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

Acuna Zegarra, M. A.; Nunez Lopez, M.; Santana Cibrian, M.; Comas Garcia, A.; Velasco-Hernandez, J. X.

The interaction and possibly interference between viruses infecting a common host population is the problem addressed in this work. We model two viral diseases both of the SIRS type that have similar mechanism of transmission and for which a vaccine exists. The vaccine is characterized by its coverage, induced temporal immunity and efficacy. The population dynamics of both diseases considers infected individuals of each disease and hosts that are susceptible to one but have recovered from the other. We do not incorporate coinfection. We postulate two main transmission factors affecting the effective contact rates: i) that the virus with higher reproduction number can superinfect the one with lower reproduction number and ii) that there is some 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. The time-dependent effective contact rate may induce either alternating outbreaks of each disease or synchronous outbreaks. We also found the existence of bi-stability triggered by a backward bifurcation, conducive to scenarios where, at the population level, vaccine application may promote persistence of both diseases provided the effective coverage and vaccine efficacy are low.