Transmission dynamics of community-and hospital-acquired infections: insights from mathematical modelling

Abstract

Hospital-associated infections (HAIs) remain a critical public health challenge, particularly in resource-limited settings where surveillance and infection control are inadequate. This study develops and analyzes a modified S E I R mathematical model, denoted by S E_cI_cE_hI_hR, to capture the transmission dynamics of infectious diseases across hospital and community settings. The model incorporates both community and hospital transmission of infections, which have not been addressed jointly in previous studies. Using the next-generation matrix approach, the basic reproduction number (R₀) was determined. Local and global stability analyses revealed that the disease-free equilibrium is stable when R₀ < 1, but unstable otherwise. Sensitivity analysis identified the recruitment rate, community contact rate, and hospital infection rate as the most influential parameters, with community transmission exerting a stronger impact on the overall dynamics than hospital transmission. Numerical simulations further confirmed the dominant role of community transmission over hospital infections. Bifurcation analysis confirmed the possibility of backward bifurcation, indicating the possible coexistence of endemic and disease-free equilibrium states, even when R₀ < 1. These findings highlight the complex interplay between hospital and community transmission and indicate that effective control strategies must prioritize reducing community contact rates while strengthening hospital infection-prevention measures. The model provides insights for policymakers and healthcare managers designing evidence-based interventions to mitigate HAIs and community outbreaks, particularly in countries facing systemic healthcare challenges.