A two-strain COVID-19 co-infection model with strain 1 vaccination

COVID-19 has caused substantial morbidity and mortality worldwide. Previous models of strain 1 vaccination with re-infection when vaccinated, as well as infection with strain 2 did not consider co-infected classes. To fill this gap, a two co-circulating COVID-19 strains model with strain 1 vaccination, and co-infected is formulated and theoretically analyzed. Sufficient conditions for the stability of the disease-free equilibrium and single-strain 1 and -strain 2 endemic equilibria are obtained. Results show as expected that (1) co-infected classes play a role in the transmission dynamics of the disease (2) a high efficacy vaccine could effectively help mitigate the spread of co-infection with both strain 1 and 2 compared to the low-efficacy vaccine. Sensitivity analysis reveals that the main drivers of the effective reproduction number $R_e$ are primarily the effective contact rate for strain 2 (${\beta }_2$), the strain 2 recovery rate (${\tau }_2$), and the vaccine efficacy or infection reduction due to the vaccine ($\eta$). Thus, implementing intervention measures to mitigate the spread of COVID-19 should not ignore the co-infected individuals who can potentially spread both strains of the disease.