Impact of general incidence function on three-strain SEIAR model

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• Understanding infectious disease dynamics is crucial for public health interventions.
• Complex models are needed to capture the nuances of multi-strain pathogen transmission.
• Generalized incidence rates significantly influence disease spread patterns.

Purpose of the Study:

• To investigate a complex mathematical model of three-strain infectious disease transmission.
• To analyze the impact of generalized incidence rates on disease dynamics.
• To determine the stability of disease equilibria and the conditions for strain dominance.

Main Methods:

• Development of a mathematical model with thirteen nonlinear ordinary differential equations.
• Compartmentalization into susceptible, exposed, symptomatic, asymptomatic, and recovered states.
• Analysis of model well-posedness (existence, positivity, boundedness) and equilibria.
• Calculation of basic reproduction numbers (R01, R02, R03) for each strain.
• Local stability analysis at the disease-free equilibrium.
• Numerical simulations to explore various incidence rate functions.

Main Results:

• The model features a disease-free equilibrium and seven endemic equilibria.
• Basic reproduction numbers indicate the potential for each strain to emerge and dominate.
• Local stability is established at the disease-free equilibrium.
• Numerical simulations demonstrate the significant influence of different incidence rates (bi-linear, saturated, Beddington-DeAngelis, non-monotone, Crowley-Martin) on disease dynamics.

Conclusions:

• The generalized incidence rate is a critical factor in determining the behavior of multi-strain infectious diseases.
• The model provides insights into strain competition and the conditions under which specific strains may prevail.
• Numerical findings support the theoretical analysis, highlighting the importance of accurate incidence rate parameterization in epidemiological models.