Finding bifurcations in mathematical epidemiology via reaction network methods

Area of Science:

• Epidemiology
• Mathematical Biology
• Theoretical Chemistry

Background:

• Mathematical Epidemiology (ME) and Chemical Reaction Network Theory (CRNT) share fundamental mathematical structures in their dynamical systems.
• Despite this core similarity, CRNT methodologies are infrequently utilized in ME research.
• This underutilization represents a missed opportunity for advancing ME modeling techniques.

Purpose of the Study:

• To investigate the applicability of Chemical Reaction Network Theory (CRNT) methods within Mathematical Epidemiology (ME).
• Specifically, to explore the use of CRNT techniques for identifying bifurcations in endemic equilibrium states of ME models.
• To bridge the gap between these two related theoretical frameworks.

Main Methods:

• Analysis of dynamical systems common to both ME and CRNT.
• Adaptation and application of established CRNT bifurcation analysis techniques.
• Testing these methods on standard endemic equilibrium models in Mathematical Epidemiology.

Main Results:

• Demonstration that CRNT bifurcation analysis methods can be successfully applied to ME models.
• Identification of specific bifurcations at endemic equilibria using CRNT approaches.
• Highlighting the potential for novel insights into disease dynamics through this interdisciplinary approach.

Conclusions:

• CRNT offers a powerful and underutilized toolkit for analyzing complex dynamics in Mathematical Epidemiology.
• Applying CRNT methods can reveal critical bifurcations in disease models, enhancing our understanding of epidemic thresholds and stability.
• This work advocates for greater integration of CRNT into the ME research landscape.