Modeling and Analysis of Transmission Dynamics of Respiratory Infectious Diseases: Co-Circulations, Mutations and Delayed Interventions

Abstract

Mathematical models are essential tools for understanding the transmission dynamics of infectious diseases and evaluating control strategies. This thesis develops compartmental mathematical models to investigate key issues observed during the COVID-19 pandemic, including the emergence of variants of concern (VOC) due to mutations, the co-circulation of respiratory pathogens, and the impact of delayed interventions. The first model assesses the effects of mutations, focusing on the emergence of new variants and variant-specific control strategies. The model analysis emphasizes the importance of rapid detection through whole genome sequencing (WGS) to manage outbreaks from two strains effectively. The second model considers concurrent epidemics of COVID-19 and influenza. The model simulates the transmission dynamics of both viruses and optimizes vaccination strategies to minimize strain on healthcare systems by delaying or separating peak infections. Finally, time-dependent removal rates are incorporated into classical SIR models to account for delays in diagnosis and isolation due to limitations of healthcare resources, and our study shows how this delay leads to oscillatory dynamics. This thesis research forms appropriate models, develops theoretical analyses, and provides valuable insights into the complex dynamics of respiratory diseases and offers strategies for managing mutations, co-circulation, and delayed interventions, ultimately improving pandemic preparedness.