's dynamics demonstrated excellent agreement with stochastic simulations.
• On a Poisson network, the basic reproduction number ([Formula: see text]) was the sum of person-to-person and person-to-water-to-person pathways.
• On other network structures, [Formula: see text] exhibited nonlinear dependence on transmission pathways.
• Type reproduction numbers were calculated to guide disease control.

Conclusions:

• The developed SIWR model provides a robust framework for studying environmentally transmitted diseases on networks.
• Network topology significantly influences disease transmission, with nonlinear effects observed on non-Poisson networks.
• The computed reproduction numbers and final epidemic size equations offer valuable quantitative tools for public health interventions and disease management.