Sensitivity analysis and numerical simulations of a poly-infection model with COVID-19, pneumonia, and influenza

The concurrent circulation of COVID-19, pneumonia, and influenza creates a significant public health crisis. Traditional epidemiological models mostly overlook poly-infection, the complex interaction dynamics among three or more pathogens. This study addresses this fundamental gap by developing a novel compartmental model to analyze the transmission of these three respiratory diseases, explicitly incorporating the impacts of vaccination and waning immunity. Using Canadian death data, we calibrated sub-models, performed extensive numerical simulations, and conducted a global sensitivity analysis (LHS-PRCC) to identify the parameters most critical to the Basic Reproduction Number ( $$\mathcal {R}_0$$ ). The results demonstrate that transmission rates and effective vaccination rates are the dominant drivers of the spread of poly-infection. To effectively mitigate the disease’s burden, public health strategies must simultaneously focus on reducing contact rates and significantly enhancing vaccination coverage. This study underscores the necessity of transitioning from single-pathogen models to integrated disease surveillance and adaptive, multi-pathogen health strategies, with the goal of managing concurrent outbreaks and enhancing global health security.