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 Script capital R0 =max(Script capital Rf,Script capital Rp) where Script capital Rf and Script capital Rp are, respectively, the reproductive numbers for flu and pneumonia. We show that in the case Script capital Rf <= 1 <= Script capital Rp, 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 Script capital Rp <= 1 <= Script capital Rf. 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 Script capital 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.