A model for the transmission dynamics of pneumococcal pneumonia and influenza co-infection

Synergistic interaction between influenza and pneumonia is well established in the literature. In this study, we present a model for the transmission dynamics of co-infection with influenza and pneumococcal pneumonia, with the goal of assessing the effects of influenza co-infection on the transmission of pneumonia. We derive an expression for the basic reproductive number R₀ = max(R_f ,R_p) where R_f and R_p are, respectively, the reproductive numbers for flu and pneumonia. We show that in the case R_f ≤ 1 ≤ R_p, infection with influenza is driven to extinction while pneumonia is endemic, with the endemic state being globally asymptotically stable. The converse result holds in the case where R_p ≤ 1≤ R_f . We also show the existence of the co-infection equilibrium. In this case, we show that the presence of co-infection results in a possible backward bifurcation in the system at R₀ = 1; epidemiologically, this means that the spread of the infection will be harder to control. Numerical simulations are presented to verify the analytic results and gain further insights.