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

The circulation of multiple pathogens, such as COVID-19, pneumonia, and influenza, presents a significant public health challenge, yet most epidemiological models focus solely on single-pathogen or co-infection dynamics. While co-infections, interactions between two pathogens, have been studied extensively, higher-order poly-infections, where three or more diseases interact, are under-explored despite their real-world implications. This study addresses this gap by developing a novel compartmental model to analyze the transmission dynamics of COVID-19, pneumonia, and influenza under poly-infection conditions. Our model incorporates disease interactions, vaccination effects, and waning immunity to evaluate how poly-infection influences outbreak severity. We performed numerical simulations and sensitivity analysis, analyzing the equilibrium points’ stability and identifying critical parameters driving disease spread. Our findings highlight that to minimize the spread of the poly-infection of COVID-19, 1 pneumonia, and influenza, public health strategies should be geared toward decreasing contact rates and increasing vaccination efforts. The results provide actionable information for policymakers, emphasizing the need for integrated disease surveillance, targeted vaccination campaigns, and adaptive public health strategies to mitigate the impact of concurrent outbreaks.