A Stochastic Multi-Strain SIR Model with Two-Dose Vaccination Rate

Infectious diseases remain a substantial public health concern as they are among the leading causes of death. Immunization by vaccination can reduce the infectious diseases-related risk of suffering and death. Many countries have developed COVID-19 vaccines in the past two years to control the COVID-19 pandemic. Due to an urgent need for COVID-19 vaccines, the vaccine administration of COVID-19 is in the mode of emergency use authorization to facilitate the availability and use of vaccines. Therefore, the vaccine development time is extraordinarily short, but administering two doses is generally recommended within a specific time to achieve sufficient protection. However, it may be essential to identify an appropriate interval between two vaccinations. We constructed a stochastic multi-strain SIR model for a two-dose vaccine administration to address this issue. We introduced randomness into this model mainly through the transmission rate parameters. We discussed the uniqueness of the positive solution to the model and presented the conditions for the extinction and persistence of disease. In addition, we explored the optimal cost to improve the epidemic based on two cost functions. The numerical simulations showed that the administration rate of both vaccine doses had a significant effect on disease transmission.