Stability analysis of delayed co-infection model of pneumonia and meningitis

Abstract

This study develops and analyzes a delay differential model to investigate the co-infection dynamics of pneumonia and meningitis in a human population. The model incorporates biologically motivated delay factors-such as isolation, social distancing, and public awareness represented through an exponential survival term. These delays capture the influence of behavioral and treatment-related interventions on disease transmission. The model’s dynamical behavior is examined through the analysis of positivity, boundedness, and equilibrium states. Both the disease-free equilibrium (DFE) and disease-existing equilibrium (DEE) are shown to be locally and globally asymptotically stable under appropriate threshold conditions. Sensitivity analysis highlights the influence of key parameters, including delay-related terms, on the basic reproduction numbers of pneumonia, meningitis, and their co-infection subsystem. Numerical simulations support the analytical results and illustrate how increasing delay-based interventions can effectively suppress disease spread. The findings provide valuable insights for public health strategies, suggesting that isolation, social distancing, and awareness campaigns can substantially mitigate co-infection risks in affected communities.