A status-based approach to multiple strain dynamics

Area of Science:

• Immunology
• Mathematical Biology
• Epidemiology

Background:

• Traditional cross-immunity models classify hosts by infection history.
• A new host representation based on current immune response status is proposed.
• This status-based framework broadens the study of cross-immunity forms.

Purpose of the Study:

• To introduce and investigate a novel model for cross-immunity.
• To analyze a specific four-strain system with partial cross-immunity.
• To explore applications in maintaining genetic strain diversity.

Main Methods:

• Representing hosts by their current immune response status.
• Analyzing a four-strain system where each strain confers partial immunity to two others.
• Utilizing system symmetries to identify a relevant invariant subspace for analysis.

Main Results:

• The new framework allows for a wider and more biologically interpretable range of cross-immunity forms.
• Substantial analytical progress was made on the four-strain system by focusing on an invariant subspace.
• The analyzed system does not exhibit sustained oscillations for any parameter values, unlike previously studied systems.

Conclusions:

• The status-based cross-immunity model provides a more flexible and interpretable approach.
• The analysis of the four-strain system offers insights into the dynamics of strain diversity.
• The absence of sustained oscillations in this model has implications for understanding pathogen evolution and control.