Dynamics of multi-strain epidemic models and the impact of masking and vaccination

Abstract

Mathematical modelling plays a pivotal role in informing public health strategies for infectious disease control. Although numerous studies have investigated multi-strain epidemic dynamics, key aspects such as asymptomatic transmission and waning immunity are often excluded. This thesis develops and analyzes two compartmental models to address these limitations.

The first model, an SIARS framework, examines multi-strain transmission in a homogeneous population without interventions. Strain-specific basic reproduction numbers are derived, and analytical conditions for the existence and stability of equilibria are established. Numerical simulations further illustrate the analytical results.

The second model, an SVIARS framework, incorporates mask usage and vaccination in a non-homogeneous population. Despite the model’s high dimensionality, strain-specific reproduction numbers are identified, enabling an explicit expression for the overall basic reproduction number. Numerical analyses quantify the impact of intervention parameters and determine critical efficacy thresholds.

The results offer practical insights for mitigating multi-strain outbreaks under realistic public health scenarios.