Dynamical analysis of two-pathogen coinfection in influenza and other respiratory diseases

Abstract

Influenza is a contagious pathogen caused by the ribonucleic acid (RNA) virus and attacks the respiratory tract. This disease is still one of the leading causes of mortality and morbidity due to the continuous emergence of new virus variants. One of the causes of the emergence of this new virus is the coinfection of two different strains. Apart from the emergence of new variants, several coinfection cases with other pathogens are reported with severe conditions. We constructed an SI1I2I3R1R2R3 model to describe the coinfection of influenza and other respiratory pathogen transmissions by considering aspects of waning immunity, reinfected with the different pathogen and coinfected individuals. Analysis of this model reveals four equilibria: disease-free, two boundary endemics, and coexistence equilibria. The first three equilibria are expressed explicitly, along with the basic reproductive ratio. Stability conditions for boundary equilibria are shown analytically for the case with no coinfection and the case of symmetry. These conditions provide possible bifurcation points for numerical coexistence exploration and the nature of their stability. Numerical simulations show that no coexistence equilibrium exists in the case of no coinfection. As with coinfection, stable coexistence occurs for a relatively large coinfection rate, and Hopf bifurcations appear at two different values of infection rate of each pathogen. Stable limit cycles exist for pathogen infection rates between the two Hopf points. We also identify the periods of limit cycle increases as the infection rate of pathogen increases and decreases after reaching the maximum value.