Co-circulation of SARS-CoV-2 and Influenza under vaccination scenarios

The interaction and possibly interference between viruses infecting a host population is addressed in this work. We model two viral diseases with a similar transmission mechanism and for which a vaccine exists. The vaccine is characterized by its coverage, induced temporary immunity, and efficacy. The population dynamics of both diseases consider infected individuals of each illness and hosts susceptible to one but recovered from the other. We do not incorporate co-infection. Two main transmission factors affecting the effective contact rates are postulated: i) the virus with a higher reproduction number can superinfect the one with a lower reproduction number, and ii) there exists some induced (indirect) protection induced by vaccination against the weaker virus that reduces the probability of infection by the stronger virus. Our results indicate that coexistence of the viruses is possible in the long term, even considering the absence of superinfection. Influenza and SARS-CoV-2 are employed to exemplify this last point, observing that the time-dependent effective contact rate may induce either alternating outbreaks of each disease or synchronous outbreaks. Finally, for a particular parameter range, a backward bifurcation has been observed for dynamics without vaccination.