The Basic Reproduction Number for Petri Net Models: A Next-Generation Matrix Approach

Area of Science:

• Epidemiology
• Computational Biology
• Graph Theory

Background:

• The basic reproduction number (R0) is a key metric in epidemiology for predicting disease outbreaks and guiding public health interventions.
• Current methods for calculating R0 are well-established for Ordinary Differential Equations (ODEs) but lack a generalized approach for Petri Net (PN) models.
• Petri Nets are increasingly utilized in epidemiology for modeling dynamic systems, highlighting the need for direct R0 calculation methods.

Purpose of the Study:

• To establish a generalized computational framework for calculating the basic reproduction number (R0) directly from Petri Net (PN) models.
• To adapt the next-generation matrix method for compatibility with various PN formalisms, including Variable Arc Weight Petri Nets (VAPNs) and stochastic continuous-time Petri Nets (SPNs).

Main Methods:

• Developed a generalized computational framework for R0 calculation from Petri Net models.
• Adapted the next-generation matrix method to work with both deterministic (VAPNs) and stochastic (SPNs) Petri Net formalisms.
• Applied the framework to diverse epidemiological models, including those with multiple strains, asymptomatic states, and nonlinear dynamics.

Main Results:

• Successfully established a generalized method for calculating R0 directly from Petri Net models.
• Demonstrated the framework's versatility across complex epidemiological models.
• Numerically validated the framework, showing strong agreement between analytically derived R0 values and simulation data.

Conclusions:

• The developed framework provides an accurate and practical method for calculating R0 from Petri Net models.
• This advancement facilitates more robust epidemiological analysis and supports informed public health decision-making.
• The method's compatibility with multiple Petri Net formalisms enhances its utility in diverse disease modeling scenarios.